THREE ESSAYS ON DEMAND FOR FREIGHT TRANSPORTATION:

OPTIMIZATION, SPATIAL ECONOMETRICS AND PARAMETRIC ESTIMATIONS

By

TOSMAI PUENPATOM

A dissertation submitted in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

WASHINGTON STATE UNIVERSITY School of Economic Sciences

DECEMBER 2006

© Copyright by TOSMAI PUENPATOM, 2006 All Rights Reserved

© Copyright by TOSMAI PUENPATOM, 2006 All Rights Reserved

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To the Faculty of Washington State University:

The members of the Committee appointed to examine the dissertation of TOSMAI PUENPATOM find it satisfactory and recommend that it be accepted.

___________________________________ Chair ___________________________________ ___________________________________ ___________________________________

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ACKNOWLEDGMENTS

I would like to express my deep and sincere gratitude to my major advisor, Dr. Ken

Casavant, for his continuous guidance, encouragement, dedication and untiring support. His

profound knowledge and intellectual comments have been of great value of this study.

I wish to kindly extend my appreciation to all my committees for their time and

knowledge in assisting me towards the completion of the dissertation. I am especially grateful to

Dr. Fred Inaba for his constructive criticism and excellent advices during the preparation of this

dissertation. My deep appreciation is also extended to Dr. Ron Mittelhammer for his invaluable

comments and intellectual discussions. I would also like to thanks Dr. Eric Jessup for his

constant interests and suggestions. I also wish to express my appreciation to Dr. Thomas Marsh

for insightful comments that substantial improved my analysis.

It is also appropriate to thank for support of all graduate student in SES and all friends in

Pullman for their endless friendship. My personal thanks goes to Kelley and Mark Cullen for

continuous friendship and infinite supports. My gratitude goes to all SES staff for their support

and help.

At last, I especially thank my wife and colleague Amy, Rajitkanok Puenpatom for her

love, dedication and understanding. I thank my son, Pat, for making the hardship of writing the

dissertation worthwhile. I am greatly indebted to my parents, Sophaphan and Mesayon

Puenpatom for their unconditional love and encouragement.

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THREE ESSAYS ON DEMAND FOR FREIGHT TRANSPORTATION:

OPTIMIZATION, SPATIAL ECONOMETRICS AND PARAMETRIC ESTIMATIONS

Abstract

by Tosmai Puenpatom, Ph.D. Washington State University

December 2006

Chair: Ken L. Casavant

The dissertation evaluates the demand for grain transportation using different

methodologies such as a spatial Tobit demand estimation and the optimization models. The first

essay, taking account of the spatial interactions, develops the Tobit demand system with different

spatial weight matrices, which represents spatial effects on demand for transportation among

neighboring elevators. I proposed the new methodology of systematically constructing an

unequal weight matrix for the spatial Tobit demand model through the use of Geographic

Information System (GIS). The main results indicate a significant negative impact of the spatial

factor in the demand for rail transportation and heterogeneity among elevator companies.

The second essay examines the effects of Identity Preserved (IP) system on grain

transportation in Washington by applying General Algebraic Modeling System (GAMS). I

develop linear programming optimization models representing three scenarios, which are the

current bulk grain transportation, the IP or containerized grain transportation and the IP system

including extra material costs. The results indicate a significant change in wheat flows as a result

of the IP system. The higher containerized transport rates and the prohibition of transshipment

contribute to the rising transport costs. In addition, the sensitivity analysis of discounting the

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containerized rail rate identifies a spatial competition between the rail mode and the truck-barge

mode.

The third study evaluates impacts of the Pacific Northwest (PNW)’s soft white wheat

(SWW) marketing plan which aims to promote wheat to buyers by providing information of the

different end-use qualities of the soft white wheat grown in different geographical areas. Under

this model, I assume that elevators voluntarily move grain only within the production zone and

there is no grain shipment across different production zones in an attempt to preserve identity of

wheat grown in a specific zone. The cost-minimizing linear programming optimization model is

applied to represent elevator managers’ decision on grain transportation. The results indicate

insignificant changes in wheat flows and a slightly increase in transport costs due to the

imposition of the marketing plan. In contrast to the IP system, the zoning policy is significantly

inexpensive as the result of the existing economies of scale.

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TABLE OF CONTENTS Page ACKNOWLEDGEMENTS................................................................................................ iii ABSTRACT.........................................................................................................................iv LIST OF TABLES...............................................................................................................ix LIST OF FIGURES ..............................................................................................................x CHAPTER 1. NEIGHBORHOOD EFFECTS AND DEMAND FOR GRAIN TRANSPORTATION: AN APPLICATION OF A SPATIAL TOBIT MODEL ..............................................................................................1 Abstract ........................................................................................................................1 1. Introduction............................................................................................................2 2. Background: grain transportation ..........................................................................4 3. Literature review....................................................................................................6 3.1. Neighborhood effects and the spatial analysis................................................6 3.2. Derived demand ..............................................................................................9 3.3. The standard Tobit model and the spatial Tobit model ................................11 4. Theoretical model ................................................................................................14 4.1. Derived freight demand ................................................................................14 4.2. Standard Tobit regression .............................................................................19 4.3. Spatial Tobit regressions...............................................................................21 5. Empirical specifications and variable selection...................................................23 5.1. Data ...............................................................................................................23 5.2. Variable selection..........................................................................................23 5.3. Spatial weight matrix ....................................................................................26

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5.3.1. Market interaction weight matrix.........................................................28 5.3.2. Company weight matrix.......................................................................30 6. Empirical results ..................................................................................................30 7. Conclusions..........................................................................................................33 REFERENCES ...................................................................................................................35 APPENDIX 1.1. A DERIVATION OF SPATIAL TOBIT.......................................................47 1.2. A VBA CODE FOR SPATIAL ANALYSIS IN GIS....................................49 1.3. GAUSS CODE FOR DOUBLE-CENSORED TOBIT .................................52 1.4. GAUSS CODE FOR SPATIAL ONE-SIDED TOBIT .................................56 CHAPTER 2. IMPACTS OF IDENTITY PRESERVED WHEAT SHIPMENTS ON GRAIN TRANSPORTATION IN WASHINGTON...................................................61 Abstract ......................................................................................................................61 1. Introduction..........................................................................................................62 2. Background..........................................................................................................64 2.1. Identity Preserved Grain ...............................................................................64 2.2. Grain transportation ......................................................................................66 3. Literature review..................................................................................................68 3.1. IP grain studies..............................................................................................68 3.2. Grain transportation studies ..........................................................................72 4. Optimization model .............................................................................................74 5. Data and assumptions ..........................................................................................76

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5.1. Data ...............................................................................................................76 5.2. Cost assumptions ..........................................................................................77 6. Model results........................................................................................................81 7. Conclusions..........................................................................................................85 REFERENCES ...................................................................................................................87 APPENDIX 2.1. GAMS CODE FOR GRAIN FLOWS OPTIMIZATION ...........................102 CHAPTER 3. IMPACTS OF THE PACIFIC NORTHWEST’S SOFT WHITE WHEAT MARKETING PLAN ON GRAIN TRANSPORTATION IN WASHINGTON ..........................................................................................................115 Abstract ....................................................................................................................115 1. Introduction........................................................................................................116 2. Background........................................................................................................118 3. Literature review................................................................................................120 3.1. Zoning policy ..............................................................................................120 3.2. Grain transportation ....................................................................................122 4. Optimization model ...........................................................................................124 5. Data and descriptive statistics............................................................................126 6. Model results......................................................................................................128 7. Conclusions........................................................................................................132 REFERENCES .................................................................................................................135 APPENDIX 3.1. GAMS CODE FOR GRAIN FLOWS OPTIMIZATION ...........................148

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LIST OF TABLES

Table 1.1 An example of spatial weight matrix (for 5 elevators) ..................................40

Table 1.2 Summary statistics .........................................................................................41

Table 1.3 Regression results of OLS, double-censored and spatial Tobit .....................42

Table 2.1 Summary statistics for WA counties..............................................................91

Table 2.2 Summary statistics for firms ..........................................................................92

Table 2.3 Summary of transportation rates used in the study........................................93

Table 2.4 Model results: modal split, volume shipped and total cost............................94

Table 2.5 Model results: wheat flows to river ports, different scenarios.......................95

Table 3.1 Distribution and characteristics of elevators by model companies..............138

Table 3.2 Distribution of elevators by counties ...........................................................138

Table 3.3 Transportation rates used in the study .........................................................139

Table 3.4 Model results: modal splits, volume shipped and total cost ........................140

Table 3.5 Model results: wheat flows to river ports, different scenarios.....................141

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LIST OF FIGURES

Figure 1.1 Isoquant curves and isocost lines from three different case ..........................43

Figure 1.2 Normal Quantile Plot of the ‘Rail’ variable...................................................43

Figure 1.3 Sample elevators used....................................................................................44

Figure 1.4 Sample elevators, railroads, and river ports...................................................45

Figure 1.5 Elevators’ market area and their interaction effects ......................................46

Figure 2.1 Distribution of sample elevators in Washington............................................96

Figure 2.2 Eastern Washington counties and Snake-Columbia River ............................97

Figure 2.3 Sample elevators, six main ports and railroad network in Washington.........98

Figure 2.4 Model results: changes in wheat flows by modes..........................................99

Figure 2.5 Model results: wheat flows at different river ports, different scenarios ......100

Figure 2.6 Model results: transportation costs from different scenarios.......................101

Figure 3.1 Grain production zones associated with SWW quality................................142

Figure 3.2 Grain shed areas within the three states.......................................................143

Figure 3.3 Sample elevators’ distribution .....................................................................144

Figure 3.4 The distribution of Firm 1 and Firm 2’s elevators.......................................145

Figure 3.5 Sample elevators and two production zones................................................146

Figure 3.6 Two transportation networks and sample elevators.....................................147

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CHAPTER 1

NEIGHBORHOOD EFFECTS AND DEMAND FOR GRAIN TRANSPORTATION:

AN APPLICATION OF A SPATIAL TOBIT MODEL

Abstract

Transportation plays an essential role in the development of the Washington grain

industry since the efficient transportation system results in lower transaction costs. Besides

direct transportation costs, spatial interactions or the ‘neighborhood effects’ may determine

demand for grain transportation. The objective of this study is to estimate the demand for grain

transportation by taking account of the spatial interactions by applying the Tobit demand

system with a spatial weight matrix. The introduction of the spatial weight matrix represents

the spatial effects on demand for transportation among neighboring elevators.

We utilize the three-year-average percentage modal split of wheat shipped by either the

rail mode or the truck-barge mode to represent the demand for each mode. Since there is a

significant proportion of zero-value in the dependent variable, the Tobit model is preferred. We

also proposed the new methodology of systematically constructing an unequal weight matrix

for the spatial Tobit demand model through the use of Geographic Information System (GIS).

By applying both traditional Tobit model and the Spatial Tobit model, the main results indicate

a significant positive impact of the spatial factor in the demand for rail transportation.

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I. Introduction

The demand for freight transportation has been studied for more than two decades but,

thus far, most studies have not taken into specific account an autocorrelation problem resulting

from a geographical interaction among observations. Recent developments in spatial

econometrics have shown an important role of the spatial interaction among geographically

distributed cross-sectional observations. It appears the lack of consideration of the spatial issue

that may result in a biased estimation.

Grain elevators in Washington may experience a spatial interaction among each other, or

so-called neighborhood effects defined by Case (1992). The interaction effect is caused by a

spatial concentration among grain elevators located within the same production region. An

elevator competes with its neighbors for wheat from nearby farms in order to fulfill its capacity

or at least the efficient level. On the other hand, a number of elevators provide grain logistical

services to their customers by utilizing the similar available capacity of nearby modes of

transportation, such as railroad, for example.

The concentration of firms from the same industry within a particular region, or so-called

industrial agglomeration, creates firm-external and industry-internal economies of scale because

the presence of other firms facilitates a local, industry-specific infrastructure of service

individuals and information, which enhance the performance of each firm through lower

transaction costs and improved diffusion of financial, production, and marketing information

(Roe et al., 2002). More specifically, a group of elevators uses the same rail track in order to

deliver wheat to export terminals. The demand for railcars by these elevators, on the other hand,

ensures the rail company, at some certain level, that there is a sufficient demand to warrant

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providing capacity into that market. Other examples of the agglomeration, such as in the hog

and dairy industry, can be found in Roe et al., 2002 and Isik, 2004.

Recently, a Tobit model has become more popular in the demand literature, especially in

the household demand issue, where there is a significant proportion of zero value of the

dependent variable in the sample set. Amemiya (1984) pointed out that when zero purchases are

present, the estimation of demand models using ordinary least squares (OLS) based on all or

positive observations may generate biased parameter estimates. Excluding zero-value

observations worsen the problem; some studies specified the Tobit model in order to take into

account the censored nature of the data at zero. In addition, several studies combined the spatial

autoregressive model with the limited dependent variable, such as with a Tobit model (Kaliba,

2002; Langyintuo and Mekuria, 2005), with a Probit model (Case, 1992; Murdoch, Sandler and

Vijverberg, 2003), and with a Logit model (Sarmiento and Wilson, 2005), in order to account for

spatial aspects in their specific objectives.

The objective of this study is to investigate the neighborhood effects on elevators’

demand for grain transportation by utilizing a spatial econometric model capable of capturing the

correlation and interaction among nearby elevators. In addition, we compare a standard Tobit

model with a spatial Tobit model in order to examine which model is more appropriate. An

important contribution of this paper is to propose a new analysis of using Geographic

Information System (GIS) to systematically construct an unequal spatial weight matrix.

The remainder of the paper is organized as follows. The next section presents a brief

background of the grain transportation. Section three reviews spatial econometric literature;

followed by brief review of the literature on the overall demand model and the Tobit model.

Section four shows the theoretical model used in this study. The variable selection, descriptive

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statistics, and the empirical specifications are provided in section five. Section six presents

empirical results. The last section concludes.

2. Background: grain transportation

Several factors affect an elevator manager’s transportation mode choice. Elevator

managers search for a transportation mode that is the least cost among available choices. Not

only do the transportation rates affect managers’ demand for transportation mode, but also

service qualities, such as accessibility and economies of scale. Accessibility is important to

elevator managers in terms of transportation cost savings. Without rail access, a branch elevator

needs to transship grain on trucks to other sub-terminal elevators in order to upload grain onto

railcars. In addition, the concept of economies of scale is an essential advantage for grain

transportation industry, especially for a large elevator or a multiple location elevator firm using

the rail mode. Hanson, Baumhover, and Baumel (1990) suggested that rail companies are more

likely to give a rail contract, either below the tariff or the guaranteeing rail car availability to an

elevator that ships large quantities of grain. Moreover, elevators with multiple locations are

more likely to receive a rail contract because of the large volume of grain that can be combined

and originated from the different locations.

In this study, we consider that the rail and the truck-barge modes as factors of production

for elevators in order to provide grain logistical service to customers. The attributes mentioned

above affect substitution between the two modes. When an elevator ships grain to its destination

by using only either the truck-barge mode or the rail mode, no substitution exists between the

two modes. On the other hand, when an elevator moves grain to its destination with a

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combination between two modes; rail and truck-barge, the elevator can substitute one with the

other mode. Figure 1 illustrates isoquant curves from the three situations.

Figure 1 illustrates the grain elevators’ decisions on supply of grain logistical services

with two inputs (rail and truck-barge) within the context of an isoquant and an isocost. In brief,

the isoquant measures a level of output at different combination of inputs, represented by curve

A, B, and C. Every point on the same isoquant implies that a firm uses different combination of

two inputs in an attempt to produce the same amount of output. In addition, the isocost xy

measures the cost of employing different combination of inputs. Similarly, every point on the

same isocost implies that the firm spends the same amount of money to employ different

combination of inputs. The slope of the isocost denotes two inputs’ price ratios, which is the

truck-barge combination rate to the rail rate ratio in our analysis.

There are three decisions of supplying logistical services, which are illustrated as

isoquant A, B, and, C as shown in Figure 1. Isoquant A represents an elevator that prefers using

railroad. The shape of the isoquant shows that the substitution effect between two modes is not

likely, unless the rate of truck-barge is very low, for example, when isocost xy becomes as flat as

isocost aa ′ . Isoquant B is an example of an elevator that prefers using the truck-barge mode to

the rail mode. Similarly, the substitution effect between the two modes is unlikely, unless

isocost xy becomes as steep as isocost bb ′ , implying that the rail rate drops significantly.

Isoquant C shows a situation that there exists a substitution effect between the two modes. A

slight change in either the rail rate or the truck-barge rate can affect an elevator’s demand for

both modes. Therefore, the decision like isoquant C displays the input-price sensitivity, while

the elevators from the first two cases are not sensitive to prices.

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3. Literature review

3.1. Neighborhood effects and the spatial analysis

The term neighborhood effects, or other similar terms such as peer group effects, spatial

externalities, and strategic interaction, is the explanation of spatial patterns or spatial dependence

among observations in the group of interest. Case (1992) suggests that any economic processes

have spatial aspects that is, unobservable variables may be spatially correlated and thereby

produce spatial correlation in the errors of equations describing economic behaviors.

While not having been applied in any great detail in grain transportation work, the

neighborhood effects have been studied in several research fields, including agriculture, real

estate, healthcare, and, public finance areas. In the agricultural sector, several studies found

strong evidences of the spatial dependence among farmers and among industry-specific firms. A

farmer takes its neighbors’ attitude into account before deciding whether to adopt a new

technology or a new crop variety. Case (1992), using Indonesian data with a spatial Probit

model, found that the neighborhood effect is a crucial determinant, among others, for a farmer

deciding whether to adopt a new harvesting technology. Langyintuo and Mekuria (2005),

applying a spatial Tobit model, also found a significant evidence of neighborhood effects among

Mozambique farmers in deciding whether to adopt a new maize variety.

Within an agricultural industry, a firm and its neighboring firms benefit from firm-

external and/or industry-internal economies of scale in the presence of industry-specific

infrastructures, implying that the firm operates more efficient when other firms, in the same

industry, are located nearby. As pointed out by Roe et al. (2002), such spillovers may arise

because the presence of other operations facilitates a local, industry-specific infrastructure of

service individuals and information, which enhances the performance of each operation through

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lower transactions costs and improved diffusion of financial, production, and marketing

information.

Roe et al. (2002) investigated spatial patterns, using the county-level data from the 1992

and 1997 Census of Agriculture, in hog production within 15 key hog production states. The

study measured the centroid-to-centroid distance across counties, and used the inverse of the

centroid-to-centroid distance between two adjacent counties to reflect spatial weight of those two

counties.1 The results showed a strong evidence of the spatial dependence among hog

production counties. Isik (2004) examined the spatial dependence in dairy production using the

county-level data from the 1992 and 1997 Census of Agriculture. The study found a positive

spatial correlation in the current-level dairy production across counties. In some cases,

geographical attributes determine spatial dependency. Anselin et al. (2004) estimated the site-

specific crop response functions for nitrogen-application to corn production in Argentina. The

study applied a spatial autoregressive model in the response function with the purpose of

capturing spatial structures of nitrogen-site and compared its result with the nonspatial response

function. The results indicated that the response function of site-specific locations leads to

profitability in farm operation, while the nonspatial response function does not since the latter

model did not take account of the spatial structures.

In the real estate sector, the spatial correlation also plays an important role in explaining

house and property values. The correlation is a result of the geographically segmented nature of

real estate markets and ignoring this effect leads to statistically biased results (Anselin, 1998).

For example, Brasington (2004) estimated impacts of school districts merger on house values in

Ohio. The study found a significant spatial correlation among house prices along with a negative

1 Geographically, a centroid refers to a center of any polygon, or sometimes called center of mass. Since a shape of each county in a map is likely to be polygon, a centroid is used to represent a reference point for each county.

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impact of school districts merger on house values because the merger creates the loss of control

over public schooling provision. In addition, Brasington and Hite (2005), using the data set from

5,051 Census Block Group (CBG) in Ohio, estimated the relationship between house prices and

environmental disamenities and then estimated a demand curve for environmental quality. They

found that the there are spatial effects in both the hedonic and demand estimations. Tse (2002)

applied a stochastic approach, which is able to correct autocorrelation bias in the hedonic

function by using Hong Kong data. The results showed that the quality of property and location

tend to exhibit highly autoregressive correlation due to spatial dependence and heterogeneity.

An example of spatial research in the healthcare sector is Mobley (2003) modeled the

hospital market pricing using price response curves, estimated from 336 hospitals in California.

The results showed significant spillover effects in pricing. When there is a substantive spatial

dependence as in the study’s price-reaction function model, the spatial lag parameter is

interpreted as the slope of the reaction function, which represents the extent of spatial spillovers

or copy-catting in prices.

In public finance, the spillover effect across geographical areas or administrative zones is

one of the main issues that researchers in this field have paid more attention. Recently, Garrett

and Marsh (2002) analyzed the impacts of cross-border lottery shopping applying data from

Kansas and its neighboring states, Oklahoma, Missouri, Nebraska, and Colorado. The results

showed that the cross-border lottery shopping lead to significant reduction in lottery revenue,

which is an important implication to all 37 lottery-dependent states. Some researchers

emphasized on the spillover effects of public infrastructure investment projects on the cost and

productivity of private enterprises. For example, Cohen and Paul (2004) analyzed 1982-1996

state-level U.S. manufacturing data to untangle the private cost-saving effects of inter- and

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intrastate public infrastructure investment. The spillovers increased the estimated magnitude and

significance of cost savings from in intrastate public infrastructure, and augmented the

productive effects.

The above literature on spatial analysis has shown that spatial patterns commonly appear

in several sectors, such as agriculture, real estate, and healthcare because of the spatial

interaction among samples. The grain industry also shows the spatial effect due to the price

competition among elevators in an attempt to attract grain from farmers. Therefore, we

theoretically implement a spatial autoregressive model in order to exhibit the spatial structure

among elevators.

3.2 Derived demand

The early studies by Spady and Friedlaender (1978), Oum (1979b, 1979c), Friedlaender

and Spady (1980) provided the systematic derivation of freight demand function. They viewed

the freight transportation as one of the production inputs for a firm to provide logistical service to

customers. In order to obtain an estimate of the demand for freight transportation, they applied

Shephard’s lemma by taking a derivative of firms’ cost function with respect to the rate of

transportation mode. They took advantages of a Translog cost function in order to estimate a

firms’ unknown cost function yielding a conditional factor demand equation.2 In addition, as

Baumol and Vinod (1970) suggested that modal attributes may affect firms’ transportation cost

through inventory costs, these studies also took all alternative transportation modes’ attributes

into account of firms’ cost function by utilizing the hedonic concept proposed by Rosen (1974).

2 Moreover, Oum and Waters (1996) point out that the translog specification is popular among empirical studies because it is capable of providing a quadratic approximation to an unknown form of a true twice continuously differentiable function. Additionally, Pels and Rietveld (2000) suggest that flexible function forms are desirable because there is no need to impose a priori restrictions on the technology, i.e., non-restricted elasticities. On the other hand, the Translog specification has a disadvantage that there are a large number of parameters to be estimated. Consequently, the computation of the model dealing with more than two outputs is quite complex (Woodland, 1979).

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Modal attributes are proved to be important for shippers and freight forwarders when

considering for mode choices. Miklius, Casavant and Garrod (1976) and Inaba and Wallace

(1989) included modes’ attributes in the Logit model in an attempt to estimate demand for

freight transportation. Miklius, Casavant and Garrod (1976) investigated effects of service

qualities on apple and cherry shipments, which are different in perishability, while Inaba and

Wallace (1989) addressed the simultaneity of decision between quantity of grain shipped and

mode/destination choices and the effect of spatial price competition. Both studies focused on

agricultural products and included modal service attributes as explanatory variables. They

pointed out that the transit time for agricultural commodities is an important determinant in the

transportation demand equation.

For the freight transportation demand, although spatial aspects have been introduced into

the freight transportation demand literature for more than a decade, only Hendrickson (2005)

introduced a spatial autoregressive model by taking account of the autocorrelation problem. The

study estimated the demand for grain transportation by barge, using the data from Upper

Mississippi and Illinois rivers on the barge mode. The results from the spatial error model

showed that there was no sufficient statistical evidence supporting the spatial correlation among

elevators along the waterway. However, the estimated demand elasticities indicated variation

along the waterway. In addition, Inaba and Wallace (1989) and Hanson, Baumhover and

Baumel (1990) consider spatial aspects by including a market boundary variable into their study.

However, the variable was not statistically significant.

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3.3 The Standard Tobit model and The Spatial Tobit model

Wales and Woodland (1983) and Lee and Pitt (1986) pointed out an economic

interpretation of zero expenditures as well as a direct and appropriate method to specify the

econometric model. They explained that the set of producer choices may be analyzed by means

of the Kuhn-Tucker conditions associated with the cost minimization program under the usual

technical constraints and the non-negativity constraints on input demands. Zero-expenditures are

obtained when non-negativity constraints are binding, leading to a corner solution of the

conventional cost minimization problem. Kuhn-Tucker conditions imply that strictly positive (at

the optimum) demands are characterized by the classical equality between price ratios and

marginal rates of substitution. On the other hand, for all inputs which are not used at the

optimum, input price is too high and above a certain threshold, i.e., the highest price at which a

positive quantity demanded occurs.

The Tobit model has been utilized in several empirical demand estimations, for example

Perali, and Chavas (2000); Angulo, Gil and Gracia (2001); Golan, Perloff and Shen (2001);

Dong, Gould and Kaiser (2004); Yen, et al. (2004); and Yen (2005). Early studies found that a

Tobit model is useful in explaining the household demand with zero-value purchases as a result

of a corner solution, such that households do not buy the product at current prices and income

levels. The demand estimation including zero-value observations in the dependent variable leads

to biased OLS parameter estimates (Amemiya, 1984). For the cigarette and alcoholic beverages

sector, Yen (2005) addressed sample-selection in his study on the demand for cigarette and

alcoholic beverages in the United States. The study developed the Multivariate Sample Selection

Method (MSSM) in order to accommodate the selection problem. Also, it was the first attempt

to address gender differences in cigarette and alcoholic beverages consumption. The data are

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compiled from the 1994-1996 Continuing Survey of Food Intakes by Individual (CSFII), by the

USDA-ARS. Additionally, Angulo, Gil, and Gracia (2001) compared results from three methods

of estimation, the Double Hurdle (DH) model, the Purchase Infrequency (PI) model, and the

Tobit model, on the Spanish demand for alcoholic beverages, which include wine, beer, spirits,

cava, and others. The results showed that the DH model is preferred implying that Spanish

consumers decide not to consume alcoholic beverages, either because their health, or tastes are

different or because their purchase is not desirable at the current level of income and prices.

Several studies applied a Tobit model on the demand for non-alcoholic beverages. Yen,

Lin, Smallwood and Andrews (2004) applied a nonlinear generalization of the linear Tobit

system to estimate the demand for milk, carbonated soft drink, juice drink, and juice. Using the

data from the National Food Stamp Program Survey (NFSPS), the study showed that the small

demand system could be estimated by using the direct maximum likelihood (ML) estimation,

while the large demand system required the ML estimator to evaluate multiple probability

integrals.

In terms of a food demand system, Dong, Gould and Kaiser (2004) developed a simulated

ML technique for the Tobit model with the objective of estimating household food demand in

Mexico. Perali and Chavas (2000) applied a two-step method to estimate the Columbian

household demand system including nine products. The study estimated the unrestricted demand

system by using the Tobit model in the first step. Followed by the application of the Minimum

Chi Square (MCS) method in the second step, their model incorporated the restrictions from

consumer theory into the restricted demand system. Moreover, the study pointed out that the

zero outcomes are more likely to be the expression of a corner solution rather than infrequency

of purchase, so that the Tobit model is applicable. Golan, Perloff and Shen (2001) used the

13

Generalized Maximum Entropy (GME) technique, instead of the traditional ML, to estimate the

five-equation of meat demand system in Mexico. They suggested that the Tobit model with a

full-information ML (FIML) technique is valid for the demand system consisting of a relatively

small number of commodities, equal or less than three.

Recently, several studies combined spatial autoregressive with the limited dependent

variable model, such as Logit, Probit and Tobit models. Kaliba (2002) and Langyintuo and

Mekuria (2005) applied the spatial autoregressive with the Tobit model, or so-called spatial Tobit

model. The former literature used spatial Tobit model to determine the influence of community

participation and sustainability indicators on economic efficiency scores, ranging between zero

and one. The study employed 450 individual samples in the region of Dodoma and Singida in

Central Tanzania. In addition, Langyintuo and Mekuria (2005) used spatial Tobit model in an

attempt to explore factors determining the adoption of improved maize varieties in Manica,

Sussundenga and Chokwe districts of Mozambique during the 2003/04 crop season. They found

that the spatial lag coefficient in the spatial Tobit regression is highly significant indicating that

the standard Tobit model is inefficient for ignoring spatial dependence.

Other related studies that combined the spatial autocorrelation with either Logit or Probit

model include Case (1992), Murdoch, Sandler and Vijverberg (2003), and Sarmiento and Wilson

(2005). Case (1992) and Murdoch, Sandler and Vijverberg (2003) applied spatial Probit in their

analyses. The former examined factors determining the adoption of sickle harvesting in

Indonesia, while the latter investigated determinants for 25 European countries whether to

participate in the Helsinki Protocol or not. In addition, Sarmiento and Wilson (2005) applied

spatial Logit model in order to examine how elevators make a decision of adopting the shuttle

14

train technology. The samples included 2,309 elevators along three main rail lines, which are

Burlington Northern-Santa Fe, Union Pacific and Canadian Pacific Railway.

4. Theoretical Model

4.1 Derived Freight Demand

Traditionally, a conditional factor demand equation is derived from the application of

Shephard’s Lemma by taking the derivative of a firm’s cost function with respect to the factor

price. Spady and Friedlaender (1978) and Oum (1979b) provided a well-established framework

of estimating the demand for freight transportation by viewing freight transportation as one of

the productive factors of production. Both studies started the analysis by taking advantages of

the Translog cost function because of its flexibility and well-defined functional form.3 In

addition, the two studies also introduced a hedonic structure into the model as to characterize

impacts of the quality-adjusted service on firm’s total costs.

Not only do transportation rates affect firms’ operation costs in the hedonic-structure

form, but modal attributes also indirectly influence on firms’ costs through inventory costs

(Baumol and Vinod, 1970). For example, a transit time of a transportation mode might incur

interest cost on capital and commodity deterioration. In addition, the delay of commodity

delivery costs firms in terms of lost sales. Therefore, the hedonic structure is included in this

study because of its capability of capturing effects of service attributes on the firms’ operation

costs.

3 The translog specification is popular among empirical studies because of its capability to provide a quadratic approximation to an unknown functional form of a true twice continuously differentiable function (Oum and Waters, 1996). Additionally, its flexible functional forms are desirable because there is no need to impose a priori restrictions on the technology, i.e., non-restricted elasticities (Pels and Rietveld, 2000).

15

Oum and Tretheway (1989) indicated that the previous costing studies ignored the

heterogeneity of outputs, which resulted in different effects on the costs. Therefore, the hedonic

structure was introduced in order to reflect differences in costs among different outputs. They

introduced the quality-separable cost function in the form of; C = C(p, h( )), where p is a vector

of input prices and h( ) is a hedonic function containing inputs’ attributes. In addition, they took

advantage of Hicksian separability by assuming that the transportation factor prices are not

affected by the non-transportation factor prices.

The specification of the Translog cost function with the hedonic structure in Oum and

Tretheway (1989) can be expressed as following:

Cln = ( ) ydzbzbpaai

ii

ii

ii lnlnlnlnln 1

2

122110 ++++∑

=

( )⎥⎦

⎤⎢⎣

⎡+++ ∑∑

= =

2

1

2

12211 lnlnlnlnlnln

21

i jjiijjiijjiij zzczzbppa

( )⎥⎦

⎤⎢⎣

⎡+++ ∑∑

= =

2

1

2

12121 lnlnlnlnlnln

21

i jjiijjiijjiij zzfzpezpd

( ) ( ) yzczbpaydi

iiyiiyiiy lnlnlnlnln21 2

121

22 ∑

=

++++ (1)

where subscript i, j = 1 indicates a rail mode, 2 indicates a truck-barge combination,

ip = per bushel freight rate of mode i,

1iz = ith mode’s 1st attribute,

2iz = ith mode’s 2nd attribute,

y = the measurement of output (a hundred thousand bushels of wheat),

( )121 ,,, dbba iii = first-order parameters of the translog cost function, and

16

⎪⎭

⎪⎬

⎫

iyiyiy

ijijij

ijijij

cba

dfed

cba

,,

,,,

,,,

2 = second-order parameters.

The linear homogeneity conditions of the Translog function are

121 =+ aa

,02111 =+ aa ,02212 =+ aa

,02111 =+ dd ,02212 =+ dd

,02111 =+ ee ,02212 =+ ee

,021 =+ yy aa

In addition, the symmetric condition of the Translog function implies that 2112 aa = .

However, with the nature of aggregated survey data, modes’ characteristics cannot be

identified precisely. Therefore, the model used in this study is the Translog cost without modes’

characteristics, as specified in (2).

Cln = ( ) ydpaai

ii lnlnln 1

2

10 ++∑

=

( ) ( ) ( )∑∑∑== =

++⎥⎦

⎤⎢⎣

⎡+

2

1

22

2

1

2

1

lnlnln21lnln

21

iiiy

i jjiij ypaydppa (2)

Applying Shephard’s Lemma, we take a derivative of the Translog cost function with

respect to ipln , and then obtain the conditional factor demand equations as followed:

1lnln

pC

∂∂ = 1S = yapapapaa y lnln

21ln

21ln 12212121111 ++++

With the homogeneity and symmetry conditions, the above equation can be rewritten into,

1S = yappaa y lnln 1

2

1111 +⎟⎟

⎠

⎞⎜⎜⎝

⎛+ (2a)

17

With the linear homogeneity condition, we can express the truck-barge share equation as

the following,

( ) yappaaS y lnln1 1

2

11112 −⎟⎟

⎠

⎞⎜⎜⎝

⎛−−= (2b)

where 1S and 2S are shares of expenditure on a rail mode and a truck-barge combination,

respectively.

We drop the truck-barge share equation, 2S , from the estimation in order to avoid the

singularity of the disturbance covariance matrix. The parameters associated with the dropped

truck-barge share equation would be derived from the relationships with the estimated

parameters.

In addition, Wales and Woodland (1983) demonstrated the method to capture effects of

household characteristics in the demand estimation. They assumed that the constant terms in the

derived demand equations were linear functions of a vector of demographic factors.

Analogously, therefore, the constant term 1a in (2a) can be assumed as a linear function of an

elevator’s characteristics as following.

∑=

+=K

kkk za

11101 µµ

Consequently, the final equation can be expressed as:

1S = ∑=

++⎟⎟⎠

⎞⎜⎜⎝

⎛+

K

kkky zya

ppa

111

2

11110 lnln µµ (2c)

2S = ∑=

−−⎟⎟⎠

⎞⎜⎜⎝

⎛−−

K

kkky zya

ppa

111

2

11110 lnln1 µµ (2d)

The following seven characteristics are hypothesized to affect an elevator’s demand for

grain transportation.

18

1z = natural logarithm of an elevator’s capacity

2z = 1 if an elevator has a rail facility, 0 otherwise

3z = proportion of wheat supplied to export markets

4z = competition within the county where the elevator resides

5z = 1 if an elevator belongs to a firm owning 1-5 elevators (small firm), 0 otherwise

6z = 1 if an elevator belongs to a firm owning 6-20 elevators (medium firm), 0 otherwise

7z = 1 if an elevator belongs to a firm owning over 20 elevators (large firm), 0 otherwise

The natural logarithm of the size of an elevator is chosen to reflect elevator-level

economies of scale, since a larger elevator is more likely to be successful in bargain for

discounted rail rates. The availability of a rail facility makes it more likely that an elevator

would choose the rail mode over the truck-barge combination. The proportion of wheat supplied

to export markets determines whether an elevator needs long distance transportation, such as the

rail mode and the barge mode, to ship grain to the export terminals. Otherwise, an elevator

manager might hire trucks to ship grain to the nearby feedlots and four-mills.

The competition within a county could affect a resided elevator’s demand for rail

transportation. A very competitive county might result in a smaller volume of grain received by

an elevator, while a monopolized county would support an elevator to ship grain by the rail mode

more often due to a larger volume of grain received. In addition, the size of a multi-location

elevator firm is the other important factor determining the potential volume of the grain pool

within the company. The larger company means a larger grain pool, which allows the firm to

bargain for discounted rail rates. In other words, the size of the company represents economies

of scale at the firm level.

19

4.2 Standard Tobit regressions

Tobin (1958) derives the likelihood function and uses the maximum likelihood (ML)

method to estimate the model. Amemiya (1973) proves that the ML estimator is strongly

consistent and asymptotically efficient under the general regularity conditions. Golan, Perloff,

and Shen (2001) suggested that the Tobit model with a full-information ML (FIML) technique is

valid for the demand system consisting of a relatively small number of commodities, equal or

less than three. Therefore, we apply the Tobit model with the ML technique to estimate the

elevators’ demand system for two inputs, which are rail and truck-barge modes.

Figure 2 illustrates the normal quantile plot of the dependent variable ‘Rail’. The plot

shows that the demand for rail transportation is restricted between zero and one. In addition, the

proportion of observations with the value of zero and the value of one are substantial. Therefore,

the double-censored Tobit model, with the lower bound at zero and the upper bound at one, is

applied to estimate coefficients in the demand equation.

After deriving a demand for rail as stated in (2c), the demand equation is represented by a

linear regression as the following:

1S = Xβ + ε (3)

where 1S = percentage of wheat shipped by the rail mode

X = kn× matrix of explanatory variables

β = 1×n coefficient vectors for the rail mode

ε = error vectors for the rail mode

Therefore, we specify the likelihood function for the double-censored Tobit model as the

following:

20

L( σβ , ) = ∏∈

⎥⎦⎤

⎢⎣⎡ ′−

Φ1

1

Li

ii xLσβ ·∏

∈⎥⎦⎤

⎢⎣⎡ ′−

⎟⎠⎞

⎜⎝⎛

Ni

ii xSσβ

φσ

11 ∏∈

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦⎤

⎢⎣⎡ ′−

Φ−2

21Li

ii xLσβ

(4)

whereΦ and φ are the cumulative probability distribution function and the standard normal

density function, respectively, and σ is the standard deviation of disturbance terms. iL1 and iL1

are the lower limit and the upper limit, which are assigned to be zero and one in order to reflect

the result of a corner solution, since there are a significant proportion of the dependent variable

reports zero-value a transportation mode purchase and 100% a transportation mode purchase. In

terms of the literature on demand systems, a significant proportion of the censored values

dependent variable results in biased and inconsistent OLS coefficients, double-censored Tobit is

more appropriate to work with in order to avoid biased estimations.

As pointed out in the previous section that the demand for grain transportation is a result

of the corner solution, it is not possible that the demand for grain transportation could be

categorized into either the infrequency of purchase problem or the abstention problem. First of

all, the elevator survey includes a question of the amount of three-year-average percentage of

wheat shipped, which is considered an significant long period of time, unlike questions in most

households surveys that focus on the amount of product purchased or sold within a month or a

week. Second, because both transportation modes are an input of production, there is no reason

for elevator managers to be unwilling to purchase transportation services.

4.3 Spatial Tobit regressions

The standard Tobit does not take account of spatial aspects, resulting in biased estimation

outcomes. To incorporate spatial aspects into the Tobit model, a key element called the spatial

weight matrix, W, is included into the spatial autoregressive model. The matrix is n rows by n

columns dimension, where n is a number of total observations in the study. Each element in the

21

matrix represents an interaction between a pair of elevators. Elements in each row of the matrix

correspond to each elevator’s spatial weights. The estimation procedure of each elevator’s

spatial weights is shown in Section 5.3.

We include spatial aspects in the Tobit model specified in (4) by adding the spatial

weight matrix in (3). Equation (3) is modified as followed.

1S = ρW 1S + Xβ + ε (5a)

and ε = λWε + u, u ~ N(0, 2σ ) (5b)

where 1S = percentage of wheat shipped by the rail mode,

W = nn× matrix of spatial weight

ρ = spatial autoregressive coefficient in the dependent variable

λ = spatial autoregressive coefficient in the error terms

X = kn× matrix of explanatory variables

β = 1×k coefficient vectors for the rail mode

ε = error vector for the rail mode

u = independent and identical distributed error vector

The ML estimation of equation (5a) and (5b) is more complicated than the one in equation (3).

Anselin (1988) suggested transforming equation (5) to a more general form, which can be

rewritten as equation (6).

[ I – ρW ] 1S = Xβ + ε

1S = [ I – ρW ] 1− Xβ + [ I – ρW ] 1− ε (6)

where ε = λWε + u, and u ~ N(0, 2σ )

ε* = [ I – λW ] 1− u

22

In addition, Case (1992) indicated that the disturbance term in the equation (6) results in

heteroskedasticity in the errors, which would render the inconsistent estimation. To correct the

heteroskedasticity problem, Heckman (1978) suggested a modification of the equation by

premultiplying a variance normalizing transformation, D = [ ]( )( ) 21** −TEdiag εε . Therefore,

equation (6) becomes

1* SD = D* [ I – ρW ] 1− Xβ + D* [ I – ρW ] 1− [ I – λW ] 1− u (7)

Premultiplying the dependent variable with the variance normalizing factor, D, does not

alter the lower bound, at zero, of the previous Tobit model, however, it does not guarantee that

there is the upper bound. Consequently, the Tobit model used for investigating the spatial effects

is a single censored, rather than a double-censored Tobit model.

The likelihood function for the spatial Tobit model is as the following:

*L ( σβρ ,, ) =

∏∈

−

⎥⎦

⎤⎢⎣

⎡ −−Φ

1

11 ][*

Li

ii XWIDLσ

βρ·∏∈

−

⎥⎦

⎤⎢⎣

⎡ −−⎟⎠⎞

⎜⎝⎛

Ni

ii XWIDSDσ

βρφ

σ

11 ][**1 (8)

In order to perform Maximum Likelihood (ML), Garett and Marsh (2002) suggested

applying the MAXIMUM LIKELIHOOD 4 applications module of GAUSS. We also apply the

Algorithmic Derivatives (AD) algorithm in order to calculate the gradient matrix. Note that a

full derivation of the Spatial Tobit estimation is shown in Appendix 1.

5. Empirical Specifications and Variable Selection

5.1 Data

The data used in this paper is collected from Clark, Jessup and Casavant (2003), which

surveyed grain elevators in eastern Washington for the Department of Transportation in 2002.

23

The data of the grain transportation survey include of three-year-average percentage modal split

of wheat shipped, rail rates and barge rates, capacity of an individual elevator, volume of wheat

received, for example. Of 394 licensed elevators in the state of Washington, 386 elevators

responded to this survey, accounting for 98% of all elevators in WA. Out of the available

samples, there are 113 observations with some missing data, leaving 273 observations with

complete information.

5.2 Variable Selection

The dependent variable is the three-year-average percentage modal split of wheat shipped

by rail mode. This analysis focuses on the rail demand equation; the dependent variable is

represented by the demand for rail mode (RAIL). The percentages of wheat shipped by different

modes are driven by the preferences of each elevator manager. The transship decisions also

influence a railroad demand because transshipment is a result of a discounted rail rate received

by an elevator. Figure 2 illustrates the obvious pattern of lower-upper censored data for the

dependent variable. In order to handle this kind of data, double-censored Tobit is considered to

be the most appropriate model.

Explanatory variables include the rail rate to the truck-barge rate ratio (RATIO),

elevator’s capacities (CAPACITY), volume of wheat received at each elevator (OUTPUT), the

rail access dummy variable (RAILACCESS), the Herfindahl-Hirschman index (HHI), proportion

of wheat supplied to export markets (EXPORT), and the dummy variables representing three

different sizes of multiple-location elevator firms (SMALL, MEDIUM, and LARGE). First, the

natural logarithm of the rail rate to truck-barge rate ratio represents the relative price of using a

rail mode to truck-barge that each elevator receives. When a rail rate is high relative to a truck-

barge rate, elevators may prefer using the truck-barge mode to the rail mode. A costly rate of

24

railroad relative to a truck-barge rate may reduce the elevators’ demand for rail mode.

Therefore, we expect the sign of RATIO to be negative. Second, the natural logarithm of the

size of an elevator (CAPACITY), measured in a hundred thousand bushels, is included in the

regression in order to investigate the effect of an individual elevator’s capacity on the demand

for grain transportation. Since a larger elevator may be able to ship a larger volume of grain, its

manager is likely to negotiate with the railroad company for discounted shipping rates.

Consequently, we expect a larger elevator is more likely to ship grain by rail, so the sign of this

variable would be positive. Third, the natural logarithm of the volume of wheat received at each

elevator (OUTPUT), measured in a hundred thousand bushels, and represents the amount of

output each elevator obtains. This variable is included according to the theoretical model shown

in the section 4, in order to serve as an output associated with the cost function. Therefore, the

sign of this variable is expected to be positive. Next, the dummy variable of the rail access

(RAILACCESS) is assigned 1 if an elevator has a rail facility, 0 otherwise. An elevator with rail

access is more likely to ship grain by rail rather than the truck-barge combination. The estimate

of the rail access variable is expected to show a positive sign in relation to the demand for

railroad.

In addition, we are interested in examining effects of the competition among elevators.

To capture the degree of market competition, the Herfindahl-Hirschman (HHI) index is applied

in order to measure the competition within each county by calculating a county-specific

elevators’ capacity as market shares within that county.4 The HHI ranges from zero to one

measuring the market competition. The market is competitive when the index is close to zero,

while the market is monopolized when the index is close to one. Moreover, we investigated the 4 Herfindahl-Hirschman index (HHI) is defined as the sum of the squares of the market shares of each individual firm. HHI ranges from 0 to 1 moving from a very large amount of very small firms to a single monopolistic producer.

25

effect of multi-location elevator firms on their elevators’ demand for the grain transportation by

including dummy variables that indicate three different sizes of a multi-location elevator firm,

measured in terms of the number of elevators owned. A small firm is assumed to own one to

five elevators, while a medium firm owns six to twenty elevators. A large firm owns twenty-one

elevators or more. The small firm dummy variable is dropped in order to avoid the perfectly

multi-collinearity.

We are also aware of the fact that some elevators serve mainly in the domestic market,

which requires only the trucking grain shipment to nearby feedlots or flour mills. This group of

elevators only supplies a small fraction of grain to export markets through either the rail or the

truck-barge transportation modes. Therefore, either rail or truck-barge modes are not the main

factors of production to the group. Since the intensity of export activity at each elevator affects

demand for either the rail or the truck-barge modes, we include the proportion of wheat supplied

to export markets in the regression model as one of the explanatory variables.

Table 2 shows descriptive statistics of variables used in this analysis. The mean of the

dependent variable RAIL is approximately 0.4 implying that less than half of the total wheat

volume from all sample elevators is shipped by rails, while about 60% of wheat is shipped by a

truck-barge mode. The mean of RATIO is slightly below 1 implying that, by overall, the rail

mode is cheaper than the truck-barge combination. In addition, the maximum value of the ratio

is reportedly three times higher than the truck-barge rate. The average size of sample elevators

(CAPACITY) is 440,000 bushels, ranging from 10,000 to 3,300,000 bushels. The standard

deviation of CAPACITY is high due to the fact that the sample elevators’ sizes are significantly

different. The mean of OUTPUT is 3.537 hundred thousand bushels, which is smaller than the

average sized of sample elevators. This means, by average, that each elevator does not utilize all

26

of its capacity. The mean of RAILACCESS is approximately 0.45 implying that almost half of

the sample elevators have rail facilities. Furthermore, the mean of HHI among different counties

is less than 0.5 implying that the market competition among elevators is moderate. The mean of

the dummy variable representing a small multi-location elevator firm is 0.16, while the mean of

the dummy variable indicating a medium and large firm are 0.33 and 0.50, respectively. As a

matter of fact, large firms represent the largest proportion in the sample set followed by medium

size firms and small firms.

5.3 Spatial Weight Matrix

The key element in spatial econometric modeling is the spatial weight matrix. How the

matrix is constructed also influences the outcome of the model. Traditionally, the matrix is

constructed by using binary values, zeros and ones, to represent spatial interaction among

observations. Zeros indicate no interaction, while ones represent spatial interaction between two

observations. The matrix assumes that every spatial interaction between two observations is the

same, no matter how far apart they are. Later on, the matrix is constructed by weighting the

spatial interaction between two observations by the distance between them. Consequently, the

further away neighboring observations would have less influences on the considering

observation than the closer neighboring observations. Also, the unequal weight matrix is a

symmetric matrix.

Both types of matrix are constructed based on the distance between two observations,

while in reality the influences of one observation on the other observation may not be only the

distance, but other factors, such as market power and market environments. More importantly,

the matrix is not necessarily symmetric. In other words, the influence of the neighboring

observation on the considering observation may not be the same in return.

27

The equally assigned weight to different neighboring observations may not be an

appropriate approach, especially, for grain elevators, since the effects of different neighboring

elevators on a specific elevator are not the same depending on the proximity factor between the

two elevators and the market power factor of the neighboring elevators. The proximity factor is

directly measurable, while the market power factor is indirectly measurable and can be

represented by their capacities.5 However, in this study, we propose using the size of each

elevator’s market area to serve as a composite index measuring both the proximity factor and the

market power factor of each elevator. Fortunately, we obtain the information of elevators’

market area size from Clark, Jessup and Casavant (2003).

In addition, we are also interested in the problem of heteroscedasticity since it is

hypothesized that each elevator firm has some influences on its elevators. Each elevator firm

might have their own business practices or management styles, which shape its elevators’ pattern

of demand for the rail mode to be differ from other companies’ elevators. Consequently, the

assumption of constant variance among observations might not be true in this study. Ignoring

heteroscedasticity problem causes inefficient estimators, because their standard errors are biased.

In order to take care of the company effect, we also proposed the company weight matrix to be

applied in the spatial Tobit model. The details of this matrix are provided in section 5.3.2.

5.3.1 Market Interaction Weight Matrix

In this paper, we apply an unequal weight matrix on the Spatial Tobit regression.

Basically, each spatial weight corresponds to an influence factor of a neighboring elevator on

one elevator. The influence factor is measured from the intersection between an elevator’s

5 Hanson, Baumhover and Baumel (1990) pointed out that an elevator firm with branches tends to receive a better rail rate than a smaller elevator due to the capability of large shipments. Consequently, the large elevator attracts more grain from farmers than the smaller elevator does. It is clearly that the capacity is playing an important role in grain transportation.

28

market area and its neighbor’s market area. In order to identify the overlapping areas among our

sample elevators, we apply Visual Basic for Application (VBA) with Geographic Information

System (GIS) Arc-INFO to program and calculate areas. We calculate the spatial weight of each

neighboring elevator by considering the overlapping area as a percentage of the total market area

of the focusing elevator. The VBA code is available in Appendix 2.

Figure 5 illustrates the overlapping areas among selected samples’ market area. The

selected samples are located in Davenport, Almira, and Ritzville. Graphically, five circles

represent five elevators’ market areas, simulated by the Buffer feature in GIS. The five selected

samples include two elevators in Almira (Almira10 and Almira20), two elevators in Davenport

(Davenport10 and Davenport50), and the other one in Ritzville (Ritzville10). We categorize the

market area into four different sizes, following Clark, Jessup and Casavant (2003), which are 1).

within 5 miles from the elevator, 2). within 10 miles, 3). within 20 miles, and 4). within 50 miles

from the facility. In Figure 5, the smallest circle represents the market area size within 10 miles

from the elevator, while the largest circle represents the market size within 50 miles from the

elevator. The medium size circle represents the market size within 20 miles. There is no

elevator with the 5 miles market area displayed in this figure.

From Figure 5, it is obvious that Davenport50, which is an elevator in Davenport

controlling the largest market area, influences on both elevators in Almira (Almira10 and

Almira20), while the closer elevator in Ritzville (or Ritzville10) does not. In addition,

Davenport50 also influences on both Davenport10 and Ritzville10. If Almira10 is the

considering elevator, the overlapping areas between Almira10 and Almira20 and also between

Almira10 and Davenport50 represent influences from both elevators on Almira10. The

overlapping area between Almira10 and Almira20 is the entire market area of Almira10, while

29

the overlapping area between Almira10 and Davenport50 equals to 0.013 square miles. GIS also

reports the total area of the smallest circle, the medium circle, and the largest circle, which are

0.066 square miles, 0.263 square miles, and 1.645 square miles, respectively.

In addition, the influence of Almira20 on Almira10 is observably larger than the influence

from Davenport50. We measure effects from different surrounded elevators on the focused

elevator by calculating ratios of the overlapping areas to the total size of its market area (circle).

Therefore, the influence of Almira20 on Almira10 is 066.0066.0 = 1, while Davenport50’s

influences on Almira10 is 066.00.013 = 0.19. Similarly, the impact of Almira10 and

Davenport50 on Almira20 are 263.00.066 = 0.25, and 0.263082.0 = 0.31, respectively. Using

the same pattern of calculation, we can estimate spatial weights on the rest three elevators and

express into the spatial weight matrix. Table 1 shows an example of the spatial weight matrix

constructed from the five selected observations. However, since there are 273 elevators included

in this study, we utilize a 273273× spatial weight matrix in the analysis.

5.3.2 Company Weight Matrix

Unlike the construction of the Market Interaction Weight Matrix, the construction of this

matrix is based on the ownership among elevators. Elevators owned by the same company are

considered receiving the same influences on business practices or management styles, while

elevators owned by different company are not affected by the practices or styles. The weight

matrix used for this part is the binary matrix of zeros and ones, in order to represent whether the

same company owns elevators. Ones represent the same ownership and zeros represent

otherwise. Therefore, this is the way to capture elevator firms’ heterogeneity and prevent

heteroscedasticity in the spatial Tobit estimation.

30

6. Empirical results

Table 3 reports the regression results from the OLS, the double-censored Tobit and the

spatial Tobit models. The spatial Tobit in column (3) and column (4) are estimated with two

different weight matrices as unrestricted models, while the double-censored Tobit is estimated as

a restricted model with similar explanatory variables. The spatial autoregressive variables, Rho

and Lambda, are additional variables used in the spatial Tobit regression. The spatial Tobit in

column (3), accounting for heterogeneity among elevator companies, indicates that the model

with only Lambda is the bestThe log likelihood values from the double-censored Tobit and the

spatial Tobit model with company weight matrix are -195.388 and -163.223, respectively. The

likelihood ratio (LR) test is applied in order to test the restriction of 0=λ . The test is specified

as following:

- 2 ln ⎟⎟⎠

⎞⎜⎜⎝

⎛

U

R

LL = 2 [ln UL - ln RL ] = 64.317.

Asymptotically, the LR test is distributed as the chi-square distribution with 1 degree of freedom.

The calculated log likelihood value is greater than the critical value, 2%)99,1(χ = 6.635, suggesting

that the spatial Tobit model with company weight matrix is more appropriate than the double-

censored Tobit model because we can reject the null hypothesis of 0:0 =λH in favor of the

spatial Tobit model.

Table 3 compares the results of the estimated coefficients from the Ordinary Least

Squares (OLS), double-censored Tobit and two spatial Tobit models. From the OLS regression,

Ratio, RailAccess, Medium and Large are statistically significant at the 5% level. Most

estimated coefficients signs are consistent with demand theory except the sign of Export. This

variable is expected to be positively correlated with the demand for the rail mode, because

31

elevators with a high proportion of wheat export are more likely to use rail for shipping grain to

Portland. On the other hand, elevators with a low proportion of wheat export may supply wheat

to local feedlots and flourmills, which would require only truck transportation for short

distances. Since the data in this analysis is censored at zero and one, the OLS regressions result

in biased estimators. The incorrect sign for Export demonstrates the bias problem.

While the signs of the OLS estimators are not consistent, the double-censored Tobit and

spatial Tobit models report consistent signs. The negative sign of Ratio confirms the demand

theory. Although Output is not statistically significant at the 5% level, the sign is positive as

expected since it was derived from the translog cost function. RailAccess is statistically

significant at the 5% level and positively correlated with the demand for rail, as an elevator with

a rail facility is more likely to ship grain by the rail mode. In terms of market competition,

although the concentration index HHI indicates a positive correlation with the demand for rail, it

is not statistically different from zero at any level.

In terms of the size of elevator companies, both the OLS and the double-censored Tobit

models show significant company effects since the company size dummy variables, Medium and

Large, are significantly different from zero. However, the regression results show that there is

no statistical evidence to support the effect of Capacity on the demand for rail. Therefore, the

regression results indicate that elevators’ demand for the rail mode is more likely to be

determined by the size of the company than the size of an individual elevator.

Ignoring the spatial effects in the demand for rail transportation may result in inefficient

estimators. Column (3) and column (4) show the results from the spatial tobit estimations, which

illustrate the effect of spatial interaction on elevators’ demand for rail transportation. The spatial

Tobit models used in this paper apply two different spatial weight matrices; the company weight

32

matrix and the market interaction weight matrix. The spatial Tobit model with the company

weight matrix is used because it is suspected to show the heterogeneity among companies. The

second result is the spatial Tobit model applying a new-proposed market interaction weight

matrix from section 5.3. The spatial Tobit associated with the company weight matrix has

shown strong statistical evidence of the heteroscedasticity among elevator firms, since the

parameter Lambda, a spatial autoregressive parameter for the error terms, is statistically

significant at the 1% level.

Comparing the results from both spatial Tobit models and the standard Tobit model, the

Spatial Tobit estimation seems to be more efficient than the double-censored Tobit because all

standard errors in the spatial Tobit model with the company weight matrix are all smaller than

that of the double-censored Tobit model. In addition, the Lambdas and Rho, which are

statistically significant at the 1% level on both models, confirm that there is statistical evidence

of the spatial effects from the company effect as well as the market interaction effect. The

negative signs indicate that elevators with different levels of demand for rail are clustering

together. The estimated coefficients of Rho and Lambda under from the spatial Tobit regression

associated with the market interaction weight matrix are statistically significant at the 1% level

implies that there are spatial effects in both the dependent variable and error terms.

Comparing both the spatial Tobit models in column (3) and column (4), all the signs are

similar in both regressions. In terms of standard errors, all standards errors under the company

weight matrix are lower than the ones using the market interaction weight matrix. In addition, the

log likelihood also confirms that the spatial Tobit model with the company weight matrix is more

efficient than the standard censored Tobit model and the spatial Tobit model with the interaction

weight matrix.

33

7. Conclusions

The interaction effect is caused by a spatial concentration among grain elevators located

within the same production region. In attempting to make the most of its capacity and/or at least

maintain its efficient level, elevators’ behavior in obtaining grain, affects other neighbor

elevators. Previous studies of the spatial models did not take into account some economic

factors such as the market competition and market power. This paper is the first attempt to

incorporate the effect of market factors on an elevator’s demand for transportation by proposing

a method of measuring an unequal weight matrix under a spatial Tobit model. Geographic

Information System software (GIS) is applied to transform the spatial interaction among

elevators into a spatial weight matrix, and also creates a new proposed methodology in order to

systematically construct an unequal weight matrix. Using the Washington elevator data of 2002,

the estimation results from the Spatial Tobit models and the standard double-censored Tobit

model are compared.

The spatial Tobit models demonstrate that the size of the elevator company affects the

demand for rail transportation. Larger companies tend to ship grain by the rail mode, while the

small companies have the least probability of shipping grain by rail. Although we hypothesize

that the size of an elevator itself may be a crucial determinant of the demand for rail

transportation, there is no statistical evidence that elevators’ capacities affect the demand for rail.

The significant effect of the elevator firms’ size, the results suggest that the firms’ size is more

important than the size of an individual elevator in determining the demand for rail

transportation.

The key results show that the spatial Tobit model is preferable to the standard censored

Tobit model. Comparing both spatial Tobit regressions using different weight matrices, the

34

spatial Tobit model with the company weight matrix seems to perform more efficiently.

However, the newly-proposed spatial Tobit with the market interaction weight matrix, which

accounts for more economic factors such as the market area size and the competition among

different sizes of elevators, is less efficient than spatial Tobit with the company weight matrix.

Moreover, the differences between the rail-truck/barge rates ratio coefficients from the

standard censored Tobit model and from the spatial Tobit model with the company weight matrix

indicate a strong impact from spatial interactions on the demand for grain transportation

compared to the effects from the price factor. Without taking into account the company

heterogeneity, the estimation results are inefficient. In addition, we conclude that the spatial

factor plays a more important role than the price factor.

35

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40

TABLES

Table 1.1 An example of spatial weigh matrix (for 5 elevators)

Elevator name Almira 10 Almira 20 Davenport 10 Davenport 50 Ritzville 10

Almira10 0.00 1.00 0.00 0.19 0.00

Almira20 0.25 0.00 0.00 0.31 0.00

Davenport10 0.00 0.00 0.00 1.00 0.00

Davenport50 0.01 0.05 0.04 0.00 0.04

Ritzville10 0.00 0.00 0.00 1.00 0.00

41

Table 1.2 Summary statistics

Variable Description Mean Min Max Std

Rail Three-year-average percentage of wheat shipped by railroad 0.390 0 1 0.390

Ratio The ratio of railroad rate to truck-barge rate 0.962 0.441 3.240 0.343

Capacity Size of an elevator in a hundred thousand bushels 4.367 0.100 33.000 4.381

Output Volume of wheat received at each elevator in a hundred thousand bushels

3.537 0.011 80 7.780

RailAccess 1 if an elevator has a rail facility, 0 otherwise 0.454 0 1 0.499

Export Proportion of wheat supplied to export markets 0.951 0 1 0.171

HHI The Herfindahl-Hirschman index within a county 0.092 0.027 1 0.147

Small 1 if the firm owns 1-5 elevators, 0 otherwise 0.161 0 1 0.368

Medium 1 if the firm owns 6-20 elevators, 0 otherwise 0.337 0 1 0.474

Large 1 if the firm owns over 21 elevators, 0 otherwise 0.502 0 1 0.501

42

Table 1.3 Regression results of OLS, Double-censored and Spatial Tobit

Variable OLS Double- Spatial Tobit

censored

Tobit

Company Weight Matrix

Market Interaction

Weight Matrix (1) (2) (3) (4)

Constant -0.3806 -1.3951 * -0.6404* -1.1707 (0.2963) (0.6199) (0.2930) (0.6218) Ratio -0.2971 * -0.4454 * -0.2224* -0.1218 (0.0812) (0.1542) (0.0883) (0.1423) Output 0.0187 0.0321 0.0157 0.0387 (0.0264) (0.0515) (0.0227) (0.0485) Capacity 0.0113 0.0007 0.0052 0.0189 (0.0360) (0.0670) (0.0290) (0.0681) Railaccess 0.1932 * 0.3796 * 0.1667* 0.1705 (0.0493) (0.0922) (0.0512) (0.0883) HHI 0.1835 0.3811 0.1225 0.2969 (0.1321) (0.2537) (0.1125) (0.2590) Export -0.0109 0.3871 0.1279 0.1772 (0.1166) (0.3423) (0.1463) (0.2618) Medium 0.2338 * 0.5145 * 0.2259* 0.3351* (0.0617) (0.1318) (0.0792) (0.1513) Large 0.4041 * 0.8496 * 0.3854* 0.5149* (0.0577) (0.1272) (0.1036) (0.1496) Rho -11.7928** (0.3875) Lambda -1.8119** -4.7364** (0.1807) (0.2299) Log likelihood -195.3880 -163.2297 -222.6245 R squared 0.3898 Note: Standard errors are shown in parentheses.

* Significant at the 5% level ** Significant at the 1% level

43

FIGURES

Figure 1.1 Isoquant curves and Isocost lines from three different cases

Figure 1.2 Normal Quantile Plot of the ‘Rail’ variable

-.50

.51

1.5

rail

-.5 0 .5 1 1.5Inverse Normal

Prefers rail to truck-barge

Prefers truck-barge to rail

A

C

B

Wheat shipped by rail

Wheat shipped by truck-barge 0

a

a′

x

y

b′

b

44

Figure 1.3 Sample elevators used

Figure

45

Figure 1.4 Sample elevators, railroads, and river ports

46

Figure 1.5 Elevators’ market area and their interaction effects

Total Area: 1.645206

Total Area: 0.065808

Total Area: 0.263232

Almira

Ritzville

Davenport0.065808

0.065808

0.0126620.082096

Davenport50

Davenport10

Almira20

Almira10

Ritzville10

47

APPENDIX APPENDIX 1.1: A DERIVATION OF SPATIAL TOBIT

Let Y is a n x 1 vector of an dependent variable, X is a n x k matrix of explanatory

variables, β is a k x 1 vector of coefficient estimates, W represents a spatial weight matrix, Rho is

a spatial parameter, and ε is a n x 1 error vector.

εβρ ++= XWYY

( ) εβρ +=− XYWI

Then, ⎩⎨⎧ +

=−0

')( ii

iii

xyWI

εβρ

otherwisexif ii 0' >+ εβ

( )dteF tx

iii 2'

21

2

21 −

∞−∫==Φσβ

π

( )( ) 22 2'

2121 σβ

πσφ ix

ii ef −==

where iΦ and iφ represent the distribution function and the density function of the standard

normal evaluated at σβ ix′ .

Prob ( )( )0=− iii yWI ρ = Prob ( )ii x'βε −<

= ( )iF−1

Prob ( )( ) ( ) ( )( )0|0 >−−⋅>− iiiiiiiii yWIyWIfyWI ρρρ = ( )( )i

iiiii F

xyWIfF2,' σβρ −−

= ( )

( ) ( )( )22 '212122

1iiii xyWIe βρσ

πσ−−−

L = ( )( )

( ) ( )( )∏ ∏ −−−−0 1

'21212

22

211 iiii xyWI

i eF βρσ

πσ

48

ln L = ( )( )

( )( ) ( )∑ ∑ ∑ ∑ −+−−−⎟⎟⎠

⎞⎜⎜⎝

⎛+−

0 1 1 1

22212

1ln'2

12

1ln1ln iiiiii xyWIF ρωβρσπσ

First order derivatives:

β∂∂ Lln = ( ) ( )( )∑ ∑ −−+

−−

0 12 '1

1 iiiiiii

i xxyWIxF

fβρ

σ = 0

ρ∂∂ Lln = ( ) ( )[ ] ∑∑

= −−−−′ 260

112 1

'1i i

iiiiiii xyWIyW

ρωω

βρσ

= 0

2

lnσ∂

∂ L = ( )[ ]21

41

20

2 '2

12

11

'2

1 ∑∑∑ −−+−− iiii

i

i xyWIFx

βρσσ

βσ

= 0

Second order derivatives:

ββ ′∂∂∂ Lln2

= ( )

( )∑ ∑ ′+′⎥⎦⎤

⎢⎣⎡ ′−−

−−

0 1222

1111 iiiiiii

i

i xxxxxFfFf

σβ

σ

βρ∂∂∂ Lln2

= ( )∑ ′1

2

1iii xyW

σ

βσ ∂∂∂

2

2 ln L = ( )[ ] iiiiii

i xxyWIF

x ′−−+− ∑∑

14

02 '1

121 βρ

σσ

ρρ ′∂∂∂ Lln2

= ( ) ( )( )∑∑

= −

′+′−

260

12

12 1

1i i

iiiiii yWyW

ρωωω

σ

2

2 lnσρ∂∂

∂ L = ( ) ( )[ ]∑ −−′−1

4 '1iiiiii xyWIyW βρ

σ

22

2 lnσσ ∂∂

∂ L = ( )

( )[ ]21

61

40

224 '12

12

11

'2

1 ∑∑∑ −−−+⎟⎠⎞

⎜⎝⎛ ′

−− iiiiii

i

i xyWIfxFx

βρσσ

βσ

βσ

49

APPENDIX 1.2: A VBA CODE FOR SPATIAL ANALYSIS IN GIS

Sub IntersectBuffer()

'Dim pInput1 As String

'Dim pInput2 As Double

'pInput1 = InputBox("Enter Town Name")

'pInput2 = InputBox("Enter Layer Number")

'Part 1: Create a cursor of a buffer feature

Dim pDoc As IMxDocument

Dim pMap As IMap

Dim pFeatLayer As IFeatureLayer

Dim pActView As IActiveView

Set pDoc = ThisDocument

Set pMap = pDoc.FocusMap

Set pFeatLayer = pMap.Layer(0)

Dim pFeatSel As IFeatureSelection

Dim pFeatSelSet As ISelectionSet

Dim pFeatCur As IFeatureCursor

Dim pQF As IQueryFilter

Set pFeatSel = pFeatLayer

50

'Select buffer

Set pQF = New QueryFilter

pQF.WhereClause = "NAME = 'Bruce'" '" & pInput1 & "'

pFeatSel.SelectFeatures pQF, esriSelectionResultNew, False

'Create a feature cursor of selected town

Set pFeatSelSet = pFeatSel.SelectionSet

pFeatSelSet.Search Nothing, False, pFeatCur

'Part 2: Select other buffers that intersect with the selection

Dim pBuffLayer As IFeatureLayer

Dim pElement As IElement

Dim pBuffSel As IFeatureSelection

Dim pBuff As IFeature

Dim pSF As ISpatialFilter

Set pBuffLayer = pDoc.FocusMap.Layer(1)

Set pBuffSel = pBuffLayer

'Prepare a spatial filter

Set pSF = New SpatialFilter

pSF.SpatialRel = esriSpatialRelIntersects

'Step on the selected buffer and select other buffers

Set pBuff = pFeatCur.NextFeature

51

'Define the geometry of the spatial filter

Set pSF.Geometry = pBuff.Shape

'Select other buffers and add them to the selection set

pBuffSel.SelectFeatures pSF, esriSelectionResultAdd, False

MsgBox pBuffSel.SelectionSet.Count

'Part 3: Draw all selected features and report number of intersect buffers

Dim pBuffSelSet As ISelectionSet

Set pActView = pDoc.FocusMap

'Draw all selected features

pActView.PartialRefresh esriViewGeoSelection, Nothing, Nothing

Set pBuffSelSet = pBuffSel.SelectionSet

MsgBox "There are " & pBuffSelSet.Count & " buffers selected."

End Sub

52

APPENDIX 1.3: GAUSS CODE FOR DOUBLE-CENSORED TOBIT new; cls; library maxlik, pgraph; /* #include maxlik.ext; */ maxset; format/m1/rd 12,8; dat = xlsreadm("freight_demand.xls","c2:u274",1,0); /*load z[260,7] = c:\freight.txt; load z2[260,9] = c:\freight2.txt;*/ cap = dat[.,1]; /*cap = cap/100000;*/ ln_cap = ln(cap); tb_r = dat[.,3]; r_tb = 1/tb_r; ln_ratio = dat[.,4]; ln_ratio2 = ln(r_tb); print; d_acc = dat[.,5]; tb = dat[.,6]; r = dat[.,7]; comsize = dat[.,8]; countyshare = dat[.,9]; withinshare = dat[.,10]; Herf = dat[.,11]; Util = dat[.,13]; Small = dat[.,14]; Med = dat[.,15]; Larg = dat[.,16]; lnY = dat[.,18]; print; Export = dat[.,19]; x = ones(273,1)~ln_ratio2~lny~d_acc~Herf~Export~med~larg; k = cols(x) - 1; df = 273-k; brols = inv(x'x)*x'r; er = r - x*brols; s2 = er'er/df;

53

vb = s2*inv(x'x); sdb1 = (vb[1,1])^0.5; sdb2 = (vb[2,2])^0.5; sdb3 = (vb[3,3])^0.5; sdb4 = (vb[4,4])^0.5; sdb5 = (vb[5,5])^0.5; sdb6 = (vb[6,6])^0.5; sdb7 = (vb[7,7])^0.5; sdb8 = (vb[8,8])^0.5; sdb = sdb1|sdb2|sdb3|sdb4|sdb5|sdb6|sdb7|sdb8; t = brols./sdb; err = r - x*brols; print; print; print err; print ""; print ""; y = r; thetastart = 0.5*ones(9,1); print thetastart; {ThetaHat, CovThetaHat} = Tobit(y, x, thetastart); print ""; print ""; print ""; std1 = sqrt(covthetahat[1,1]); std2 = sqrt(covthetahat[2,2]); std3 = sqrt(covthetahat[3,3]); std4 = sqrt(covthetahat[4,4]); std5 = sqrt(covthetahat[5,5]); std6 = sqrt(covthetahat[6,6]); std7 = sqrt(covthetahat[7,7]); std8 = sqrt(covthetahat[8,8]); std9 = sqrt(covthetahat[9,9]); std = std1|std2|std3|std4|std5|std6|std7|std8|std9; t_theta = thetahat[1:9,.]./std; /* x = ones(273,1)~ln_ratio2~lny~d_acc~Herf~Export~Util~med~larg; */

54

print ; print " Thetahat. t Std."; print " Const " Thetahat[1,.]~t_theta[1,.]~std[1,.]; print " LnRatio " Thetahat[2,.]~t_theta[2,.]~std[2,.]; print " LnY " Thetahat[3,.]~t_theta[3,.]~std[3,.]; print " Access " Thetahat[4,.]~t_theta[4,.]~std[4,.]; print " Herfin " Thetahat[5,.]~t_theta[5,.]~std[5,.]; print " Export " Thetahat[6,.]~t_theta[6,.]~std[6,.]; /* print " Utilize " Thetahat[7,.]~t_theta[7,.]~std[7,.]; */ print " Medium " Thetahat[7,.]~t_theta[7,.]~std[7,.]; print " Large " Thetahat[8,.]~t_theta[8,.]~std[8,.]; print ""; print ""; print " Est. t Std."; print " Const " brols[1,.]~t[1,.]~sdb[1,.]; print " LnRatio " brols[2,.]~t[2,.]~sdb[2,.]; print " LnY " brols[3,.]~t[3,.]~sdb[3,.]; print " Access " brols[4,.]~t[4,.]~sdb[4,.]; print " Herfin " brols[5,.]~t[5,.]~sdb[5,.]; print " Export " brols[6,.]~t[6,.]~sdb[6,.]; /* print " Utilize " brols[7,.]~t[7,.]~sdb[7,.]; */ print " Medium " brols[7,.]~t[7,.]~sdb[7,.]; print " Large " brols[8,.]~t[8,.]~sdb[8,.]; predict = x*thetahat[1:8,.]; dis = y - predict; x = y~x; {thmax,f,g,covmax,ret} = MAXLIK(x,0,&doubletobit,thetastart); call maxprt(thmax,f,g,covmax,ret); end; /* Procedure for the Tobit ML estimation problem */ proc (2) = Tobit(y, x, ThetaStart); local Thetahat, fhat, ghat, recode,covhat,npar; npar = rows(ThetaStart); {Thetahat, fhat, ghat, recode} = QNewton(&NegTobit, ThetaStart); covhat = Hessp(&NegTobit, Thetahat); covhat = inv(covhat);

55

retp(Thetahat, covhat); endp; /* Procedure for the negative log-likelihood function */ proc NegTobit(Theta); local Beta, Sigma, npar, loglik, loglik1, loglik2, work, work1, work2, e, midy; npar = rows(Theta); Beta = Theta[1:npar-1]; Sigma = Theta[npar]; work1 = selif(x*Beta,y.<= 0); loglik1 = sumc(ln(cdfn(-work1/Sigma))); work2 = selif(1 - x*Beta,y.>= 1); loglik2 = sumc(ln(1-cdfn((1-work2)/Sigma))); e = (y.gt 0) .and (y.lt 1); work = selif(y-x*beta,e); midy = selif(y,e); loglik = loglik1 - 0.5*sumc(midy)*ln(2*pi*Sigma*Sigma) - 0.5*sumc((work/Sigma)^2) + loglik2; retp(-loglik); endp; proc doubletobit(b,x); local sigma, npar, ncol, work, work1, work2, loglik, loglik1, loglik2, e, midy; ncol = cols(x); npar = rows(b); sigma = b[npar]; @ make sure sigma is a standard error @ if sigma <= 1e-4; retp(error(0)); endif; work1 = selif(x[.,2:ncol]*b[1:npar-1],y.<= 0); loglik1 = sumc(ln(cdfn(-work1/Sigma))); work2 = selif(1 - x[.,2:ncol]*b[1:npar-1],y.>= 1); loglik2 = sumc(ln(1-cdfn((1-work2)/Sigma))); e = (y.gt 0) .and (y.lt 1); work = selif(y-x[.,2:ncol]*b[1:npar-1],e); midy = selif(y,e); loglik = loglik1 - 0.5*sumc(midy)*ln(2*pi*Sigma*Sigma) - 0.5*sumc((work/Sigma)^2) + loglik2; retp(loglik); endp;

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APPENDIX 1.4: GAUSS CODE FOR SPATIAL ONE-SIDED TOBIT new; cls; library maxlik, ad, pgraph; /* #include maxlik.ext; */ #include ad.sdf; #include maxlik.ext; ad tobit.fct d_1_tobit.fct; maxset; format/m1/rd 12,8; dat = xlsreadm("freight_demand.xls","c2:t274",1,0); dis = xlsreadm("freight_demand.xls","a1:a273",3,0); _max_MaxIters=5000; _max_UserGrad=&gradp4d_2_1; /* _max_Algorithm=4; @ Newton-Raphson method @ _max_LineSearch=4; @ Brent's step length method @ */ cap = dat[.,1]; /*cap = cap/100000;*/ ln_cap = ln(cap); tb_r = dat[.,3]; r_tb = 1/tb_r; ln_ratio = dat[.,4]; ln_ratio2 = ln(r_tb); print; d_acc = dat[.,5]; tb = dat[.,6]; r = dat[.,7]; comsize = dat[.,8]; countyshare = dat[.,9]; withinshare = dat[.,10]; Herf = dat[.,11]; Util = dat[.,13]; Small = dat[.,14]; Med = dat[.,15]; Larg = dat[.,16];

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lnY = dat[.,17]; lnY2 = lnY^2; Export = dat[.,18]; x = ones(273,1)~ln_ratio2~lny~ln_cap~d_acc~Herf~Export~med~larg; k = cols(x) - 1; df = 273-k; print corrx(r~x[.,2:9]); weight1 = xlsreadm("weight 1.xls","b2:es274",1,0); weight12 = xlsreadm("weight 12.xls","b2:dv274",1,0); weight2 = xlsreadm("weight 2.xls","b2:es274",1,0); weight22 = xlsreadm("weight 22.xls","b2:dv274",1,0); H = weight1~weight12; L = weight2~weight22; W = H + L; /* E = sumc(W)~W'; E = delif(E, E[.,1] .<= 0); E = E[.,2:274]'; total = sumc(E')~E~r~x; total = delif(total, total[.,1] .<= 0); W = total[.,2:229]; r = total[.,230]; x = total[.,231:cols(total)]; */ W = lowmat(W); W = W+W'; /* sr = sumc(W'); W = W./sr; */ N = 228; p = 0.05; /*z = zeros(260,1);*/ /*z[2,1] = 1;*/ /*W = toeplitz(z);*/ /*W = W./sumc(W');*/ I = eye(N);

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let beta = -1.391496 -0.4453425 0.0325535 0.5 0.3797491 0.3808798 0.3872518 0.5146162 0.8498102; rho1 = -0.008576; /* rho2 = -0.75; */ sig2 = 0.254193439; sig = sqrt(sig2); y = r; v = y~x; thetastart = beta|rho1|sig2; /* ssq = er'er/(n-cols(x)); */ print ; /* g = gradp4d_2_1(&tobit,thetastart,v); print g; */ {thmax,f,g,covmax,ret} = MAXLIK(v,0,&tobit,thetastart); call maxprt(thmax,f,g,covmax,ret); end; proc tobit(b,x); local m, u, t, y, sigma, npar, ncol, nrow, work, work1, loglik, loglik1, rho1, rho2, sp1, sp2, heck, dw, D; ncol = cols(x); nrow = rows(x); npar = rows(b); rho1 = b[npar-1]; /*rho2 = b[npar-1];*/ sigma = sqrt(b[npar]); @ make sure sigma is a standard error @ b = b[1:npar-2]; if sigma <= 1e-4; retp(error(0)); endif; y = x[.,1]; x = x[.,2:ncol]; sp1 = (eye(nrow) - rho1*W); /* sp2 = (eye(nrow) - rho2*NW); */ heck = (sigma^2)*invswp(sp1)*invswp(sp1)';

59

D = diagrv(eye(nrow),1./(diag(heck))^0.5); m = D*invswp(sp1)*x*b; u = D*y./=0; /* work1 = selif(x*b,y.<= 0); loglik1 = sumc(ln(cdfn(-work1/Sigma))); work = selif(y-x*b,y.>0); loglik = loglik1 - 0.5*sumc(y)*ln(2*pi*Sigma*Sigma) - 0.5*sumc((work/Sigma)^2); */ t = y - m; loglik = u.*(lnpdfmvn(t,sigma^2)) + (1-u).*(ln(cdfnc(m/sigma))); retp(loglik); endp; proc(1) = gradp4d_2_1(f,xin,y); local f:proc; local n,k,grdd,dh,ax0,xdh,arg,dax0,i,f0; local no_dim4; // debugging /* check for complex input */ if iscplx(xin); if hasimag(xin); errorlog "ERROR: Not implemented for complex matrices."; end; else; xin = real(xin); endif; endif; f0 = f(xin,y); no_dim4 = cols(f0); // how many extra outputs n = rows(f0); k = rows(xin); local dim3, dim4, x0, xarg, ans3d, ans4d, ftmp; dim4 = 0; do while(dim4 < no_dim4); dim4 = dim4 +1; dim3 = 0; do while(dim3 < cols(xin)); dim3 = dim3 +1; x0 = xin[.,dim3]; grdd = zeros(n,k);

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/* Computation of stepsize (dh) for gradient */ ax0 = abs(x0); if x0 /= 0; dax0 = x0./ax0; else; dax0 = 1; endif; dh = (1e-8)*maxc((ax0~(1e-2)*ones(rows(x0),1))').*dax0; xdh = x0+dh; dh = xdh-x0; /* This increases precision slightly */ arg = diagrv(reshape(x0,k,k)',xdh); i = 1; do until i > k; xarg = xin; xarg[.,dim3] = arg[.,i]; ftmp = f(xarg,y); grdd[.,i] = ftmp[.,dim4]; i = i+1; endo; grdd = (grdd-f0[.,dim4])./(dh'); if (dim3 == 1); ans3d = grdd; else; ans3d = aconcat(ans3d,grdd,3); endif; endo; if (dim4 == 1); ans4d = ans3d; else; ans4d = aconcat(ans4d,ans3d,4); endif; endo; retp(ans4d); endp;

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CHAPTER 2

IMPACTS OF IDENTITY PRESERVED WHEAT SHIPMENTS

ON GRAIN TRANSPORTATION IN WASHINGTON

Abstract

This chapter examines the effects of Identity Preserved (IP) system on grain

transportation in Washington by applying General Algebraic Modeling System (GAMS). I

develop linear programming optimization models representing three scenarios, which are the

current bulk grain transportation, the IP or containerized grain transportation and the IP system

including extra material costs. The results indicate a significant change in wheat flows as a result

of the IP system. The higher containerized transportation rates and the prohibition of

transshipment contribute to the rising transportation costs. In addition, the sensitivity analysis of

the discounted containerized rail rate identifies a spatial competition between the rail mode and

the truck-barge mode.

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1. Introduction

The growth of the Identity Preserved (IP) grain market over the last decade has caused

changes in components of the grain logistic system. Traditionally, elevators move of grains in

bulk shipments, but with IP grain, multi-location elevator companies store only one type of grain

in an elevator or elevator section and ship different type of grains in different containers. A

contributing motivation for IP market development comes from a growing concern of consumers

in many parts of the world on Genetically Modified Organisms (GMOs) contamination. In

Japan, for example, the government had to reject the entire shipment of the U.S. corn

contaminated with the genetically modified StarLink corn in 2000, in order to satisfy Japanese

consumer groups’ pressure. Thus, because of health awareness, consumers and buyers always

prefer a better distribution system with documentable segregation and identity preservation of

non-genetically modified grain from genetically modified grain.

The IP system also supports the idea of differentiating grain for each specific end-use by

the buyer. Each IP grain shipment is loaded inside a container and treated as a different

commodity in an attempt to prevent the risks of co-mingling different types of grains.

Consequently, the volume of each IP shipment is limited by the size of a container, which carries

about 330 bushels (approximately 20,000 lbs) for a twenty-foot unit equivalent (TEU) container,

or only 660 bushels for a forty-foot unit equivalent (FEU) container. This can be contrasted to

the jumbo hopper railcar, which can move approximately 3,500 bushels of a bulky grain

shipment.

The successful IP grain or containerized grain system requires a strict segregation at

every point in the grain supply chain, i.e. farms, elevators, processors, and food manufacturing

levels. Adopting strict segregation practices at an elevator imposes higher cost and extra work

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such as cleaning facilities and equipment for the receiving of alternative types of grains. Baumel

and McVey (2001) suggested that the multi-location elevator firms are able to reduce the

segregation costs by dedicating an elevator to store only one type/grade of grain. This

arrangement includes prohibition of transshipping grain among elevators, which can affect the

multi-location elevator firms’ cost experience directly.

Adoption of the containerized grain system can result in several significant changes in the

grain transportation industry, including the prohibition of the transshipment option. The current

bulk system allows multi-location elevator companies to transship grain from branch or satellite

elevators in order to collect a larger grain pool at sub-terminal elevators with rail access as the

option to minimize the transportation costs. To do so, they consider whether the trucking costs

plus the received rail rate at the sub-terminal is lower than the cost of shipping grain directly to

the market using other alternative modes. Usually, when elevators move a large volume of grain

by the rail mode (i.e. 350,000 bushels on a unit train), there is a high probability of receiving a

lower rail rate. Consequently, the transshipment option highlights the economies of scale

concept in grain transportation, especially in the rail mode. Without the transshipment option,

shipping grain under the IP system is expected to be more expensive than moving grain under the

bulk system.

Even though the segregation system is necessary to the growth of the IP market, the

segregation system is currently limited in Washington State because the system is expensive and

no one wants to pay for it.1 Information on the cost structure is required in order to assist the

industry to decide whether the new technology is possible. The transportation cost estimation

under the IP system would assist the grain transportation industry to better understand the

1 IMPACT Center E-News, http://impact.wsu.edu/newsletter_blog/pdf/feb2006/DemandForaSegration.pdf February 2006

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changes due to the containerized system and determine the premium in the market needed to

cover the increased costs.

In this study, we evaluate the impact of the IP system by quantifying the impact on the

cost of wheat transportation in Washington. This paper is the first attempt to measure impacts of

the IP system on the costs of Washington grain distribution system from elevators to the export

market. This paper is organized as follows. The next section presents the grain transportation

background. Section 3 explores available literature on IP grain studies and the demand and

optimization technique. Section 4 discusses data and methodology. Section 5 reports results

from different scenarios, and the final section offers some conclusions.

2. Background

2.1 Identity Preserved Grain

The Identity Preservation (IP) system is relatively a new method of transporting grain

from farms to end-users. The system is primarily designed to keep a certain grain product away

from being contaminated by undesirable substances (such as genetically modified organisms or

GMOs, pesticide, or other chemical materials), co-mingling with different qualities/grades grain,

or decreases in value (due to the weather and other environmental factors). Typically, a

shipment of IP grain is moved in a container, either 20-foot or 40-foot sizes, which satisfies all

requirements as mentioned above. The undesirable contamination, especially GMOs, is one of

the major concerns in grain transportation. Many grain-imported countries, such as Japan and

European Union countries, require imposing a very low tolerance rate of 5% and 1%,

respectively. Recently, Japanese consumers have placed more pressure on their government to

lower the tolerance rate to 1% as is the European Union’s (Matsumoto, 2004).

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Under the IP system, a sealed container cargo ensures that there is no contamination at

any point during the delivery. Moreover, since consumers have been aware of their health and

food consumption, food processors are required by the market to respond to the healthy

consumption trend. A number of food processors order specific qualities and agree to pay

premium prices for a specific quality (Peterson and Ross, 2002). Co-mingling among different

qualities/grades, which results in the lost of any IP premium, can be avoided under the IP system

by following segregation rules at different points in the grain supply chain. Finally, weather is a

major result in a decline in bulk grain quality. Moisture level and protein content inside grain

might be affected due to the change in temperature during the delivery. As Reichert and Vachal

(2003) found, a sealed container acts as storage anywhere along the transportation route, and

therefore the weather factor cannot lower the quality of grain inside the shipment under the IP

system.

Although the containerized grain offers several advantages over the bulk grain in terms of

the grain quality fortification, the disadvantage of the containerized grain is that the cost of using

container cargos can be quite expensive compared to movement by bulk. Also, due to the

product-specific nature, a small volume containerized grain movement does not allow shippers to

take advantage of economies of scale feature as is in bulk grain movements. Moreover,

segregation rules require training for all involving parties in the supply chain in order to

understand new practices; such training entails costs.

The American Soybean Association (ASA)’s background for the production and the

transportation of identity preserved grain can be summarized as follows.2 First, growers produce

IP crops on an individual contract, which specifies variety and premium. Next, farm activities

such as growing, storing, and harvesting for specified varieties are performed separately from 2 http://www.food.gov.uk/multimedia/pdfs/ paperfsa021103ann2a.pdf

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other unspecified varieties. At this step, buyers often provide their own seeds. Unlike the bulk

grain production, buyers participate more closely in the IP production process. Later, farmers

transfer the IP product to bags or sealed containers in order to maintain separate distribution lines

of the specified products. Elevators must grade and handle the IP product by using special

procedures and store them in separate bins, containers or silos.

During the trans-oceanic trip, the IP shipments have to be loaded onto container ships

into separate holds or compartments and stored completely separated from other shipments.

When the IP shipments arrive at ports of destination, the distribution of the IP product from the

port of entry to customers can be by coastal vessel, barge, truck or railroad, while still maintains

separation from other crops throughout the movement. Last, customers store the IP deliveries in

separate dedicated storage, and process specific varieties using separate batch lines in order to

distribute to retailers.

2.2 Grain Transportation

The decision to ship grain from elevators to an export market made by elevator managers

is complicated because it depends on several factors such as transportation mode choices,

location, and volumes. Tolliver (1994) reviewed the grain supply chain in the U.S. In general,

elevator managers strive to minimize the grain distribution cost, especially on the transportation

cost by choosing the lowest cost transportation option. In Washington, there are three major

transportation options available to elevator managers, railroad, truck-barge, and transshipment

among elevators. All elevators can ship grain by using the truck-barge mode, but only elevators

with rail access can transportation grain by railroad. Transshipping grain is usually available

only for elevators under the multi-location elevator company.

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The cost of using the truck-barge mode depends on trucking rates/costs and barge rates.

Trucking costs depend significantly on the distance from an elevator to a destination facility. An

elevator manager can choose either an upstream port, closer to the elevator or a downstream port,

farther from the elevator. Typically, a barge rate charged by the upstream port is more expensive

than a rate charged at the downstream location. At the same time, using the distant downstream

port could be costly comparing to the nearby upstream one because of the expensive trucking

costs. Therefore, managers must simultaneously take both costs into consideration in choosing a

river port.

Rail rates are the main expenditure determining the costs of using rails because grain at

an elevator with rail facilities is uploaded onto railcars at the originating location. Rail rates for

each elevator are different primarily depending on the amount of grain to be shipped by rail and

distance to destination. A larger volume or shorter distance implies a higher chance of receiving

lower rail rates.

Transshipment, which is a significant source of economies of scale in the grain

transportation, is available only to the multi-location elevator firms. Normally, in Washington a

firm owns several elevators, some with rail access and some without or some with capacity to

handle only small number of cars. Elevators with rail access are sub-terminal elevators, while

elevators without good rail access are satellite elevators. Satellite elevators collect grains from

nearby areas and transship them to sub-terminal elevators if the cost of transshipment is lower

than shipping grains to markets directly. Sub-terminal elevators, obtaining a higher amount of

grain from satellite elevators, are more likely to receive a lower rail rate (multiple-car, unit trains,

etc.) making the transshipment option attractive.3 Without transshipment, managers at sub-

3 Generally, the grain that is stored at a satellite elevator is transshipped through the sub-terminal as opposed to being shipped directly to the terminal market if the transshipment cost is lower. That is, when the sum of the grain

68

terminal elevators do not get the volume to take good advantage of the lower rate, while

managers at satellite elevators just ship grains to the market directly.

To sum up, Washington grain transportation consists of three major modes of

transportation. A manager at a single-location elevator firm with rail access determines whether

to ship grain by the rail mode or the truck-barge mode. A manager at a single-location elevator

firm (without rail access) has only two options: truck-barge or transshipment. Managers at sub-

terminal elevator ship grains by either rail or truck-barge, while managers at satellite elevators

choose either transshipping grains to one of the sub-terminal elevators or to markets directly by

truck-barge or smaller rail shipments.

3. Literature Review

3.1. IP Grain Studies

In the U.S., where used, Identity Preserved (IP) grain has changed grain logistic and

supply chain procedures significantly. Economically, IP products are viewed as product

differentiated since each IP shipment is treated as a different product for the use of a specific

purpose due to its selected attributes, such as protein content, moisture level, and fiber

components. Consequently, each shipment with a specific grade requires segregating from other

grades for the entire logistic procedure. Containerization has become an alternative for grain

logistic under the IP system, rather than the traditionally bulk shipment.

The containerized grain with unique qualities has reported receiving a price higher than

that of bulk grain. Tirole (1988) pointed out that a price of a differentiated product at the level

above its marginal cost could be sustained because of the low cross-elasticity. Therefore, the

trucking rate to the sub-terminal, the additional cost of handling the grain at the facility, and the outbound elevator rate is less than the transportation rate from the satellite elevator to the market, the commodity should be transshipped.

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premium between the bulk grain and the containerized grain exists. Vachal, VanWechal, and

Reichert (2003) reported containerized grain premiums received by shippers. These premiums

varied from commodity to commodity; for example, containerized soybean-export received an

average premium of $4.60 per hundredweight or $2.75 per bushel above the local market price

and the containerized pulse-export received an average premium of $1.10 per hundredweight. In

addition, Bullock, Desquilbet, and Nitsi (2000) investigated premiums for non-GMO soybeans

futures, identified as identity preserved soybean, in Tokyo Grain Exchange (TGE). The study

found that the average premium for future non-GMO soybeans at the TGE between December

2000 and August 2001 was approximately $17.66 per ton or 8.5 percent higher than the U.S.

soybean future. Moreover, Gloy, and Dooley (2003) investigated effects of identity preserved

premiums, received from 2003 Value Project by the University of Illinois, on elevator grain

flows by using stochastic simulation across the harvest season. They found IP premiums for

nutritionally dense corn were $0.22 per bushel, followed by $0.10, $0.90 and $1.45 per bushel

for white corn, high protein soybeans and tofu soybeans, respectively.

While others paid attention on premiums received from selling differentiated products,

Hurburgh (2003) focused on the certification procedure, which has been the most crucial step in

the IP distribution system for distinguishing IP products from bulk commodities. The analysis

discussed Source Verification (SV), which allows end users to trace products from their initial

components through a production and distribution system. The SV is a part of Quality

Management Systems (QMS) and was introduced in order to respond to consumers’ concerns on

food safety, biotechnology, environmental and social values.

The adoption of the IP system has brought changes to the cost structure in the grain

distribution system due to the introduction of new handling practices. Several studies focused on

70

identifying cost items in the IP grain logistic, both actual and hidden costs. Maltsbarger and

Kalaitzandonakes (2000), focusing on elevator operation costs, found that opportunity costs from

under-utilized storage, lost grind margin and spread opportunity play a significant proportion in

the operation costs. The study employed the Process & Economic Simulation of IP (PRESIP)

simulation model to estimate elevator operation costs, assuming parameters and coefficients for

Missouri and Illinois elevators. They also identified segregation costs, which included sample

analysis cost, misgrades, maintenance, disputes/labor and others, and revealed that the sample

analysis cost was the largest part in the segregation costs. Baumel and McVey (2001) argued

that the study by Maltsbarger and Kalaitzandonakes (2000) did not take risk costs into

consideration. Therefore, they incorporated risk costs, along with opportunity costs as the hidden

costs, into the segregation costs of the IP production and distribution system. They primarily

discussed segregation costs throughout the entire grain logistic process, which consists of

farmers, elevators, processors, exports and handlers. Such risk costs could be a result of volume

mismatch, quality deviation, and non-IP contamination.

Since the containerization has become one of the important parts for the IP distribution

system, the identification of container handling and transportation costs is necessary for

successful IP costs estimation. Kosior, Prentice, and Vido (2002) provided a logistical costs

comparison between IP and bulk systems based on different scenarios from Canadian

experiences. The results varied from one scenario to another due to different milling rates.

Moreover, the study reported that the cost of elevation, the container loadout, and Free on Board

(FOB) charges were $13.58 per ton and the drayage to intermodal terminal was $3.62 per ton.

Reichert and Vachal (2003) investigated monetary costs of the IP system compared to the bulk

system. The study identified different cost items of the IP distribution, such as storage, handling

71

and transportation. The results showed that the in-land/ocean freight rate of a 20 feet container

of soybeans shipment originating from an Iowa farm to Japan was $60 per trip. The quoted cost

was based on an industry rate and was the comprehensive freight rate offered by shipping lines

and third party providers. In addition, the inland drayage is $0.05 per ton-mile and the marketing

costs are $8.00 per hour. The study also pointed out that the grain can be either loaded directly

on the top of a canvas-topped container or by using container liners (or bags). The liners’ prices

range from $225-$350 and add about 150 pound to the weight.

The growth of the IP market is determined by several factors (Vachal, VanWechal, and

Reichert, 2003). The study surveyed 47 container shippers from 19 states and covering 13

commodities, allowing ranking of factors determining the IP market growth factors. The ocean

shipping rates for containers is the most important factor determining a success in IP products,

followed by the availability of containers, and the rail shipping rates, respectively. The ocean

freight rate by containers for the grain delivery is expensive compared to bulk shipment, which is

the obvious reason for the continuing dominant role of bulk grain shipments. Considering

container availability, Kosior, Prentice and Vido (2002), as well as Vachal and Reichert (2002),

indicated that both Canada and the United States have experienced imbalanced trade on the

Trans-Pacific corridor, where there are more of the containerized imports than the containerized

exports, resulting in a large amount of empty containers sitting at the west coast ports or interior

markets.4 In addition, both studies suggested that empty containers sitting at the ports could be

an opportunity for IP products to grow further. In order to avoid moving empty containers back

to Asia, ocean liners do charge reduced container rates to commodity moving west including IP

4 Also, Sam Ruda, the director of the Port of Portland, has confirmed this incident according to his testimony before the U.S.-China Economic and Security Review Commission on January 13th, 2005. He reported that for every three imported containers moving to the United States from Asia, there is only one full exported container.

72

exporters, which would potentially increase containerized grain competitiveness with the bulk

grain.

3.2. Grain Transportation Studies

The demand for freight transportation has been studied for more than three decades.

Traditionally, it is derived from the demand for commodity. Oum (1979), Friedlaender and

Spady (1980), and Vickerman (2003) among others suggested that freight transportation should

be treated analytically like other factors of production because the demand for freight

transportation is more complex than an ordinary derived demand model. Usually, a firm jointly

determines transportation rates and shipment characteristics that affect inventory costs, e.g.,

length of haul, size of shipment (Friedlaender and Spady, 1980). Therefore, the freight demand

model can be represented in terms of rates in combination with the relevant shipment

characteristics.

A decision-making process in freight transportation like grain logistics is complicated. In

order to ship grains from elevators to markets, elevator managers take several factors into

consideration such as transportation rates, trucking costs, and availability of transportation

modes. A deterministic optimization model has been developed to solve the agricultural

transportation problems in the United States with the aim of improving the efficiency of the grain

distribution system (Koo and Larson, 1985).

One of the deterministic models is the Interregional model, which is applied to optimize

freight flows between producing region and consuming region. The model is represented by a

system of equations, either linear, non-linear or both, which correspond to an objective function

and constraints. Several studies on grain transportation, Koo (1985); Koo, Thompson and

Larson (1985 and 1988) and Jessup (1998) for example, applied mathematical programming

73

based on the Interregional model to evaluate impacts of changes in exogenous factors on a grain

distribution system.

The interregional model can be categorized into a linear and a nonlinear programming

model, in which each model has its own advantage over the other. Because commodity prices

and other exogenous factors, such as transportation rates, regulations, technologies and market

conditions, affect commodity flows differently, the analysis of each of their impacts are not the

same. Koo (1985) applied a quadratic programming interregional model to analyze the impact of

an increase in import tariffs in oversea markets which changes commodity import prices on the

U.S. grain export flows.

In addition to a nonlinear programming model, several studies apply a linear

programming interregional model to assess impacts of a change in transportation rates,

regulations and market conditions in which they do not affect quantity demanded and quantity

supplied. Koo, Thompson and Larson (1985) used a linear programming model to evaluate

impacts of capacity constraints in the U.S. grain distribution system, considering both rail and

barge transportation, on spatial grain flows. Also, the same authors (1988) evaluated impacts of

changes in ocean freight rates on the U.S. grain distribution system with an application of a

linear programming. Moreover, Jessup (1998) utilized a linear programming model to assess

effects of the dam drawdown to protect salmon in the Columbia-Snake River on grain flows in

Washington.

In terms of the transshipment model, literature on this issue is commonly found in the

Operations Research area (Hillier and Lieberman 2005, and Lee, Moore, and Taylor 1990).

Tolliver (1994) provides an informative explanation of the transshipment model in the context of

grain transportation.

74

4. Optimization model

A linear programming cost-minimization model was utilized to reflect elevator managers’

decisions on transportation mode choices. Truck-barges and railcars represent the factor of

production for elevators in order to provide grain logistic services to customers. In this model,

elevator managers search for the lowest total transportation mode in order to ship wheat from

elevators to export terminals in Portland, Oregon.

We impose four assumptions regarding the wheat distribution system. First, we

anticipate that the IP shipment may be smaller than the current bulk system in which the bulk

system does not handle the IP products (Reichert and Vachal, 2003). Therefore, only the small

trains (the 26-railcar type) are included in this model because the total volume of IP products is

less likely to fill up the 52-railcar type.5 Second, the study does not impose capacity constraints

on the linear programming model because a sub-terminal elevator can store transshipped wheat

either, in the Pacific Northwest, inside its facility or as outdoor storage. Third, grain stored at

satellite elevators is transshipped to sub-terminal elevators within the same company, implying

that there is no transshipment across companies, reflecting the large cooperatives in the stole.

Fourth, the model evaluates only the shipment of wheat to the export market because wheat is

the main export product of Washington.

We apply an optimization procedure using General Algebraic Modeling System (GAMS)

to analyze a linear programming model. The objective function of the model is to of minimize

total transportation costs while moving a known amount of quantities of wheat from elevators to

their destinations. Therefore, the objective function can be expressed mathematically as the

following:

5 Rail companies generally provide at least two types of freight trains; the large trains (52-railcar or more) and the small trains (26-railcars).

75

Min ( )[ ]∑∑∑= = =

=n

i

m

j kijkijk XCTC

1 1

2

1

Where:

TC = Total transportation and handling costs

Cijk = Transportation and handling charges for shipping wheat from

the ith origin to the jth destination on mode k

Xijk = Decision variables representing wheat flow from the

the ith origin to the jth destination on mode k

i = Origin points (i = 1,…, n)

j = Destination points (j = 1,…, l, l+1,…, m)

k = Mode of transportation (truck-barge or rail26)

The model also assume a fixed amount of quantity demanded and quantity supplied in

both producing and consuming regions, which satisfies the spatial equilibrium condition in the

study area.6 This implies that commodity prices are fixed. An unconstrained optimization

system identifies the origin points and the quantities to be shipped, the collection of possible

routes on various modes, the cost associated with each route option, and the final destinations.

Consequently, it allows the linear programming to solve for the minimum cost solution.

In order to evaluate impacts on transportation modes from the IP system, we impose three

scenarios of transportation to mimic a real situation, which are 1) the traditional grain

transportation with transshipment among elevators, 2) the IP grain transportation without

6 Hence, the solution obtained from the model cannot be viewed as a global optimal solution, but a conditional optimal solution under predetermined demand and supply conditions (Koo and Larson, 1985).

76

transshipment, and 3) the IP grain transportation without transshipment with handling costs such

as packaging and labor expenses.

5. Data and Assumptions

5.1 Data

The majority of the data for this study are collected from Clark, Jessup and Casavant

(2003), which reported on a survey of Washington grain elevators in 2002. The survey included

grain transportation data such as rail rates, barge rates, modal split and rail facilities/ river ports

used. Of 394 licensed elevators, 386 elevators responded to the survey.

Since the IP system does not allow transshipment among elevators, which affects

elevators from multi-location elevator firms directly (Baumel and McVey, 2001), we include 10

multi-location elevator companies in this study in an attempt to evaluate changes in

transportation costs and patterns of grain flows before and after adopting the IP system. The

selected 10 multi-location elevator firms own 225 elevators located in eleven counties.7 After

screening out observations with missing data, 213 of the elevators are left in this study. These

sample elevators received 56,259,784 bushels of wheat or approximately 45 percent of the total

received volume, in 2002.

Almost 70% of the elevators in this study are located in Whitman , Lincoln , and Adams

counties while only three elevators (1.4%) are located in Chelan, Okanogan, and Stevens

counties (Table 1). The average capacity of the sample is 445,000 bushels. The capacity of

sample elevators ranges from 10,000 bushels to 3,003,000 bushels. The largest elevator is in

Columbia County, while the smallest is in Douglas County. The elevator with the largest

7 Eleven counties in Washington include Adams, Chelan, Columbia, Douglas, Franklin, Grant, Lincoln, Okanogan, Spokane, Stevens, and Whitman.

77

volume of wheat received is located in Whitman County, receiving 3,600 thousands bushels,

whereas the elevator receiving the smallest amount of wheat is in Spokane County (3,000

bushels). Overall, all sample elevators utilize only approximately 73% of their total capacity.8

Selected multi-location elevator firms, mostly cooperatives, own elevators all over

eastern Washington. The summary statistics of sample elevators categorized by multi-location

elevator firms in 2002 are reported in Table 2. In terms of the number of elevators owned by the

firms, the largest firm possesses 43 elevators while the smallest firm owns nine elevators. In

terms of total capacity, the largest company operates with the total capacity of 18,127,000

bushels, and this firm is also the largest in terms of wheat volume received (12,169,000

bushels).

5.2 Cost Assumptions

The cost structure of wheat transportation is composed of modal transportation costs and

handling/loading-out costs involved with the inland and ocean transportation services. Under the

bulk system, both services are charged separately from different service providers. However,

they could be jointly charged by a single service provider under the containerized system. Both

transportation and handling/ loading-out cost parameters in this study were collected from

several sources.

The transportation costs of the rail mode and the truck-barge mode vary by areas. This

study utilizes rail rates and barge rates, for bulk commodities, at different locations in Clark,

Jessup and Casavant (2003). The trucking costs (per bushel mile) are estimated by following the

trucking cost equation in Jessup (1998).9 By applying Geographic Information System (GIS), we

are able to find the distance parameter measuring the shortest path from an elevator to a river 8 The average utilization rate is the ratio of average wheat received to average capacity. 9 Trucking Cost per bushel Mile = ( ) ⎟

⎠⎞

⎜⎝⎛++

milesmiles 151866.0*001911.0036018.0

78

port. Rail rates and barge rates for the bulk system used in this study are reported in Table 3. The

barge rates range from $0.15 per bushel at Port of Pasco to $0.20 per bushel at Port of Wilma,

while the rail rates range from $0.28 to $0.65 per bushel. The estimated total truck-barge rates

range from $0.15 to $1.00 per bushel. The range of the truck-barge rate is wider than the rail rate

because of a large variation in distance to river ports.

Handling/loading-out costs and the ocean freight rate for bulk grain were collected from

Reichert and Vachal (2003). They suggest that the handling costs for the rail mode and the

truck-barge mode are $0.12, and $0.04 per bushel, respectively, while the ocean freight rate is

$0.35 per bushel.

The survey of containerized grain shippers by Vachal, VanWechel and Reichert (2003)

pointed out that the three most important factors for the growth of the IP market were ocean

shipping rates for container, rail shipping rates for containers, and an availability of containers.

The study also indicated that the most common packaging pattern among containerized grain

exporters is to fill grain into small bulk bags before loading the bags into a container. The

maximum capacity of each grain bag is 2,000 lbs. Since shippers are most heavily concerned

with transportation rates, assumptions on the containerized transportation rates are carefully

made later in this section. The third factor reflected a concern on availability of containers. We

assume that containers are always available because of a new container service called

‘RailRunner’, which can provide containers to anywhere with road access. The business has

received a permanent approval from the Federal Railroad Administration since March 2005. In

any cases, eastbound containers have always been available in recent years.

The rest of this section focuses on containerized transportation rates (Table 3). The

ocean freight rates for containerized grain were collected from the USDA/AMS Ocean Rate

79

Bulletin, which estimates the cost of moving containerized soybeans to Yokohama, Japan, from

Seattle, WA.10 In this study, we assume that the costs of moving containerized soybeans and the

containerized wheat are not significantly different. An annual average of the quoted container

rate in 2002 was $1,446 per Twenty-foot Equivalent Unit (TEU).11 It is worth noting that the

quoted container rates are publicly filed tariff rates and are typically about 20 percent higher than

the negotiated service contract rates. The rates are considered as “port-to-port” rates and do not

include the inland transportation cost. The 20 percent discounted container rate can be converted

to approximately $3.50 per bushel.12

We use the estimation rates of inland containerized rail shipment by HDR Engineering

Inc. in 2000 (quoted in Kratochvil, 2005) which is $550 per Forty-foot Equivalent Unit (FEU)

moving from Lewiston to Portland and to Seattle.13 The rail shipment rate is considered as the

upper bound of the containerized grain scenario. The capacity of a 40ft. container is twice as

large as a 20ft. container’s capacity. Therefore, the maximum capacity of a 40ft. container is

equivalent to 20 bags of 2,000-lbs, or 40,000 lbs (or nearly 660 bushels). However, in reality, IP

shipments may not be able to utilize the maximum capacity regularly. We assume that only a

half of the maximum capacity is filled or equivalent to 330 bushels. Accordingly, the estimated

containerized rail rate is $1.67 per bushel.

The barge rates for moving a 20 ft. container from Lewiston (ID)/Wilma (WA)/

Clarkston (WA) and from Pasco (WA) to Portland (OR) are based on the quoted rates from

Tidewater and Foss Maritime, the two main bargelines on the river. Container rates at Pasco and

10 http://www.ams.usda.gov/tmd/Ocean/Index.asp 11 TEU is a measurement of a container’s capacity. 12 William Logan, Director of Material Handling FELLFAB Limited, estimated using 10 bags of 2,000lb-bag to carry 20,000 lbs of grain in a 20ft. container, or equivalent to 330 bushels per container (Prentice, Duncan, and Sokol, 2004). 13 Two TEU containers equal to one FEU container.

80

at Lewiston/Wilma/Clarkston are quoted at $85 and $120 per TEU, $0.26 and $0.36 per bushel,

respectively. The barge rates for a containerized shipment at the river ports between Port of

Pasco and Port of Wilma are assumed to be equal to an average rate at both ports. The

containerized handling/loading-out cost, from Kosior, Prentice, and Vido (2002), is $0.22 per

bushel.

In order to calculate the containerized truck rates, we obtained the trucking cost from

Lewiston (ID) to Portland (OR), $700 per FEU, from HDR Engineering Inc. The distance from

Lewiston to Portland is approximately 350 miles, resulting in $2 per mile per FEU. Since the

actual trucking costs should reflect both directions of truck movements, i.e. Lewiston-to-Portland

and Portland-to-Lewiston, the trucking rate is estimated at $4 per miles per FEU. The container

utilization assumption is the same as for the rail rate, therefore elevators can utilize only a half of

one FEU or only 330 bushels. The trucking rate is therefore converted into a flat rate of $0.012

per bushel mile.

The last IP grain cost component is the cost of extra materials required for containerized

grain shipments. A common practice among containerized grain shippers is to fill selected grain

in small bulk bags before loading them into a container. Alternatively, a shipper installs only a

large container liner (one large bag) into the container. We initially assume that the shipper uses

ten 2000 lb-bags to hold IP grain inside a 20ft. container. Each bag roughly costs $25 per piece,

so the total cost of additional materials is $250. On the other hand, if the shipper installs a

container liner inside the container, it costs $225-$350 per piece, or approximately $290 per

piece. The assumption on the extra materials is applied to the third scenario of this study.

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6. Model results

The analytical results of the impacts of shifting grain transportation from bulk shipment

to moving grain in a container are reported in Table 4. The shift in technology affects several

aspects in grain transportation, i.e. the direction of grain flows and the transportation costs.

a. Grain flows:

The wheat flows and transportation costs from the bulk scenario and the IP scenario are

reported in Table 4. Under the current bulk system represented by the first scenario, the selected

companies ship wheat by the rail mode to the export terminal in Portland, due to the advantages

of rail access availability and the cost-minimizing transshipment among their elevators.

Approximately 55% of the wheat volume in this study is shipped by the rail mode, while nearly

45% is shipped by the truck-barge combination. In addition, bulk system results also show that

about 13% of the wheat volume in this study is transshipped among elevators of the selected

companies in order to decrease costs.

The results from the Identity Preserved scenario, which prohibits transshipment among

elevators and uses only the containerized system to ship grain, are displayed in Table 4 and

Figure 4. The flows of wheat have been significantly altered from the previous scenario.

Around 90% of the wheat volume is shipped by the truck-barge combination, while only 10% is

left to be shipped by the rail mode. One of the reasons is the costly containerized rail rate

relative to the containerized barge rates. The containerized rail rate is assumed to be a flat rate

across the region, denoting the upper bound for the analysis. Later, we examine further the

impacts of changes in the rail rate by using the sensitivity analysis.

The sensitivity analysis assumes discounts of 5% and 10% in the rail rate. The 5%

discounted rail rate results in an additional 15-percentage point in grain volume moved by the

82

rail mode. Consequently, 20% of the total wheat volume is shipped by rail. Alternatively, the

10% discounted rail rate increases the demand for rail transportation to ship grain by nearly 20-

percentage points relative to the non-discount setting. The results from the sensitivity analysis

suggest a diminishing response in the marginal wheat volume to be shipped by the rail mode.

The diminishing rate implies that a further decrease in the rail rate might not be profitable

enough for other elevators to switch from shipping grain by the truck-barge combination to

shipping grain by the rail mode. Economically, the rail mode might not be a good substitute for

the truck-barge mode at some areas unless the rail rate is much lower than the truck-barge

combination.

In terms of the grain flows to river ports, Table 5 shows that Port of Almota receives the

largest grain flows of around 11 million bushels under the current bulk system, while the Port of

Pasco receives the smallest flows of wheat of roughly 0.63 million bushels. After the IP system

is applied, the flows of grain to the river ports are changed significantly. There is not any grain

shipment moved to Port of Wilma under the containerized grain scenario in contrast to

approximately one million bushels under the bulk system scenario. The grain flow to Port of

Pasco under the IP scenario is 12 times higher than the flow it receives under the bulk system. In

addition, Port of Windust receives the largest grain flows of 24.6 million bushels, whereas

Central Ferry receives only 0.9 million bushels.

The sensitivity analysis shows the impacts of a change in the containerized rail rate on

the demand for truck-barge transportation. Port of Windust is mostly affected by the change

followed by Port of Pasco and Lyons Ferry, while Central Ferry, Port of Almota and Port of

Wilma are not affected. The 5% discounted rail rate results in a decrease of grain flows to Port

of Windust by seven million bushels, or about 29% reduction. In addition, the 10% discounted

83

rail rate causes a decline in grain flows to Port of Windust by 9.4 million bushels, or 38% lower

than the non-discount rail rate setting. Port of Pasco and Lyons Ferry are also affected by the

discounted rates, but with a less significant degree. Port of Pasco receives around one million

bushels less when the rail rate is discounted at either 5% or 10%. Grain flows to Lyons Ferry are

reduced by 0.4 and 0.57 million bushels when the rail rate is discounted at 5% and 10%,

respectively. It can be seen that the impacts of the discounted rail rates are exhibited in an area

surrounding Port of Windust and its neighbor, see Figure 3 and Figure 5. On the other hand, the

region far away from Port of Windust is not affected by the discount rate. The elevators in the

region above Port of Windust, such as Grant, Douglas, and Lincoln Counties, are sensitive to the

change of the containerized rail rate. Therefore, the grain shipment from them to Port of

Windust, Port of Pasco, and Lyons Ferry is redirected to be shipped by the rail mode instead.

This confirms that geographical positioning plays an important role in determining

substitutability between the two modes. In other words, the competition between the rail mode

and the truck-barge mode is limited by the geographical factor.

b. Transportation costs:

In terms of monetary costs, the bulk system’s total costs are $26.41 million in order to

move 56 million bushels of grain from the eastern Washington to the export terminal at Portland

(see Table 4). Elevators ship grain either by the truck-barge combination or the rail mode. Some

of them transship grain between each other as the way to minimize the transportation costs while

maximizing the rail mode utilization. In contrast to the bulk system, the Identity Preserved

system does not allow transshipment among elevators and requires shipping grain in containers.

Therefore, the total cost of moving the same amount of grain under the containerized scenario is

84

a lot more expensive than the bulk system by $45.41 million, for a total cost of the containerized

scenario of $71.82 million. The sensitivity analysis causes a slight decline in the total cost of

$71.01 and $69.92 million when the 5% and 10% discount are applied to the containerized rail

rate, but the containerized transportation cost is still substantially higher than the total cost from

the bulk system.

c. Additional costs:

The containerized grain transportation also requires either a large container liner (big

bag) or several small bags to hold products before loading into the container. The cost of a

container liner is fixed no matter how many bushels of grain is loaded. On the other hand, the

cost of small bags varies on the amount of grain loaded into the container. In addition, small

bags are more convenient for farmers to load grain at their farm before trucking it to an elevator.

It also facilitates the transfer process at the destination ports and buyers’ logistic process.

Under the third scenario, after taking the extra cost of small bags and/or a container liner

into account, the total containerized cost becomes $170.7 million and $177.6 million,

respectively. The total cost with liners is more expensive than the total cost with small bags

since shippers pay for a liner in every container while they pay for different numbers of small

bag for different containerized shipments. The extra material costs do not affect grain flows in

the model since the installation of either a liner or small bags in a container moved by the rail

mode are the same as the truck-barge mode.

85

7. Conclusion

This paper evaluates the probable impact of the IP system by quantifying the impact on

the cost of wheat transportation in Washington, using a survey of Washington grain elevators.

Two significant changes in the Washington wheat distribution occur as a result of the IP system.

First, we found that grain transportation costs are much higher because of the new grain

logistical system. Second, wheat elevators are more likely to use a truck-barge mode instead of

railroads. Third, the competition among ports is affected, with the Port of Windust being

affected the most among the six river ports. The results from the optimization model show that

the transportation costs increase by 550-570% as a result of either higher trucking costs or more

expensive containerized rail rates. The higher trucking cost is mainly caused by the lack of

transshipment among elevators, which forces wheat shipments to go to the port facility directly.

The expensive rail rate is explained by the lack of economies of scale and multiple-car rates,

since which the amount of shipped grain is too small. This analysis although the total

transportation costs increase under the IP system, an adoption of IP system in Washington wheat

market is still possible if the premium of the IP wheat over the bulk wheat is in the range of $2.5-

$2.7 per bushel. Otherwise, an investment in the IP system might not be profitable.

In terms of grain flows, more elevators ship grain by using the truck-barge combination

under the IP scenario as a result of the higher containerized rail rate. Applying 5% and 10%

discounts in the containerized rail rate indicates that Douglas, Grant, Adams and Lincoln

counties are the most responsive area. Counties near the eastern border are less sensitive than

the four counties due to the higher substitutability between the two modes. In addition, the

results also indicate a significant increase in the grain flows from the Port of Windust (29%).

86

Since Port of Windust is the main port providing barge service to elevators in the four sensitive

counties, therefore it is the most sensitive to the change in the containerized rail rate.

In sum, the analysis indicated that implementing an IP system in the state of Washington

is an expensive proposition and one that has geographical and modal impacts. The barge mode

and the area with competitive rates gain from the new logistical technologies. The premium

required to cause the adoption of the technology is substantial, and varies by location.

87

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TABLES

Table 2.1 Summary statistics for WA counties

Number Capacity Wheat Received Avg.

County of (1000 bushels) (1000 bushels) Utilization

elevators Mean Min Max Mean Min Max Rate

Adams 36 509 101 1,971 337 14 1,100 0.89

Chelan 1 506 506 506 258 258 258 0.51

Columbia 12 600 28 3,003 356 16 1,500 0.64

Douglas 12 474 10 674 328 7 674 0.68

Franklin 2 323 245 401 64 49 78 0.22

Grant 22 523 116 1,750 239 36 568 0.48

Lincoln 51 435 62 1,597 254 6 1,191 0.65

Okanogan 1 412 412 412 369 369 369 0.9

Spokane 17 380 75 836 213 3 936 0.98

Stevens 1 56 56 56 95 95 95 1.69

Whitman 58 377 11 1,243 228 13 3,600 0.75

Total 213 445 10 3,003 264 3 3,600 0.73 Source: Clark, Jessup and Casavant (2003)

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Table 2.2 Summary Statistics for firms

Number Capacity Wheat Received Firm

of (1000 bushels) (1000 bushels)

elevators Mean Min Max Total Mean Min Max Total

1 10 375 62 1,070 3,747 304 46 780 3,041

2 9 475 56 1,193 4,275 182 26 343 1,637

3 43 369 72 1,971 15,851 182 6 928 7,818

4 28 435 74 1,215 12,191 226 35 673 6,342

5 38 326 11 997 12,400 144 3 936 5,490

6 13 611 137 1,669 7942 399 50 1,100 5,186

7 11 628 142 1,243 6,909 252 36 544 2,773

8 18 347 58 1,213 6,239 418 25 3,600 7,533

9 31 585 10 1,750 18,127 392 7 1,191 12,167

10 12 600 28 3,003 7,195 356 16 1,500 4,274

Total 213 445 10 3,003 94,876 264 3 3,600 56,260 Source: Clark, Jessup and Casavant (2003)

93

Table 2.3 Summary of transportation rates used in the study

Rail Barge Truck* Bulk System (1) $0.28 - $0.65 $0.15 - $0.20 $0.036018 + ($0.001911*miles) + ($0.151866/miles) Handling charges (2) $0.12 $0.04 Containerized System (3), (4) $1.67 $0.26 - $0.36 $0.012 Handling charges (5) $0.22 $0.22 Extra materials - Container Liner (2) $290 $0.88 per container per bushel - SuperSack (6) $25 each $0.75

10 for a full

container per bushel

Note: * for both directions

Sources:(1) Clark, Jessup, and Casavant (2003) (2) Reichert and Vachal (2003) (3) Kratochvil (2005) (4) Tidewater qouted rates on the Port of Portland website http://www.flypdx.com/cntner_brgng_rates.aspx (5) Kosior, Prentice, and Vido (2002) (6) William Logan – Director, Material Handling FELLFAB Limited in Prentice, Duncan and Sokol (2004)

94

Table 2.4 Model results: modal split, volume shipped and total cost

Wheat

Volume Truck - Barge Rail

Trans -shipment Total Cost

thousand thousand thousand thousand $ thousand bushels bushels bushels bushels 1st Scenario 56,260 25,093 31,167 7,053,506 26,407 44.60% 55.40% 12.54% 2nd Scenario 56,260 53,459 2,800 71,817 95.02% 4.98% 5% Discounted Rail Rate 56,260 45,009 11,251 71,091 80.00% 20.00% 10% Discounted Rail Rate 56,260 42,424 13,836 69,919 75.41% 24.59% Difference from 1st Scenario 28,366 -28,366 45,411 Percentage Change 113.05% -91.01% 171.97% Small Container Bags Liner 3rd Scenario 170,698 177,517 Difference from 1st Scenario 145,605 151,111 Percentage Change 551.40% 572.25% Addition from 2nd Scenario 98,881 105,700 Percentage Change 137.68% 147.18%

95

Table 2.5 Model results: wheat flows to river ports, different scenarios (1)

Wheat Flows (bushels) 1st Scenario 2nd Scenario Non-discount 5% 10% Pasco 289,888 3,517,511 2,471,946 2,418,946 Windust 7,770,019 24,578,759 17,570,879 15,208,538 Lyons Ferry 4,274,200 8,677,476 8,280,252 8,110,457 Central Ferry 626,060 889,499 889,499 889,499 Port of Almota 11,098,770 15,796,143 15,796,143 15,796,143 Port of Wilma 1,034,000 0 0 0 Wheat Flows (percentage) 1st Scenario 2nd Scenario Non-discount 5% 10% Pasco 0.52% 6.25% 4.39% 4.30% Windust 13.81% 43.69% 31.23% 27.03% Lyons Ferry 7.60% 15.42% 14.72% 14.42% Central Ferry 1.11% 1.58% 1.58% 1.58% Port of Almota 19.73% 28.08% 28.08% 28.08% Port of Wilma 1.84% 0.00% 0.00% 0.00%

(1) No change occurs from scenario 2 to 3

96

FIGURES

Figure 2.1 Distribution of sample elevators in Washington

Source: Author acquires elevators’ location from Clark, Jessup and Casavant (2003)

97

Figure 2.2 Eastern Washington counties and Columbia-Snake River

98

Figure 2.3 Sample elevators, six main ports and railroad network in Washington

99

Figure 2.4 Model results: changes in wheat flows by modes

0

10,000

20,000

30,000

40,000

50,000

60,000

Bulk system IP system IP system (5%) IP system (10%)

Thou

sand

bus

hels

Truck-Barge Rail

100

Figure 2.5 Model results: wheat flows at different river ports from different scenarios

0

5,000

10,000

15,000

20,000

25,000

Pasco Windust Lyons Ferry Central Ferry Port of Almota Port of Wilma

Thou

sand

bus

hels

Bulk system IP system IP system (5%) IP system (10%)

101

Figure 2.6 Model results: transportation costs from different scenarios

0

20

40

60

80

100

120

140

160

180

200

Bulk system IP system IP system(5%)

IP system(10%)

With smallbags

WithContainer

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illio

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102

APPENDIX

APPENDIX 2.1: GAMS CODE FOR GRAIN FLOWS OPTIMIZATION SET N NODES FOR THE ENTIRE NETWORK / EL01179001, EL01179002, EL00179003, EL00179004, EL01179005, EL01179006, EL01179007, EL01179008, EL01179009, EL01179010, EL01289001, EL01289002, EL01289003, EL01289004, EL01289005, EL00289006, EL00289007, EL01289008, EL01289009, EL01295001, EL01295002, EL01295003, EL00295004, EL00295005, EL00295006, EL00295007, EL01295008, EL00295009, EL01295010, EL00295011, EL00295012, EL00295013, EL00295014, EL00295015, EL00295016, EL00295017, EL01295018, EL00295019, EL01295020, EL00295021, EL01295022, EL01295023, EL01295024, EL01295025, EL00295026, EL00295027, EL00295028, EL00295029, EL00295030, EL00295031, EL00295032, EL00295033, EL00295034, EL00295035, EL01295036, EL00295037, EL00295038, EL01295039, EL01295040, EL00295041, EL00295042, EL01295043, EL01305001, EL01305002, EL01305003, EL01305004, EL01305005, EL00305006, EL00305007, EL00305008, EL00305009, EL00305010, EL00305011, EL01305012, EL01305013, EL01305014, EL01305015, EL01305016, EL01305017, EL01305018, EL01305019, EL01305020, EL01305021, EL01305022, EL01305023, EL01305024, EL01305025, EL01305026, EL01305027, EL01305028, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL00337011, EL00337012, EL01337013, EL01337014, EL00337015, EL00337016, EL00337017, EL00337018, EL01337019, EL01337020, EL00337021, EL01337022, EL00337023, EL01337024, EL01337025, EL00337026, EL01337027, EL00337028, EL01337029, EL00337030, EL01337031, EL00337032, EL01337033, EL00337034, EL00337035, EL00337036, EL00337037, EL00337038, EL01474001, EL01474002, EL01474003, EL01474004, EL00474005, EL01474006, EL00474007, EL01474008, EL01474009, EL01474010, EL01474011, EL01474012, EL00474013, EL01534001, EL01534002, EL00534003, EL00534004, EL01534005, EL01534006, EL01534007, EL00534008, EL01534009, EL01534010, EL01534011, EL01074001, EL00074002, EL00074003, EL00074004, EL00074005, EL00074006, EL00074007, EL00074008, EL01074009, EL01074010, EL00074011, EL01074012, EL01074013, EL01074014, EL00074015, EL00074016, EL00074017, EL00074018, EL00852001, EL00852002, EL00852003, EL00852004, EL01852005, EL01852006, EL00852007, EL00852008, EL00852009, EL00852010, EL00852011, EL00852012, EL00852013, EL00852014, EL01852015, EL01852016, EL01852017, EL01852018, EL01852019, EL01852020, EL01852021, EL01852022, EL01852023, EL01852024, EL01852025, EL01852026, EL00852027, EL00852028, EL00852029, EL01852030, EL01852031, EL01852032, EL01852033, EL01898001, EL01898002, EL00898003, EL00898004, EL01898005, EL01898006, EL00898007, EL00898008, EL00898009, EL00898010, EL00898011, EL00898012, PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST, PORTLAND/ A(N,N) DIRECTED ARCS M MODES /TRUCK, RAIL26, RAIL110, BARGE/ ******** WHEAT RELATED NODES *********** WPRI(N) WHEAT PRIMARY NODES / EL01179001, EL01179002, EL00179003, EL00179004, EL01179005, EL01179006, EL01179007, EL01179008, EL01179009, EL01179010, EL01289001, EL01289002, EL01289003, EL01289004, EL01289005, EL00289006, EL00289007, EL01289008,

103

EL01289009, EL01295001, EL01295002, EL01295003, EL00295004, EL00295005, EL00295006, EL00295007, EL01295008, EL00295009, EL01295010, EL00295011, EL00295012, EL00295013, EL00295014, EL00295015, EL00295016, EL00295017, EL01295018, EL00295019, EL01295020, EL00295021, EL01295022, EL01295023, EL01295024, EL01295025, EL00295026, EL00295027, EL00295028, EL00295029, EL00295030, EL00295031, EL00295032, EL00295033, EL00295034, EL00295035, EL01295036, EL00295037, EL00295038, EL01295039, EL01295040, EL00295041, EL00295042, EL01295043, EL01305001, EL01305002, EL01305003, EL01305004, EL01305005, EL00305006, EL00305007, EL00305008, EL00305009, EL00305010, EL00305011, EL01305012, EL01305013, EL01305014, EL01305015, EL01305016, EL01305017, EL01305018, EL01305019, EL01305020, EL01305021, EL01305022, EL01305023, EL01305024, EL01305025, EL01305026, EL01305027, EL01305028, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL00337011, EL00337012, EL01337013, EL01337014, EL00337015, EL00337016, EL00337017, EL00337018, EL01337019, EL01337020, EL00337021, EL01337022, EL00337023, EL01337024, EL01337025, EL00337026, EL01337027, EL00337028, EL01337029, EL00337030, EL01337031, EL00337032, EL01337033, EL00337034, EL00337035, EL00337036, EL00337037, EL00337038, EL01474001, EL01474002, EL01474003, EL01474004, EL00474005, EL01474006, EL00474007, EL01474008, EL01474009, EL01474010, EL01474011, EL01474012, EL00474013, EL01534001, EL01534002, EL00534003, EL00534004, EL01534005, EL01534006, EL01534007, EL00534008, EL01534009, EL01534010, EL01534011, EL01074001, EL00074002, EL00074003, EL00074004, EL00074005, EL00074006, EL00074007, EL00074008, EL01074009, EL01074010, EL00074011, EL01074012, EL01074013, EL01074014, EL00074015, EL00074016, EL00074017, EL00074018, EL00852001, EL00852002, EL00852003, EL00852004, EL01852005, EL01852006, EL00852007, EL00852008, EL00852009, EL00852010, EL00852011, EL00852012, EL00852013, EL00852014, EL01852015, EL01852016, EL01852017, EL01852018, EL01852019, EL01852020, EL01852021, EL01852022, EL01852023, EL01852024, EL01852025, EL01852026, EL00852027, EL00852028, EL00852029, EL01852030, EL01852031, EL01852032, EL01852033, EL01898001, EL01898002, EL00898003, EL00898004, EL01898005, EL01898006, EL00898007, EL00898008, EL00898009, EL00898010, EL00898011, EL00898012 / WINT(N) WHEAT INTERMEDIATE NODES / EL01179001, EL01179002, EL01179005, EL01179006, EL01179007, EL01179008, EL01179009, EL01179010, EL01289001, EL01289002, EL01289003, EL01289004, EL01289005, EL01289008, EL01289009, EL01295001, EL01295002, EL01295003, EL01295008, EL01295010, EL01295018, EL01295020, EL01295022, EL01295023, EL01295024, EL01295025, EL01295036, EL01295039, EL01295040, EL01295043, EL01305001, EL01305002, EL01305003, EL01305004, EL01305005, EL01305012, EL01305013, EL01305014, EL01305015, EL01305016, EL01305017, EL01305018, EL01305019, EL01305020, EL01305021, EL01305022, EL01305023, EL01305024, EL01305025, EL01305026, EL01305027, EL01305028, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL01337013, EL01337014, EL01337019, EL01337020, EL01337022, EL01337024, EL01337025, EL01337027, EL01337029, EL01337031, EL01337033, EL01474001, EL01474002, EL01474003, EL01474004, EL01474006, EL01474009, EL01474010, EL01474011, EL01474012, EL01534001, EL01534002, EL01534005, EL01534006, EL01534007, EL01534009, EL01534010, EL01534011, EL01074001, EL01074009, EL01074010, EL01074012, EL01074013, EL01074014, EL01852005, EL01852006, EL01852015, EL01852016, EL01852017, EL01852018, EL01852019, EL01852020, EL01852021, EL01852022, EL01852023, EL01852024, EL01852025, EL01852026, EL01852030, EL01852031, EL01852032, EL01852033, EL01898001,

104

EL01898002, EL01898005, EL01898006, PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST / RELEV(N) ELEVATORS WITH RAIL / EL01179001, EL01179002, EL01179005, EL01179006, EL01179007, EL01179008, EL01179009, EL01179010, EL01289001, EL01289002, EL01289003, EL01289004, EL01289005, EL01289008, EL01289009, EL01295001, EL01295002, EL01295003, EL01295008, EL01295010, EL01295018, EL01295020, EL01295022, EL01295023, EL01295024, EL01295025, EL01295036, EL01295039, EL01295040, EL01295043, EL01305001, EL01305002, EL01305003, EL01305004, EL01305005, EL01305012, EL01305013, EL01305014, EL01305015, EL01305016, EL01305017, EL01305018, EL01305019, EL01305020, EL01305021, EL01305022, EL01305023, EL01305024, EL01305025, EL01305026, EL01305027, EL01305028, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL01337013, EL01337014, EL01337019, EL01337020, EL01337022, EL01337024, EL01337025, EL01337027, EL01337029, EL01337031, EL01337033, EL01474001, EL01474002, EL01474003, EL01474004, EL01474006, EL01474009, EL01474010, EL01474011, EL01474012, EL01534001, EL01534002, EL01534005, EL01534006, EL01534007, EL01534009, EL01534010, EL01534011, EL01074001, EL01074009, EL01074010, EL01074012, EL01074013, EL01074014, EL01852005, EL01852006, EL01852015, EL01852016, EL01852017, EL01852018, EL01852019, EL01852020, EL01852021, EL01852022, EL01852023, EL01852024, EL01852025, EL01852026, EL01852030, EL01852031, EL01852032, EL01852033, EL01898001, EL01898002, EL01898005, EL01898006 / ELEV(N) ELEVATORS WITHOUT RAIL / EL00179003, EL00179004, EL00289006, EL00289007, EL00295004, EL00295005, EL00295006, EL00295007, EL00295009, EL00295011, EL00295012, EL00295013, EL00295014, EL00295015, EL00295016, EL00295017, EL00295019, EL00295021, EL00295026, EL00295027, EL00295028, EL00295029, EL00295030, EL00295031, EL00295032, EL00295033, EL00295034, EL00295035, EL00295037, EL00295038, EL00295041, EL00295042, EL00305006, EL00305007, EL00305008, EL00305009, EL00305010, EL00305011, EL00337011, EL00337012, EL00337015, EL00337016, EL00337017, EL00337018, EL00337021, EL00337023, EL00337026, EL00337028, EL00337030, EL00337032, EL00337034, EL00337035, EL00337036, EL00337037, EL00337038, EL00474005, EL00474007, EL00474013, EL00534003, EL00534004, EL00534008, EL00074002, EL00074003, EL00074004, EL00074005, EL00074006, EL00074007, EL00074008, EL00074011, EL00074015, EL00074016, EL00074017, EL00074018, EL00852001, EL00852002, EL00852003, EL00852004, EL00852007, EL00852008, EL00852009, EL00852010, EL00852011, EL00852012, EL00852013, EL00852014, EL00852027, EL00852028, EL00852029, EL00898003, EL00898004, EL00898007, EL00898008, EL00898009, EL00898010, EL00898011, EL00898012 / IPORT(N) INTERMEDIATE PORTS / PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST / DESPL(N) WHEAT PRIMARY DESTINATION NODE / PORTLAND / DES1(N) WHEAT PRIMARY DESTINATION NODE / PORTLAND /

105

DES2(N) WHEAT SECONDARY DESTINATIONS / EL01179001, EL01179002, EL01179005, EL01179006, EL01179007, EL01179008, EL01179009, EL01179010, EL01289001, EL01289002, EL01289003, EL01289004, EL01289005, EL01289008, EL01289009, EL01295001, EL01295002, EL01295003, EL01295008, EL01295010, EL01295018, EL01295020, EL01295022, EL01295023, EL01295024, EL01295025, EL01295036, EL01295039, EL01295040, EL01295043, EL01305001, EL01305002, EL01305003, EL01305004, EL01305005, EL01305012, EL01305013, EL01305014, EL01305015, EL01305016, EL01305017, EL01305018, EL01305019, EL01305020, EL01305021, EL01305022, EL01305023, EL01305024, EL01305025, EL01305026, EL01305027, EL01305028, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL01337013, EL01337014, EL01337019, EL01337020, EL01337022, EL01337024, EL01337025, EL01337027, EL01337029, EL01337031, EL01337033, EL01474001, EL01474002, EL01474003, EL01474004, EL01474006, EL01474009, EL01474010, EL01474011, EL01474012, EL01534001, EL01534002, EL01534005, EL01534006, EL01534007, EL01534009, EL01534010, EL01534011, EL01074001, EL01074009, EL01074010, EL01074012, EL01074013, EL01074014, EL01852005, EL01852006, EL01852015, EL01852016, EL01852017, EL01852018, EL01852019, EL01852020, EL01852021, EL01852022, EL01852023, EL01852024, EL01852025, EL01852026, EL01852030, EL01852031, EL01852032, EL01852033, EL01898001, EL01898002, EL01898005, EL01898006, PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST/ ; PARAMETERS RAILCAPW(N) RAIL CAPACITY FOR WHEAT / EL01179001 238000.00 EL01179008 350000.00 EL01179009 110000.00 EL01179010 42000.00 EL01289001 179221.94 EL01289002 126052.83 EL01289003 239224.34 EL01289004 138292.26 EL01289005 43778.91 EL01289008 20932.13 EL01289009 274417.92 EL01295001 844261.43 EL01295002 502233.83 EL01295003 687869.63 EL01295018 193362.00 EL01295036 114757.02 EL00295038 5343.00 EL01295043 103756.99 EL01305001 22128.68 EL01305002 18113.77 EL01305003 24649.67 EL01305004 113444.49 EL00305006 179400.00 EL01305012 122551.00 EL01305013 137244.62 EL01305014 107232.13 EL01305015 109107.91

106

EL01305016 106294.24 EL01305017 25635.67 EL01305018 163505.55 EL01305019 267611.38 EL01305020 336390.00 EL01305021 105273.16 EL01305022 82598.94 EL01305023 23969.89 EL01305024 182365.50 EL01305025 52474.62 EL01305026 48401.18 EL01305027 83691.15 EL01305028 46808.23 EL01337001 82479.00 EL01337002 6532.26 EL01337003 193686.65 EL01337004 58122.19 EL01337005 13467.74 EL01337006 47726.61 EL01337007 95583.76 EL01337008 28790.32 EL01337009 125108.60 EL01337010 17027.99 EL01337013 224000.00 EL01337014 104952.22 EL01337019 2548.51 EL01337020 448000.00 EL01337022 33828.93 EL01337024 234000.00 EL01337027 613263.83 EL01337031 187118.64 EL01337033 17627.12 EL01474001 10000.00 EL01474002 25000.00 EL01474003 15000.00 EL01474004 9700.00 EL01474006 500000.00 EL01474008 1100000.00 EL01534001 220000.00 EL01534005 74177.32 EL01534006 30000.00 EL01534007 120000.00 EL01534009 46965.05 EL01534010 70835.46 EL01534011 18022.17 EL01074001 612000.00 EL01074012 576000.00 EL00852004 967377.36 EL01852005 424022.64 EL01852015 369000.00 EL01852016 604200.00 EL01852017 143550.00 EL01852018 365901.01 EL01852019 529161.78 EL01852020 95167.08 EL01852021 465170.12

107

EL01852022 218091.21 EL01852023 235365.76 EL01852024 539829.73 EL01852025 1071900.00 EL01852031 255420.00 EL01852032 462600.00 / WSUP(N) AVAILABLE WHEAT BU / EL01179001 340000.000 EL01179002 45880.000 EL00179003 700000.000 EL00179004 780000.000 EL01179005 265000.000 EL01179006 90000.000 EL01179007 280000.000 EL01179008 370000.000 EL01179009 110000.000 EL01179010 60000.000 EL01289001 224027.421 EL01289002 157566.031 EL01289003 299030.425 EL01289004 153658.067 EL01289005 48643.234 EL00289006 289888.000 EL00289007 94614.000 EL01289008 26165.162 EL01289009 343022.401 EL01295001 927759.815 EL01295002 551905.312 EL01295003 755900.693 EL00295004 89108.551 EL00295005 160600.100 EL00295006 40850.898 EL00295007 620000.000 EL01295008 45272.893 EL00295009 356000.000 EL01295010 348000.000 EL00295011 12129.879 EL00295012 62298.116 EL00295013 124427.003 EL00295014 118276.619 EL00295015 121588.364 EL00295016 258000.000 EL00295017 408000.000 EL01295018 222000.000 EL00295019 36000.000 EL01295020 49000.000 EL00295021 242000.000 EL01295022 32468.521 EL01295023 57786.237 EL01295024 20628.731 EL01295025 6339.037

108

EL00295026 80516.325 EL00295027 27729.689 EL00295028 51116.173 EL00295029 17397.296 EL00295030 14240.824 EL00295031 19379.266 EL00295032 89188.667 EL00295033 78000.000 EL00295034 330000.000 EL00295035 374000.000 EL01295036 118919.192 EL00295037 138000.000 EL00295038 137000.000 EL01295039 37000.000 EL01295040 180180.000 EL00295041 213000.000 EL00295042 138060.000 EL01295043 107520.202 EL01305001 42555.149 EL01305002 34834.173 EL01305003 47403.204 EL01305004 218162.474 EL01305005 96233.000 EL00305006 390000.000 EL00305007 289294.000 EL00305008 200752.000 EL00305009 118569.000 EL00305010 503011.000 EL00305011 432198.000 EL01305012 245102.009 EL01305013 274489.240 EL01305014 214464.258 EL01305015 218215.819 EL01305016 212588.477 EL01305017 51271.339 EL01305018 327011.099 EL01305019 535222.755 EL01305020 672780.005 EL01305021 169795.413 EL01305022 133224.094 EL01305023 38661.109 EL01305024 294137.901 EL01305025 84636.483 EL01305026 134447.719 EL01305027 232475.423 EL01305028 130022.858 EL01337001 82479.004 EL01337002 13064.516 EL01337003 193686.649 EL01337004 72652.739 EL01337005 26935.484 EL01337006 47726.615 EL01337007 119479.700 EL01337008 57580.645 EL01337009 125108.601 EL01337010 21284.982

109

EL00337011 79504.950 EL00337012 230000.000 EL01337013 280000.000 EL01337014 104952.215 EL00337015 41629.213 EL00337016 118275.862 EL00337017 42640.449 EL00337018 81586.207 EL01337019 2548.509 EL01337020 560000.000 EL00337021 83316.832 EL01337022 42286.165 EL00337023 100000.000 EL01337024 260000.000 EL01337025 91351.351 EL00337026 250000.000 EL01337027 613263.829 EL00337028 30000.000 EL01337029 55945.946 EL00337030 340000.000 EL01337031 935593.220 EL00337032 16507.666 EL01337033 88135.593 EL00337034 28160.136 EL00337035 50000.000 EL00337036 34795.571 EL00337037 115000.000 EL00337038 55000.000 EL01474001 200000.000 EL01474002 500000.000 EL01474003 300000.000 EL01474004 135800.000 EL00474005 250000.000 EL01474006 500000.000 EL00474007 250000.000 EL01474008 1100000.000 EL01474009 400000.000 EL01474010 150000.000 EL01474011 50000.000 EL01474012 1000000.000 EL00474013 350000.000 EL01534001 400000.000 EL01534002 544050.000 EL00534003 400000.000 EL00534004 234000.000 EL01534005 148354.646 EL01534006 75000.000 EL01534007 300000.000 EL00534008 400000.000 EL01534009 93930.094 EL01534010 141670.929 EL01534011 36044.331 EL01074001 680000.000 EL00074002 320000.000 EL00074003 67860.000 EL00074004 165000.000

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EL00074005 430000.000 EL00074006 385000.000 EL00074007 190000.000 EL00074008 50000.000 EL01074009 140000.000 EL01074010 259740.000 EL00074011 50000.000 EL01074012 640000.000 EL01074013 101130.221 EL01074014 108869.779 EL00074015 260000.000 EL00074016 60000.000 EL00074017 25000.000 EL00074018 3600000.000 EL00852001 375736.527 EL00852002 288263.473 EL00852003 77000.000 EL00852004 1074863.735 EL01852005 471136.265 EL01852006 310769.231 EL00852007 469230.769 EL00852008 582352.144 EL00852009 6647.856 EL00852010 337000.000 EL00852011 187000.000 EL00852012 146215.385 EL00852013 674215.385 EL00852014 475569.231 EL01852015 369000.000 EL01852016 636000.000 EL01852017 319000.000 EL01852018 385158.963 EL01852019 557012.401 EL01852020 100175.874 EL01852021 489652.762 EL01852022 229569.694 EL01852023 247753.432 EL01852024 568241.816 EL01852025 1191000.000 EL01852026 148000.000 EL00852027 441000.000 EL00852028 215000.000 EL00852029 184435.058 EL01852030 53000.000 EL01852031 258000.000 EL01852032 514000.000 EL01898001 683501.684 EL01898002 16498.316 EL00898003 430000.000 EL00898004 60000.000 EL01898005 365000.000 EL01898006 340000.000 EL00898007 120000.000 EL00898008 214200.000 EL00898009 200000.000 EL00898010 70000.000

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EL00898011 1500000.000 EL00898012 275000.000 / ALIAS(N,NP); TABLE WARCS(N,NP,M) TRANSPORT AND HANDLING COSTS BY MODE TRUCK RAIL26 RAIL110 BARGE BURBANK.PORTLAND 0.15800 CENTRALFERRY.PORTLAND 0.19371 LYONSFERRY.PORTLAND 0.18343 PASCO.PORTLAND 0.17229 PORTALMOTA.PORTLAND 0.19486 PORTWILMA.PORTLAND 0.20257 WINDUST.PORTLAND 0.15800 EL01305001.WINDUST 0.16270 EL01305001.LYONSFERRY 0.18304 EL01305001.PORTLAND 0.36176 0.33235 EL01305002.WINDUST 0.16270 EL01305002.LYONSFERRY 0.18304 EL01305002.PORTLAND 0.36176 0.33235 EL01305003.WINDUST 0.16270 EL01305003.LYONSFERRY 0.18304 EL01305003.PORTLAND 0.36176 0.33235 EL01305004.WINDUST 0.16270 EL01305004.LYONSFERRY 0.18304 EL01305004.PORTLAND 0.36176 0.33235 EL01305005.WINDUST 0.18227 EL01305005.LYONSFERRY 0.20270 EL01305005.PORTLAND 0.37206 0.34265 EL00305006.EL01305014 0.07016 EL00305006.EL01305015 0.07016 EL00305006.EL01305016 0.07016 EL00305006.WINDUST 0.18327 EL00305006.LYONSFERRY 0.20370 EL00305007.EL01305001 0.07035 EL00305007.EL01305002 0.07035 EL00305007.EL01305003 0.07035 EL00305007.EL01305004 0.07035 EL00305007.WINDUST 0.15220 EL00305007.LYONSFERRY 0.17247 EL00305008.EL01305001 0.07023 EL00305008.EL01305002 0.07023 EL00305008.EL01305003 0.07023 EL00305008.EL01305004 0.07023 EL00305008.WINDUST 0.14750 EL00305008.LYONSFERRY 0.16775 EL00305009.EL01305001 0.07012 EL00305009.EL01305002 0.07012 EL00305009.EL01305003 0.07012 EL00305009.EL01305004 0.07012 EL00305009.WINDUST 0.15115 EL00305009.LYONSFERRY 0.17493

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EL00305010.EL01305001 0.07172 EL00305010.EL01305002 0.07172 EL00305010.EL01305003 0.07172 EL00305010.EL01305004 0.07172 EL00305010.WINDUST 0.14849 EL00305010.LYONSFERRY 0.15832 EL00305011.EL01305012 0.07713 EL00305011.EL01305013 0.07713 EL00305011.WINDUST 0.14009 EL00305011.LYONSFERRY 0.14988 EL01305012.WINDUST 0.19065 EL01305012.LYONSFERRY 0.18544 EL01305012.PORTLAND 0.36176 0.33235 EL01305013.WINDUST 0.19065 EL01305013.LYONSFERRY 0.18544 EL01305013.PORTLAND 0.36176 0.33235 EL01305014.WINDUST 0.18461 EL01305014.LYONSFERRY 0.17941 EL01305014.PORTLAND 0.36176 0.33235 EL01305015.WINDUST 0.18461 EL01305015.LYONSFERRY 0.17941 EL01305015.PORTLAND 0.36176 0.33235 EL01305016.WINDUST 0.18461 EL01305016.LYONSFERRY 0.17941 EL01305016.PORTLAND 0.36176 0.33235 EL01305017.WINDUST 0.18791 EL01305017.LYONSFERRY 0.18271 EL01305017.PORTLAND 0.35000 0.32059 EL01305018.WINDUST 0.18791 EL01305018.LYONSFERRY 0.18271 EL01305018.PORTLAND 0.35000 0.32059 EL01305019.WINDUST 0.18791 EL01305019.LYONSFERRY 0.18271 EL01305019.PORTLAND 0.35000 0.32059 EL01305020.WINDUST 0.18791 EL01305020.LYONSFERRY 0.18271 EL01305020.PORTLAND 0.35000 0.32059 EL01305021.WINDUST 0.22703 EL01305021.LYONSFERRY 0.22178 EL01305021.PORTLAND 0.37941 0.35000 EL01305022.WINDUST 0.24763 EL01305022.LYONSFERRY 0.24239 EL01305022.PORTLAND 0.37941 0.35000 EL01305023.WINDUST 0.21390 EL01305023.LYONSFERRY 0.20865 EL01305023.PORTLAND 0.37941 0.35000 EL01305024.WINDUST 0.21390 EL01305024.LYONSFERRY 0.20865 EL01305024.PORTLAND 0.37941 0.35000 EL01305025.WINDUST 0.21390 EL01305025.LYONSFERRY 0.20865 EL01305025.PORTLAND 0.37941 0.35000 EL01305026.WINDUST 0.21142 EL01305026.LYONSFERRY 0.23755 EL01305026.PORTLAND 0.37206 0.34265 EL01305027.WINDUST 0.21142

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EL01305027.LYONSFERRY 0.23755 EL01305027.PORTLAND 0.37206 0.34265 EL01305028.WINDUST 0.21142 EL01305028.LYONSFERRY 0.23755 EL01305028.PORTLAND 0.37206 0.34265 ; VARIABLES W(N,NP,M) FLOW FROM N TO NP VIA MODE K TC TOTAL COST WTC WHEAT TOTAL COST; POSITIVE VARIABLE W; EQUATIONS WNB(N) NODE BALANCE WHEAT WSB(N) SUPPLY BALANCE WHEAT WCOST ACCTING: TOTAL COST WHEAT DESBAL; * DESBAL..SUM((WINT,DES1,M)$WARCS(WINT,DES1,M),W(WINT,DES1,M)) =E= 6341558.000; WSB(WPRI)..SUM((WINT,M)$WARCS(WPRI,WINT,M),W(WPRI,WINT,M)) =L= WSUP(WPRI); WNB(WINT)..SUM((WPRI,M)$WARCS(WPRI,WINT,M),W(WPRI,WINT,M)) =E= SUM((DES1,M)$WARCS(WINT,DES1,M),W(WINT,DES1,M)); WCOST..TC =E= SUM((WPRI,WINT,M)$WARCS(WPRI,WINT,M),WARCS(WPRI,WINT,M)*W(WPRI,WINT,M)) + SUM((WINT,DES1,M)$WARCS(WINT,DES1,M),WARCS(WINT,DES1,M)*W(WINT,DES1,M)); *SUM((N,NP,M)$WARCS(N,NP,M),WARCS(N,NP,M)*W(N,NP,M)); MODEL TEST /ALL/; OPTION LIMROW = 5; OPTION LIMCOL = 5; OPTION RESLIM = 5000; OPTION ITERLIM = 100000; SOLVE TEST MINIMIZING TC USING LP; DISPLAY W.L, TC.L; FILE RES /'EJ.DAT'/; PUT RES; PUT "TOTAL COST = "/; PUT TC.L /; PUT /; *** PUT "WHEAT ARCS"/; *** LOOP ((N,NP,M),

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*** IF (W(N,NP,M) GT 0, *** PUT N.TL, NP.TL, M.TL, W(N,NP,M)/)); PUT "WHEAT ARCS FOR ELEVATORS TO ELEVATORS WITH RAIL"/; LOOP ((ELEV, RELEV, M), IF (W.L(ELEV,RELEV,M)GT 0, PUT ELEV.TL, RELEV.TL, M.TL, W.L(ELEV,RELEV,M)/)); PUT "WHEAT ARCS FOR ELEVATORS TO RIVER PORTS"/; LOOP ((ELEV, IPORT, M), IF (W.L(ELEV,IPORT,M)GT 0, PUT ELEV.TL, IPORT.TL, M.TL, W.L(ELEV,IPORT,M)/)); PUT "WHEAT ARCS FOR ELEVATORS WITH RAIL TO PORTLAND"/; LOOP ((IPORT,DES1,M), IF (W.L(IPORT,DES1,M)GT 0, PUT IPORT.TL, DES1.TL, M.TL, W.L(IPORT,DES1,M)/));

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CHAPTER 3

IMPACTS OF THE PACIFIC NORTHWEST’S SOFT WHITE WHEAT

MARKETING PLAN ON GRAIN TRANSPORTATION IN WASHINGTON

Abstract

This chapter evaluates impacts of the Pacific Northwest (PNW)’s soft white wheat

(SWW) marketing plan which aims to promote wheat to buyers by providing information of

the different end-use qualities of the soft white wheat grown in different geographical areas.

Under this model, I assume that elevators voluntarily move grain only within the production

zone and there is no grain shipment across different production zones in an attempt to preserve

identity of wheat grown in a specific zone. The cost-minimizing linear programming

optimization model is applied to represent elevator managers’ decision on grain transportation.

The results indicate insignificant changes in wheat flows and a slightly increase in

transportation costs due to the imposition of the marketing plan. In contrast to the IP system,

the zoning policy is significantly inexpensive as the result of the existing economies of scale.

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1. Introduction

Grain is one of the most important exports from Washington, accounting for almost

20% of the total value of agricultural export. Recent interest in Identity Preserved (IP) grain is

due to an increase in consumer awareness of the contamination of Genetically Modified

Organisms (GMOs) and the desire for “known quality characteristics”. Such an increase in the

demand results in a rise in the amount of containerized grain shipped from the U.S. to various

Asian markets, especially to Japan and China. The IP system containerizes all products in

order to prevent the contamination of GMOs during the transportation process. All products

shipped by containers are less likely to be exposed to any adverse factor (such as temperature

and humidity), or commingle with different-quality products. In addition, each containerized

grain shipment can be efficiently sorted by specific types of wheat with the minimum variation

in wheat quality.

In 2004, the Washington Wheat Commission (WWC), the Idaho Wheat Commission

(IWC), and the Oregon Wheat Commission (OWC) jointly proposed a new marketing plan for

soft white wheat, referred to as the Pacific Northwest Soft White Wheat (PNW SWW)

marketing plan. The objective of the policy is to promote wheat to oversea buyers by

providing, and potentially guarantee the qualities of the soft white wheat crop. By separating

the production of wheat types into different production zones, this program assists consumers

in making purchase decisions by reducing their search and risk costs. The production zones

associated with end-use quality are identified from three years of collecting samples of wheat.

In order to allow the plan to be exercised most effectively, farmers and elevators are

encouraged to concentrate on wheat flows that do not allow transshipment across different

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zones. Compared to the containerized IP system, the grain zoning concept may lower the

transportation cost because producers are still able to ship grain using a bulk system.

Although both the grain zoning policy and the IP system aim to differentiate grain

products by quality measures, the processes are different in significant ways. While the

containerized IP system strictly treats each grain shipment differently from the others, an

effective zoning policy allows shipping grain in bulk under a condition that the products must

originate from the same zone. The IP system encourages elevator companies to dedicate one

elevator to storing a specific type of grain. In addition, the IP system does not allow

transshipment among elevators, in order to avoid grain commingling. As a result, each of the

IP shipments is small and becomes costly. On the other hand, the zoning policy allows

elevators to pool grain originating from the same zone and ship them in bulk to the export

market. With the restriction on the grain origins, the volume of each grain shipment is smaller

than that of the shipment without the restriction. However, the volume of such shipment is

still substantially larger than that of the volume of each IP shipment.

This study expands upon the study from the previous study on IP system, which

investigated the impacts of the IP system on the grain transportation costs without the zoning

policy. The objective of this study is to estimate impacts of the zoning policy on the grain

transportation cost structure. Two case studies are included in the analysis in order to compare

effects of the grain zoning policy on transportation costs of two elevator companies. The two

case studies are (1) a multi-location elevator company that owns elevators located in the same

zone, and (2) a multi-location elevator company that owns elevators located in two different

zones. Furthermore, we analyze the difference in transportation costs between the traditional

bulk system with the grain zoning policy and the containerized IP system in order to evaluate

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the possibility of the grain zoning policy becoming an alternative to the IP system while still

achieving similar goals.

The organization of the paper is as follows. The next section describes the background

of the grain zoning policy. Section 3 reviews the previous related literature in the field of

zoning and transportation. Section 4 illustrates the details of the optimization model followed

by the data descriptive and summary statistics in Section 5. Section 6 reports and analyzes

empirical results from all three scenarios, with conclusion offered in Section 7.

2. Background: the grain zoning policy

Grain quality identification facilitates the grain industry in efficiently matching the

demand for and supply of each grade of wheat/grain. The identification efforts through the

supply chain can be carried out in two ways, either by using a IP system or by using a grain

zoning policy. Unlike the traditional transportation system, the IP system encourages elevator

companies to dedicate an elevator to store one specific type/grade of wheat. The system

strictly segregates different grade/type of grain and does not allow transshipment among

elevators in order to avoid wheat commingling. To do so, IP grains are required to be stored

and transported by using separate containers. Alternatively, the wheat production zone is the

alternative transportation approach to identify quality of wheat produced in particular areas.

The effort to identify wheat quality by zones has been undertaken in the three Pacific

Northwest (PNW) states, Washington, Idaho, and Oregon, since 2001.

The PNW SWW marketing plan originated from the cooperation of the Washington,

Idaho, and Oregon wheat commissions, the Wheat Marketing Center, Inc. (WMC) and U.S.

Wheat Associates in 2004. In 2001, the Pacific Northwest (PNW) wheat commissions

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initiated a plan to differentiate soft white wheat harvest quality testing throughout the region

based on grainsheds, which are defined by identifying key rail loading facilities or river barge

ports and outlining the production region which contributes to each facility’s grain supply.

Such facilities serve as the focal point of each grainshed, and the production area and the

elevators that feed into that particular facility make up the area surrounding each grainshed.

After collecting three years of data, the commissions created the six production zones within

the PNW, based on the patterns of end-use wheat quality (see Figure 1). The quality report

shows that the North Central (NC-PNW) Production Zone supplies low wheat ash contents,

while low moisture wheat (less than 10%) prevailed in the North Central, Northeast (NE-

PNW), Central (C-PNW) and Southeast (SE-PNW) Production Zones. In addition, finished

product tests indicated that very good sugar snap cookies were made using low protein

samples from the NC-PNW, NE-PNW, C-PNW and SE-PNW Production Zones. Also,

average sponge cake scores and volumes were higher in samples from the NC-PNW and SE-

PNW Production Zones.

The Eastern Washington region is confined inside two assigned zones: NC-PNW and

NE-PNW. NC-PNW includes Lincoln, Grant, Douglas, Chelan, Okanogan, Adams, Franklin,

Benton, Yakima, Kittitas, and North Walla Walla counties, while NE-PNW covers Columbia,

Garfield, Whitman, Spokane, Astoria, Stevens, Pend Oreille, and Ferry counties. The NC-

PNW production zone is separated into two different grain shed areas, namely area F and area

H, while the NE-PNW production zone is assigned into four different grainshed areas: area K,

J, L, and M (see Figure 2).

With an objective to differentiate wheat qualities from different zones, the wheat

shipment from one zone will not be allowed to commingle with other wheat shipments from

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different zones, otherwise the differentiation would not be effectively achieved.

Consequently, the grain zoning policy requires for multi-location elevator companies the

transshipment among a company’s elevators is not allowed across two different zones. Unlike

the traditional transportation system, the transshipping prohibition implies that any elevator

company under the zoning policy may not take an advantage of the economies of scale from

pooling a larger volume of grain from all of its satellite elevators. Without a large volume of

wheat, a company may not be able to negotiate with rail companies for a discounted rail rate

and utilize a posted multiple-car rate. As a result, the available truck-barge combination,

which is an alternative mode of transportation, is expected to be more competitive to the rail

mode, if the discounted rail rates are not available.

3. Literature review

3.1. Zoning policy

A zoning policy affects the grain and IP grain transportation system in several ways.

First, it may reduce the trucking distance, since all trucks cannot go beyond the zone boundary.

Second, the zoning policy may alter elevators’ transportation mode choices. Since grain

cannot be shipped from a satellite elevator to other sub-terminal elevators outside the

boundary, the policy limits the number of destination elevators. Third, the zone’s boundary

may increase or decrease the cost of grain shipment. Under the policy, some trucks are forced

to go to smaller elevators or river ports inside the assigned zone, causing use of more

expensive rail rates or barge rates. However, since production and elevators are limited to the

same zone, the cost for transshipment itself may decrease.

In terms of transportation studies, Taylor, Whicker and Usher (2001) studied impact of

multi-zone dispatching in truckload trucking. They pointed out that the multi-zone dispatching

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reduces the haul length because the trip is restricted within the zone’s boundary. Moreover,

Taylor et al. (1999) studied the performance of delivery services among three strategies:

delivery lanes, hubs and zones. The study found that the zoning strategy performs better than

the other two in terms of fewer drivers utilized, fewer first dispatch empty miles, and less late

hours.

Several studies found that the travel decision also depends on a zoning strategy.

Limanond et al. (2005), using the data in Puget Sound area of Washington, estimated a

neighborhood shopping demand model. The results showed that the level of service and the

zone attractions influence decisions about mode and destination.

In several cases, the zoning policy is applied in order to control air pollution in big

cities. Rapaport (2002) analyzed benefits of a unique Swedish transportation-planning tool

called the Environmental Zone for the case of Stockholm Municipality. The Environmental

Zone clearly forces new technology on the market by encouraging the purchase of cleaner or

upgrading of vehicles, which has noted effects on nitrogen and particle emission and

concentrations. Moreover, Hsu and Guo (2005) adopted a continuum approximation method

based on long-term planning to describe the continuous characteristics of air pollution

dispersion, street and rail transit network flow as well as household distribution in Taipei

metropolitan area. The results show that air pollution within the study zones diminished are

diminished after rail transit networks are completed

In addition, various studies paid attention to analyzing the external effects of the zoning

policy imposition. Among others, Paarlberg, Seitzinger, and Lee (2004) observed the trade-off

between the cost of economic activity inside the Foot-Mouth-Disease (FMD) quarantine zone,

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in England, and the benefits of reduced disease spread. As the size of the zone was extended,

the cost on non-agricultural activities, such as tourist industry, was increased rapidly.

3.2 Grain transportation

Transportation studies have applied a deterministic optimization model to solve the

agricultural transportation problems in the United States, with the aim of improving the

efficiency of the grain distribution system (Koo and Larson, 1985). In order to ship grains

from elevators to markets, elevator managers take several factors into consideration, such as

transportation rates, trucking costs, and availability of transportation modes.

Several studies developed a linear programming interregional model to assess impacts

of a change in transportation rates, regulations and market conditions in which they do not

affect quantity demanded and quantity supplied. Koo, Thompson and Larson (1985) applied a

linear programming model to evaluate impacts of capacity constraints in the U.S. grain

distribution system, considering both rail and barge transportation, on spatial grain flows.

Also, the same author (1988) evaluated impacts of changes in ocean freight rates on the U.S.

grain distribution system, using the linear programming. Later, Jessup (1998) developed a

linear programming model to assess effects of the dam drawdown for salmon restoration on

the Columbia-Snake River on grain flows in Washington.

Recently, Puenpatom (2006) studied the effect of IP grain on grain transportation by

applying a least cost linear programming optimization model with 10 multi-location elevator

companies in Washington. The study evaluated a combination of three transportation

conditions, which include 1). a traditional grain transportation with handling costs, 2). an IP

grain with handling costs, and 3). an IP grain with handling costs plus extra materials. The

123

study found that after an introduction of the IP system, which does not allow transshipment

among elevators, logistical costs was increased up to five times that of the bulk system.

In terms of cost, the adoption of the IP system has brought changes to the cost structure

in the grain distribution system due to the introduction of new handling practices. Several

studies focused on identifying cost items in the IP grain logistic, both actual and hidden costs.

Maltsbarger and Kalaitzandonakes (2000), focusing on elevator operation costs, found that

opportunity costs from under-utilized storage, lost grind margin and spread opportunity play a

significant proportion in the operation costs. The study, assuming cost parameters for

Missouri and Illinois elevators, employed the Process & Economic Simulation of IP (PRESIP)

simulation model to estimate elevator operation costs. They also identified segregation costs,

which included sample analysis cost, misgrades, maintenance, disputes/labor and others, and

revealed that the sample analysis cost was the largest part in the segregation costs. However,

Baumel and McVey (2001) argued that the study by Maltsbarger and Kalaitzandonakes (2000)

did not include risk costs into the consideration. Therefore, they incorporated risk costs, along

with opportunity costs as the hidden costs, into the segregation costs of the IP production and

distribution system. They primarily discussed segregation costs throughout the entire grain

logistic process, which consists of farmers, elevators, processors, exports and handlers. The

risk costs may arise due to volume mismatch, quality deviation, and non-IP contamination.

The growth of the IP market is determined by several factors, as reported by Vachal,

VanWechal and Reichert (2003). Among other factors, the ocean shipping rates for containers

was the most important factor determining success in IP business, followed by the availability

of containers and the rail shipping rates for containers. For the ocean freight rate factor, the

124

cost of shipping a container is more expensive than shipping the same volume of bulk grain,

which is the reason for the dominant role of bulk grain shipments.

The imbalance of containers from an export and an import markets is a main

problem/opportunity in the IP grain industry. Kosior, Prentice and Vido (2002), and Vachal

and Reichert (2002) indicated that the United States have experienced imbalanced trade on the

Trans-Pacific corridor, consisting of more containerized imports than containerized exports,

resulting in a large amount of empty containers remaining at the west coast ports or at inland

markets. In order to avoid move empty containers back to Asia, ocean liners have typically

offered reduced container rates to IP and other exporters, which would make the containerized

grain competitive to the bulk grain transportation.

4. The optimization model

A linear programming cost-minimization model is utilized in order to represent

elevator managers’ decisions on transportation mode choices. Truck-barge and railroad

represent the two transportation choices for elevators in order to provide grain logistic services

to customers. In this model, elevator managers search for the lowest cost transportation mode

in order to ship grain from elevators to export terminals in Portland, Oregon.

The study imposes four assumptions regarding the wheat distribution system in Pacific

Northwest. First, we anticipate that the IP shipment may be smaller than the current bulk

system’s in which the bulk system cannot handle the IP products (Reichert and Vachal, 2003).

Therefore, only the small trains (the 26-railcar type) are included in this model because the

125

total volume of IP products is less likely to fill up the 52-railcar type.1 Second, the study does

not impose capacity constraints on the linear programming model because a sub-terminal

elevator can store transshipped wheat either inside its facility or is outdoor storage. Third,

grain stored at satellite elevators is transshipped to sub-terminal elevators within the same

company, implying that there is no transshipment across companies. Fourth, the model

evaluates only the shipment of wheat to the export market because wheat is the main export

product of Washington, almost 90% of the overall volume.

We apply an optimization procedure using General Algebraic Modeling System

(GAMS) on a linear programming model. The objective function of the model is to minimize

elevators’ total transportation costs while moving a known amount of quantities of wheat from

elevators to their destinations. Therefore, the objective function can be expressed

mathematically as the following:

Min ( )[ ]∑∑∑= = =

=n

i

m

j kijkijk XCTC

1 1

2

1

Where:

TC = Total transportation and handling costs

Cijk = Transportation and handling charges for shipping wheat from

the ith origin to the jth destination on mode k

Xijk = Decision variables representing wheat flow from the

the ith origin to the jth destination on mode k

i = Origin points (i = 1,…, n)

j = Destination points (j = 1,…, l, l+1,…, m)

1 Rail companies provide three types of freight rates; the large trains (52-railcar or more) and the smaller trains (26 or single and 3railcars). In this study, only the larger two movement sizes are used, to reflect actual movements derived by the survey.

126

k = Mode of transportation ( truck-barge or rail)

Under this model, the two decision multi-location elevator firms include Firm 1 and

Firm 2. Two modes of transportation, the truck-barge mode and the rail mode, are available.

The model assumes a fixed amount of quantity demanded and quantity supplied in both

producing and consuming regions, which satisfies the spatial equilibrium condition in the

study area.2 This implies that commodity prices are fixed. An unconstrained optimization

system identifies the origin places and the quantities to be shipped, the collection of possible

routes on various modes, the cost associated with each route option, and the final destinations.

Consequently, it allows the linear programming to solve for the minimum cost solution.

In order to evaluate impacts on transportation modes from the PNW SWW marketing

plan, we impose three scenarios of transportation to simulate real world situations. The first

scenario is the traditional grain transportation system or the bulk transportation system, which

allows transshipment among elevators. The next scenario is the bulk grain transportation with

the imposition of the PNW SWW marketing plan, which does not allow moving grain across

two different zones. Finally, the last scenario is the grain transportation with the containerized

IP system, where there is no transshipment.

5. Data and descriptive statistics

The data used in the paper are from Clark, Jessup and Casavant (2003), which surveyed

Washington grain elevators in 2002. This study includes 83 elevators owned by two of the

largest multi-location elevator firms, which are the firms used as basis for this analysis. For

2 Hence, the solution obtained from the model cannot be viewed as a global optimal solution, but a conditional optimal solution under predetermined demand and supply conditions (Koo and Larson, 1985).

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confidentiality reasons, the firms are not identified and are slightly modified. Of 394 elevators

in Washington, Firm 1 owns 46 elevators, while Firm 2 owns 40 elevators, accounting for 12%

and 10% of the total number of Washington elevators. Because of incomplete information

from the survey, 43 elevators of Firm 1 are able to be used in this study. The descriptive

statistics of the two model firms are summarized in Table 1.

Elevators from Firm 1 are generally larger than Firm 2’s in terms of capacity. The total

capacities of the two companies are 15.85 million bushels and 12.67 million bushels,

respectively. An average size of each elevator owned by Firm 1 is 0.37 million bushels, while

an average size of each elevator owned by Firm 2 is 0.32 million bushels. The largest elevator

in this sample is from Firm 1, accounting for approximately 2 million bushels of its capacity

while the smallest elevator from this sample is from Firm 2 with the maximum capacity at

0.011 million bushels. From the sample, the size of the largest elevator owned by Firm 2 is

nearly 1 million bushels, which is only half of the largest elevator from Firm 1.

The characteristics of elevators categorized by county are reported in Table 2. The

majority of elevators in this study are located in Adams County (31 elevators or 37%), whereas

only two elevators (2.4%) are located in Franklin County. On average, each sample elevator in

Adams has the capacity of 456 thousand bushels, followed by average capacity of elevator in

Grant, Spokane, Franklin, Whitman, and Lincoln Counties. Eighteen and seventeen elevators

are located in Adams and Spokane counties, respectively. The largest elevator in this sample

is located in Adams County with the size of almost 2 million bushels, while the smallest

elevator is located in Whitman County with the size of 0.011 million bushels.

The spatial distribution of the two companies’ elevators included in this study are

illustrated in Figure 3. All elevators are located in six counties of the eastern region of

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Washington, i.e. Adams, Franklin, Grant, Lincoln, Spokane and Whitman. In a smaller scale,

a pattern of the two isolated clusters of elevators from the two companies is shown in Figure 4.

The elevators of Firm 2 (green dots) are clustered only within the Whitman and Spokane

counties, while elevators of RW (red dots) are scattered all over the five counties. Two

assigned zones, NE-PNW and NC-PNW, and the two clusters of elevators are shown in Figure

5. It is clearly shown that Firm 2’s elevators are located only within the NE-PNW zone, while

Firm 1’s elevators are located in both NE-PNW and NC-PNW zones. Eight of them are

located in NE-PNW zone, while the rest elevators are located in the NC-PNW zone.

In terms of wheat volume received, Firm 1 received nearly 0.18 million bushels on

average, while elevators from Firm 2 received slightly less than 0.15 million bushels.

Considering wheat volume received by county, Adams County received the highest average of

0.3 million bushels per elevator, followed by Spokane, Grant, Whitman, Franklin and Lincoln

counties (Table 2). Elevators in Lincoln County received wheat volume slightly less than 0.06

million bushels on average.

Not all elevators are able to get access to rail facilities. Rail access represents 1 if an

elevator owns rail facilities, and 0 otherwise. Only 37% of elevators belonging to Firm 1 are

on rail facilities, while about 45% of Firm 2 elevators are on rail facility (Table 1). In terms of

location, 76% of elevators in Spokane have access to rail facilities (Table 2). On the other

hand, elevators in Franklin have no access to rail facilities.

6. Empirical Results

The cost minimizing results from the three scenarios are reported in Tables 4 5. First,

we report the optimization results from the traditional bulk system (Scenario 1). Next, the

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results from Scenario 2 (the transportation with the PNW SWW marketing plan) and the

results from Scenario 3 (the containerized IP system) are compared with the traditional system.

Scenario 1: The traditional bulk system with transshipment among elevators.

Under the traditional bulk transportation system, more than half of the grain shipment

from Firm 1 is moved by the truck-barge combination (Table 4). The results are consistent

with the SFTA survey.3 Approximately 40% of the grain volume from RW is moved by the

rail mode and only 2.5% of the grain volume is transshipped among them. Central Ferry and

Port of Windust are the only two ports that serve the company for the barge service. Firm 2,

on the other hand, moves more than half of its grain volume by railroad to the export terminal

in Portland, while moving approximately 40% of the grain shipment by barge. There is no

transshipment among Firm 2’s elevators. Forty percent of Firm 2’s grain is moved toward Port

of Almota and only a small fraction is transported toward Port of Windust.

Scenario 2: Grain transportation with consideration of the PNW SWW marketing plan

The analysis is grouped into two sections, which are 1) the impacts on directions of

grain flows and 2) the changes in the transportation costs of the two main decision makers.

The change in grain flows from each company’s elevators as a result of different assumptions

on the grain logistic system is shown in Table 4, followed by the directions of changes in grain

flows from the two companies’ elevators to river ports in Table 5.

a. Modal split and Grain flows

It appears that the PNW SWW marketing plan or the grain zoning policy does not

change the transportation mode choice between truck-barge and rail of Firm 1, whose elevators 3 Strategic Freight Transportation Analysis (SFTA): more details available at www.sfta.wsu.edu

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are located in two different production zones. The results from the bulk scenario and the grain

zoning scenario (with a bulk system) show that the truck-barge combination is the main

transportation mode, accounting for 60% of the company’s grain volume while rail mode

accounts only 40% of its grain volume. For Firm 2, there are only slight changes in the modal

split between rail and truck-barge. Under the second scenario, the rail shipment has increased

by 50 thousand bushels or less than one percent through transshipment among the company’s

elevators compared to the first scenario. The rail mode still plays a major role in moving grain

for Firm 2 with nearly 61% of the company’s grain volume.

Alternative grain flows from Firm 1 and Firm 2 toward river ports are shown in Table

5. Under the bulk scenario, Port of Windust and Central Ferry are the only two ports serving

Firm 1. Almost half of the company’s grain volume moves toward Port of Windust, followed

by Central Ferry, which accounts for nearly 11% of grain from RW. In contrast to the first

scenario, the results from the grain zoning scenario indicates more grain movement toward

Central Ferry, which slightly increases to 14%, due to the prohibition of moving grain across

different zones. Consequently, only 46% of grain volume from Firm 1 was shipped to Port of

Pasco.

For Firm 2, Port of Almota and Port of Windust serve the company as its main river

ports under the bulk scenario. Approximately 39% of the company’s grain volume is shipped

to Port of Almota, while less than one percent of its grain is shipped to Port of Windust.

However, the grain zoning scenario changes the flows pattern slightly by prohibiting grain

movement from company’s elevators inside the NE-PNW zone to Port of Pasco within the

NC-PNW zone.

b. Transportation costs

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A slight increase in the transportation costs occurs when shifting to the grain zoning

scenario from no zone. Under the bulk system, the transportation cost of shipping 7.8 million

bushels of grain from Firm 1 to the export terminal in Portland is around $3.38 million. The

transportation cost of shipping the same amount of grain from Firm 1 under the bulk-zoning

scenario becomes $3.40 million. The change in the transportation cost is only a 0.31%

increase. Likewise, moving grain from Firm 2 to Portland under the bulk-zoning scenario also

only slightly increases the transportation cost in the bulk scenario by 0.04 %.

Scenario 3: Grain transportation with the containerized IP system

The analysis in this scenario highlights the grain flows and the transportation costs

under the Identity Preserved (IP) grain logistic or containerized grain transportation. The IP

system requires a highly strict segregation process for every grain shipment. Elevator

companies are recommended to store each type/grade of grain in an elevator in order to avoid

commingling and to lower segregation costs. Consequently, transshipment among elevators is

prohibited in this logistical system.

a. Modal split and Grain flows

Grain flows from Firm 1 and from Firm 2 are reported in Table 4. Under the IP

system, moving grain by rail is not profitable for either companies. They ship all of their

containerized grain by truck-barge to Portland, due to a cheaper barge rate. In contrast to this

scenario, both companies ship some grain by rail under the first two scenarios.

Grain flows from both companies to different river ports are shown in Table 5. For

Firm 1, about 66% of its grain is moved toward Port of Windust, followed by Lyons Ferry,

Central Ferry, and Port of Pasco, at 19%, 11% and 3%, respectively. Under the first two

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scenarios, only Central Ferry and Port of Windust serve the company as two river port

destinations. On the other hand, Firm 2 relies heavily on Port of Almota by shipping its entire

grain volume to the port under the containerized grain system. In the previous scenarios, CAP

ships only 40% of its entire volume to Port of Almota.

b. Transportation costs

In terms of the transportation cost, a large gap exists between the current bulk system

and the containerized system for both companies (Table 4). Firm 1 would experience more

than twice an increase in total transportation costs. Firm 1’s total transportation cost rises up

from $3.4 million to $7.3 million. Also, Firm 2 would have experienced a similar impact.

Firm 2’s total transportation cost rises up from $2.7 million to $7.2 million. The increase in

the total transportation cost under the IP scenario in both companies are by far more significant

than comparable to the slightly increase in the cost under the grain zoning scenario. Therefore,

the grain zoning scenario would be the best alternative for the elevators to the containerized

scenario.

7. Conclusion

This paper evaluates the impacts of the PNW SWW marketing policy or the zoning

policy on the grain transportation cost structure and port destinations. We apply the cost-

minimization linear programming optimization model in order to estimate changes in grain

flows and transportation costs. The analysis constructs three types of transportation scenarios

which are; 1) the traditional bulk system, 2) the transportation under the PNW SWW

marketing plan (with the bulk system) and 3) the containerized IP system. We mainly focus

on the changes in transportation modal splits, grain flows to river ports and transportation costs

133

by comparing impacts of the Zoning system with the IP system. Two elevator companies are

selected as the representatives of two decision makers in the study. Firm 1 owns elevators in

two different zones, while all elevators owned by Firm 2 are in the same zone.

Both Bulk-Zoning and IP systems also serve the same purpose of enhancing the value

of grain products through product differentiation. The system with cost effectiveness would be

more desirable for the industry. The key results show that the zoning policy is more preferable

to the IP system because it is more cost effective. The results show that the IP system costs

both firms’ transportation spending more than two folds of that of the Bulk-Zoning system.

Under the IP system, elevators are required to pay costly containerized rates and they are

prohibited to transship grain among elevators. Moreover, since elevators under the IP system

are required to store only one specific type/grade of grain, the storage cost tends to be higher

than elevators under the Bulk-Zoning system in which are able to segregate grain.

Under the grain zoning system, Firm 1, which own elevators in two zones, experience a

higher transportation costs by larger percentage points than that of Firm 2, whose elevators are

located in the same zone. The zoning system also causes a change in Firm 1’s grain flows to

river ports, in which almost three percent of its grain is redirected from one river port to the

other. In terms of modal splits, the Bulk-Zoning system does not affect Firm 1’s mode of

transportation used, but it affects Firm 2 slightly. In that the system causes Firm 2 to switches

approximately one percent of its grain from using the truck-barge combination to using the rail

mode due to the restriction of moving grain across zones.

The implication of the PNW SWW plan or the zoning policy on river ports is

substantial since elevators and farmers are encouraged not to ship grain across two different

zones; NC-PNW and NE-PNW. In another word, grain products from counties in NC-PNW,

134

such as Douglas, Grant, Lincoln, Adams and Franklin, are not allowed to delivered to any

other river ports rather than either Tri-Cities (Pasco, Kennewick and Burbank) or Port of

Windust. At the same time, grain products from counties in NE-PNW, such as Whitman,

Spokane, Ferry and Stevens, are only moved to Lyons Ferry, Central Ferry, Almota, and Port

of Wilma. Under this constraint, the results indicate that the zone restriction reduces grain

flows to Port of Windust by almost seven percent of the grain flows from the companies to the

port under the Bulk system scenario.

In terms of transportation costs, the optimization results show that there is only a slight

increase in the transportation cost and the unit cost from switching from the traditional bulk

system to the grain zoning system. That is under the grain zoning system, Firm 1, that own

elevators on both zones experience an additional transportation cost of $11,000 and the cost of

firm 2 increases by $2,000, accounting only 0.33 % and 0.069 %, respectively. Moreover,

shipping grain under the grain zoning system results in an increase in Firm 1’s and Firm 2’s

unit cost by only 0.14 cent/bushel and 0.034 cent/bushel.

135

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TABLES

Table 3.1 Distribution and characteristics of elevators by model companies

No. of Elevators capacity (’000 bushels) Wheat received

(’000 bushels) Rail elevator Total Mean Min Max Total Mean Min Max Access*

Firm 1 43 15,851 369 72 1,971 7,818 182 6 928 0.37

Firm 2 40 12,670 317 11 997 5,887 147 3 936 0.45

Total 83 28,521 343 11 1,971 13,705 165 3 936 0.41

Note: * = 1, if there is rail access, 0 otherwise Table 3.2 Distribution of elevators by counties

No. of Elevators capacity

(’000 bushels) Wheat received

(’000 bushels) Rail Elevator Total Mean Min Max Total Mean Min Max Access*

Adams 18 8,205 456 101 1,971 5,406 300 14 928 0.33

Franklin 2 646 323 245 401 127 64 49 78 0.00 Grant 5 2,261 452 248 543 622 124 36 222 0.20

Lincoln 10 1,942 194 72 529 593 59 6 242 0.20 Spokane 17 6,457 380 75 836 3,624 213 3 936 0.76 Whitman 31 9,010 291 11 997 3,333 108 13 340 0.39

Total 83 28,521 343 11 1,971 13,705 165 3 936 0.41

Note: * = 1, if there is rail access, 0 otherwise

138

139

Table 3.3 Transportation rates used in the study

Rail Barge Truck* Bulk System (1) $0.28 - $0.65 $0.15 - $0.20 $0.036018 + ($0.001911*miles) + ($0.151866/miles) Handling charges (2) $0.12 $0.04 Containerized System (3), (4) $1.67 $0.26 - $0.36 $0.012 Handling charges (5) $0.22 $0.22 Note: * for both directions

Sources:(1) Clark, Jessup, and Casavant (2003) (2) Reichert and Vachal (2003) (3) Kratochvil (2005) (4) Tidewater qouted rates on the Port of Portland website http://www.flypdx.com/cntner_brgng_rates.aspx (5) Kosior, Prentice, and Vido (2002)

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Table 3.4 Model results: modal splits, volume shipped and total cost

Scenario Total wheat ('000 bushels) Truck-Barge Rail Transshipment

Total transportation

cost ('000 USD)

Company: Firm #1 1 7,818 4,699 3,118 195 3,382 60.11% 39.89% 2.50% 2 7,818 4,699 3,118 195 3,393 60.11% 39.89% 2.50%

3 7,818 7,818 0 0 7,314

100.00% 0.00% 0.00%

Company: Firm #2 1 5,887 2,349 3,538 0 2,869

39.90% 60.10% 0.00% 2 5,887 2,299 3,588 50 2,871

39.05% 60.95% 0.85%

3 5,887 5,887 0 0 7,228 100.00% 0.00% 0.00%

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Table 3.5 Model results: wheat flows to river ports, different scenarios

Scenario Total wheat ('000 bushels)

River ports (destination)

Volume shipped ('000 bushels)

Volume/Total wheat (%)

Company: Firm #1

1. Traditional bulk system 7,818 Central Ferry 852 10.90% Lyons Ferry 0 0.00% Windust 3,847 49.21% Pasco 0 0.00%

2. With the PNW SWW marketing plan 7,818 Central Ferry 1,070 13.68%

Lyons Ferry 0 0.00% Windust 3,630 46.43% Pasco 0 0.00%

3. Containerized system 7,818 Central Ferry 889 11.38% Lyons Ferry 1,483 18.96% Windust 5,188 66.36% Pasco 258 3.30%

Company: Firm #2

1. Traditional bulk system 5,887 Port of Almota 2,299 39.05% Windust 50 0.85%

2. With the PNW SWW marketing plan 5,887 Port of Almota 2,299 39.05%

Windust 0 0.00%

3. Containerized system 5,887 Port of Almota 5,887 100.00% Windust 0 0.00%

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FIGURES Figure 3.1 Grain production zones associated with SWW quality

Source: Washington Wheat Commission

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Figure 3.2 Grain shed areas within the three states Source: Washington Wheat Commission

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Figure 3.3 Sample elevators’ distribution

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Figure 3.4 The distribution of Firm 1 and Firm 2’s elevators

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Figure 3.5 Sample elevators and two production zones

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Figure 3.6 Two transportation networks and sample elevators

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APPENDIX

APPENDIX 2.1: GAMS CODE FOR GRAIN FLOWS OPTIMIZATION SET N NODES FOR THE ENTIRE NETWORK / EL01295001, EL01295002, EL01295003, EL00295004, EL00295005, EL00295006, EL00295007, EL01295008, EL00295009, EL01295010, EL00295011, EL00295012, EL00295013, EL00295014, EL00295015, EL00295016, EL00295017, EL01295018, EL00295019, EL01295020, EL00295021, EL01295022, EL01295023, EL01295024, EL01295025, EL00295026, EL00295027, EL00295028, EL00295029, EL00295030, EL00295031, EL00295032, EL00295033, EL00295034, EL00295035, EL01295036, EL00295037, EL00295038, EL01295039, EL01295040, EL00295041, EL00295042, EL01295043, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL00337011, EL00337012, EL01337013, EL01337014, EL00337015, EL00337016, EL00337017, EL00337018, EL01337019, EL01337020, EL00337021, EL01337022, EL00337023, EL01337024, EL01337025, EL00337026, EL01337027, EL00337028, EL01337029, EL00337030, EL01337031, EL00337032, EL01337033, EL00337034, EL00337035, EL00337036, EL00337037, EL00337038 PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST, PORTLAND/ A(N,N) DIRECTED ARCS M MODES /TRUCK, RAIL26, RAIL110, BARGE/ ******** WHEAT RELATED NODES *********** WPRI(N) WHEAT PRIMARY NODES / EL01295001, EL01295002, EL01295003, EL00295004, EL00295005, EL00295006, EL00295007, EL01295008, EL00295009, EL01295010, EL00295011, EL00295012, EL00295013, EL00295014, EL00295015, EL00295016, EL00295017, EL01295018, EL00295019, EL01295020, EL00295021, EL01295022, EL01295023, EL01295024, EL01295025, EL00295026, EL00295027, EL00295028, EL00295029, EL00295030, EL00295031, EL00295032, EL00295033, EL00295034, EL00295035, EL01295036, EL00295037, EL00295038, EL01295039, EL01295040, EL00295041, EL00295042, EL01295043, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL00337011, EL00337012, EL01337013, EL01337014, EL00337015, EL00337016, EL00337017, EL00337018, EL01337019, EL01337020, EL00337021, EL01337022, EL00337023, EL01337024, EL01337025, EL00337026, EL01337027, EL00337028, EL01337029, EL00337030, EL01337031, EL00337032, EL01337033, EL00337034, EL00337035, EL00337036, EL00337037, EL00337038 / WINT(N) WHEAT INTERMEDIATE NODES / EL01179001, EL01179002, EL01179005, EL01179006, EL01179007, EL01179008, EL01179009, EL01179010, EL01289001, EL01289002, EL01289003, EL01289004, EL01289005, EL01289008, EL01289009, EL01295001, EL01295002, EL01295003, EL01295008, EL01295010, EL01295018, EL01295020, EL01295022, EL01295023, EL01295024, EL01295025, EL01295036, EL01295039, EL01295040, EL01295043,

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EL01305001, EL01305002, EL01305003, EL01305004, EL01305005, EL01305012, EL01305013, EL01305014, EL01305015, EL01305016, EL01305017, EL01305018, EL01305019, EL01305020, EL01305021, EL01305022, EL01305023, EL01305024, EL01305025, EL01305026, EL01305027, EL01305028, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL01337013, EL01337014, EL01337019, EL01337020, EL01337022, EL01337024, EL01337025, EL01337027, EL01337029, EL01337031, EL01337033, EL01474001, EL01474002, EL01474003, EL01474004, EL01474006, EL01474009, EL01474010, EL01474011, EL01474012, EL01534001, EL01534002, EL01534005, EL01534006, EL01534007, EL01534009, EL01534010, EL01534011, EL01074001, EL01074009, EL01074010, EL01074012, EL01074013, EL01074014, EL01852005, EL01852006, EL01852015, EL01852016, EL01852017, EL01852018, EL01852019, EL01852020, EL01852021, EL01852022, EL01852023, EL01852024, EL01852025, EL01852026, EL01852030, EL01852031, EL01852032, EL01852033, EL01898001, EL01898002, EL01898005, EL01898006, PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST / RELEV(N) ELEVATORS WITH RAIL / EL01295001, EL01295002, EL01295003, EL01295008, EL01295010, EL01295018, EL01295020, EL01295022, EL01295023, EL01295024, EL01295025, EL01295036, EL01295039, EL01295040, EL01295043, EL01337001, EL01337002, EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL01337013, EL01337014, EL01337019, EL01337020, EL01337022, EL01337024, EL01337025, EL01337027, EL01337029, EL01337031, EL01337033 / ELEV(N) ELEVATORS WITHOUT RAIL / EL00295004, EL00295005, EL00295006, EL00295007, EL00295009, EL00295011, EL00295012, EL00295013, EL00295014, EL00295015, EL00295016, EL00295017, EL00295019, EL00295021, EL00295026, EL00295027, EL00295028, EL00295029, EL00295030, EL00295031, EL00295032, EL00295033, EL00295034, EL00295035, EL00295037, EL00295038, EL00295041, EL00295042, EL00337011, EL00337012, EL00337015, EL00337016, EL00337017, EL00337018, EL00337021, EL00337023, EL00337026, EL00337028, EL00337030, EL00337032, EL00337034, EL00337035, EL00337036, EL00337037, EL00337038 / IPORT(N) INTERMEDIATE PORTS / PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST / DESPL(N) WHEAT PRIMARY DESTINATION NODE / PORTLAND / DES1(N) WHEAT PRIMARY DESTINATION NODE / PORTLAND / DES2(N) WHEAT SECONDARY DESTINATIONS / EL01295001, EL01295002, EL01295003, EL01295008, EL01295010, EL01295018, EL01295020, EL01295022, EL01295023, EL01295024, EL01295025, EL01295036, EL01295039, EL01295040, EL01295043, EL01337001, EL01337002,

150

EL01337003, EL01337004, EL01337005, EL01337006, EL01337007, EL01337008, EL01337009, EL01337010, EL01337013, EL01337014, EL01337019, EL01337020, EL01337022, EL01337024, EL01337025, EL01337027, EL01337029, EL01337031, EL01337033, PORTALMOTA, BURBANK, CENTRALFERRY, LYONSFERRY, PASCO, PORTWILMA, WINDUST/ ; PARAMETERS RAILCAPW(N) RAIL CAPACITY FOR WHEAT / EL01295001 844261.43 EL01295002 502233.83 EL01295003 687869.63 EL01295018 193362.00 EL01295036 114757.02 EL00295038 5343.00 EL01295043 103756.99 EL01337001 82479.00 EL01337002 6532.26 EL01337003 193686.65 EL01337004 58122.19 EL01337005 13467.74 EL01337006 47726.61 EL01337007 95583.76 EL01337008 28790.32 EL01337009 125108.60 EL01337010 17027.99 EL01337013 224000.00 EL01337014 104952.22 EL01337019 2548.51 EL01337020 448000.00 EL01337022 33828.93 EL01337024 234000.00 EL01337027 613263.83 EL01337031 187118.64 EL01337033 17627.12 / WSUP(N) AVAILABLE WHEAT BU / EL01295001 927759.815 EL01295002 551905.312 EL01295003 755900.693 EL00295004 89108.551 EL00295005 160600.100 EL00295006 40850.898 EL00295007 620000.000 EL01295008 45272.893 EL00295009 356000.000 EL01295010 348000.000 EL00295011 12129.879 EL00295012 62298.116 EL00295013 124427.003 EL00295014 118276.619

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EL00295015 121588.364 EL00295016 258000.000 EL00295017 408000.000 EL01295018 222000.000 EL00295019 36000.000 EL01295020 49000.000 EL00295021 242000.000 EL01295022 32468.521 EL01295023 57786.237 EL01295024 20628.731 EL01295025 6339.037 EL00295026 80516.325 EL00295027 27729.689 EL00295028 51116.173 EL00295029 17397.296 EL00295030 14240.824 EL00295031 19379.266 EL00295032 89188.667 EL00295033 78000.000 EL00295034 330000.000 EL00295035 374000.000 EL01295036 118919.192 EL00295037 138000.000 EL00295038 137000.000 EL01295039 37000.000 EL01295040 180180.000 EL00295041 213000.000 EL00295042 138060.000 EL01295043 107520.202 EL01337001 82479.004 EL01337002 13064.516 EL01337003 193686.649 EL01337004 72652.739 EL01337005 26935.484 EL01337006 47726.615 EL01337007 119479.700 EL01337008 57580.645 EL01337009 125108.601 EL01337010 21284.982 EL00337011 79504.950 EL00337012 230000.000 EL01337013 280000.000 EL01337014 104952.215 EL00337015 41629.213 EL00337016 118275.862 EL00337017 42640.449 EL00337018 81586.207 EL01337019 2548.509 EL01337020 560000.000 EL00337021 83316.832 EL01337022 42286.165 EL00337023 100000.000 EL01337024 260000.000 EL01337025 91351.351 EL00337026 250000.000 EL01337027 613263.829

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EL00337028 30000.000 EL01337029 55945.946 EL00337030 340000.000 EL01337031 935593.220 EL00337032 16507.666 EL01337033 88135.593 EL00337034 28160.136 EL00337035 50000.000 EL00337036 34795.571 EL00337037 115000.000 EL00337038 55000.000 / ALIAS(N,NP); TABLE WARCS(N,NP,M) TRANSPORT AND HANDLING COSTS BY MODE TRUCK RAIL26 RAIL110 BARGE BURBANK.PORTLAND 0.15800 CENTRALFERRY.PORTLAND 0.19371 LYONSFERRY.PORTLAND 0.18343 PASCO.PORTLAND 0.17229 PORTALMOTA.PORTLAND 0.19486 PORTWILMA.PORTLAND 0.20257 WINDUST.PORTLAND 0.15800 EL01305001.WINDUST 0.16270 EL01305001.LYONSFERRY 0.18304 EL01305001.PORTLAND 0.36176 0.33235 EL01305002.WINDUST 0.16270 EL01305002.LYONSFERRY 0.18304 EL01305002.PORTLAND 0.36176 0.33235 EL01305003.WINDUST 0.16270 EL01305003.LYONSFERRY 0.18304 EL01305003.PORTLAND 0.36176 0.33235 EL01305004.WINDUST 0.16270 EL01305004.LYONSFERRY 0.18304 EL01305004.PORTLAND 0.36176 0.33235 EL01305005.WINDUST 0.18227 EL01305005.LYONSFERRY 0.20270 EL01305005.PORTLAND 0.37206 0.34265 EL00305006.EL01305014 0.07016 EL00305006.EL01305015 0.07016 EL00305006.EL01305016 0.07016 EL00305006.WINDUST 0.18327 EL00305006.LYONSFERRY 0.20370 EL00305007.EL01305001 0.07035 EL00305007.EL01305002 0.07035 EL00305007.EL01305003 0.07035 EL00305007.EL01305004 0.07035 EL00305007.WINDUST 0.15220 EL00305007.LYONSFERRY 0.17247 EL00305008.EL01305001 0.07023 EL00305008.EL01305002 0.07023 EL00305008.EL01305003 0.07023

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EL00305008.EL01305004 0.07023 EL00305008.WINDUST 0.14750 EL00305008.LYONSFERRY 0.16775 EL00305009.EL01305001 0.07012 EL00305009.EL01305002 0.07012 EL00305009.EL01305003 0.07012 EL00305009.EL01305004 0.07012 EL00305009.WINDUST 0.15115 EL00305009.LYONSFERRY 0.17493 EL00305010.EL01305001 0.07172 EL00305010.EL01305002 0.07172 EL00305010.EL01305003 0.07172 EL00305010.EL01305004 0.07172 EL00305010.WINDUST 0.14849 EL00305010.LYONSFERRY 0.15832 EL00305011.EL01305012 0.07713 EL00305011.EL01305013 0.07713 EL00305011.WINDUST 0.14009 EL00305011.LYONSFERRY 0.14988 EL01305012.WINDUST 0.19065 EL01305012.LYONSFERRY 0.18544 EL01305012.PORTLAND 0.36176 0.33235 EL01305013.WINDUST 0.19065 EL01305013.LYONSFERRY 0.18544 EL01305013.PORTLAND 0.36176 0.33235 EL01305014.WINDUST 0.18461 EL01305014.LYONSFERRY 0.17941 EL01305014.PORTLAND 0.36176 0.33235 EL01305015.WINDUST 0.18461 EL01305015.LYONSFERRY 0.17941 EL01305015.PORTLAND 0.36176 0.33235 EL01305016.WINDUST 0.18461 EL01305016.LYONSFERRY 0.17941 EL01305016.PORTLAND 0.36176 0.33235 EL01305017.WINDUST 0.18791 EL01305017.LYONSFERRY 0.18271 EL01305017.PORTLAND 0.35000 0.32059 EL01305018.WINDUST 0.18791 EL01305018.LYONSFERRY 0.18271 EL01305018.PORTLAND 0.35000 0.32059 EL01305019.WINDUST 0.18791 EL01305019.LYONSFERRY 0.18271 EL01305019.PORTLAND 0.35000 0.32059 EL01305020.WINDUST 0.18791 EL01305020.LYONSFERRY 0.18271 EL01305020.PORTLAND 0.35000 0.32059 EL01305021.WINDUST 0.22703 EL01305021.LYONSFERRY 0.22178 EL01305021.PORTLAND 0.37941 0.35000 EL01305022.WINDUST 0.24763 EL01305022.LYONSFERRY 0.24239 EL01305022.PORTLAND 0.37941 0.35000 EL01305023.WINDUST 0.21390 EL01305023.LYONSFERRY 0.20865 EL01305023.PORTLAND 0.37941 0.35000 EL01305024.WINDUST 0.21390

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EL01305024.LYONSFERRY 0.20865 EL01305024.PORTLAND 0.37941 0.35000 EL01305025.WINDUST 0.21390 EL01305025.LYONSFERRY 0.20865 EL01305025.PORTLAND 0.37941 0.35000 EL01305026.WINDUST 0.21142 EL01305026.LYONSFERRY 0.23755 EL01305026.PORTLAND 0.37206 0.34265 EL01305027.WINDUST 0.21142 EL01305027.LYONSFERRY 0.23755 EL01305027.PORTLAND 0.37206 0.34265 EL01305028.WINDUST 0.21142 EL01305028.LYONSFERRY 0.23755 EL01305028.PORTLAND 0.37206 0.34265 ; VARIABLES W(N,NP,M) FLOW FROM N TO NP VIA MODE K TC TOTAL COST WTC WHEAT TOTAL COST; POSITIVE VARIABLE W; EQUATIONS WNB(N) NODE BALANCE WHEAT WSB(N) SUPPLY BALANCE WHEAT WCOST ACCTING: TOTAL COST WHEAT DESBAL; * DESBAL..SUM((WINT,DES1,M)$WARCS(WINT,DES1,M),W(WINT,DES1,M)) =E= 6341558.000; WSB(WPRI)..SUM((WINT,M)$WARCS(WPRI,WINT,M),W(WPRI,WINT,M)) =L= WSUP(WPRI); WNB(WINT)..SUM((WPRI,M)$WARCS(WPRI,WINT,M),W(WPRI,WINT,M)) =E= SUM((DES1,M)$WARCS(WINT,DES1,M),W(WINT,DES1,M)); WCOST..TC =E= SUM((WPRI,WINT,M)$WARCS(WPRI,WINT,M),WARCS(WPRI,WINT,M)*W(WPRI,WINT,M)) + SUM((WINT,DES1,M)$WARCS(WINT,DES1,M),WARCS(WINT,DES1,M)*W(WINT,DES1,M)); *SUM((N,NP,M)$WARCS(N,NP,M),WARCS(N,NP,M)*W(N,NP,M)); MODEL TEST /ALL/; OPTION LIMROW = 5; OPTION LIMCOL = 5; OPTION RESLIM = 5000; OPTION ITERLIM = 100000; SOLVE TEST MINIMIZING TC USING LP; DISPLAY W.L, TC.L; FILE RES /'EJ.DAT'/;

155

PUT RES; PUT "TOTAL COST = "/; PUT TC.L /; PUT /; *** PUT "WHEAT ARCS"/; *** LOOP ((N,NP,M), *** IF (W(N,NP,M) GT 0, *** PUT N.TL, NP.TL, M.TL, W(N,NP,M)/)); PUT "WHEAT ARCS FOR ELEVATORS TO ELEVATORS WITH RAIL"/; LOOP ((ELEV, RELEV, M), IF (W.L(ELEV,RELEV,M)GT 0, PUT ELEV.TL, RELEV.TL, M.TL, W.L(ELEV,RELEV,M)/)); PUT "WHEAT ARCS FOR ELEVATORS TO RIVER PORTS"/; LOOP ((ELEV, IPORT, M), IF (W.L(ELEV,IPORT,M)GT 0, PUT ELEV.TL, IPORT.TL, M.TL, W.L(ELEV,IPORT,M)/)); PUT "WHEAT ARCS FOR ELEVATORS WITH RAIL TO PORTLAND"/; LOOP ((IPORT,DES1,M), IF (W.L(IPORT,DES1,M)GT 0, PUT IPORT.TL, DES1.TL, M.TL, W.L(IPORT,DES1,M)/));