lecture-10: freight mode choice - ce.memphis.edu

F R E I G H T T R A V E L D E M A N D M O D E L I N G

C I V L 7 9 0 9 / 8 9 8 9

D E P A R T M E N T O F C I V I L E N G I N E E R I N G

U N I V E R S I T Y O F M E M P H I S

1

Lecture-10: Freight Mode Choice

11/14/2014

Outline2

1. Objective of Mode Choice

2. A simple Example

3. Discrete Choice Framework

4. The Random Utility Model

5. Binary Choice Models

6. Freight Mode Choice Models

7. Case Studies

Basics of Mode Choice (1)3

• Mode choice determines the number of trips between zones that are made by different modes (such as truck, rail, water, and air).

truck

rail


1 2 3

1 a11 a12 a13

2 a21 a22 a23

3 a31 a32 a33

Trip Distribution

(Number of trips from origin->destination)

Mode Choice

(Number of trips from origin->destination

by mode)

1 2 3

1 𝑎11𝑚1 𝑎12

𝑚1 𝑎13𝑚1

2 𝑎21𝑚1 𝑎22

𝑚1 𝑎23𝑚1

3 𝑎31𝑚1 𝑎32

𝑚1 𝑎33𝑚1

1 2 3

1 𝑎11𝑚2 𝑎12

𝑚2 𝑎13𝑚2

2 𝑎21𝑚2 𝑎22

𝑚2 𝑎23𝑚2

3 𝑎31𝑚2 𝑎32

𝑚2 𝑎33𝑚21 2 3

1 𝑎11𝑚3 𝑎12

𝑚3 𝑎13𝑚3

2 𝑎21𝑚3 𝑎22

𝑚3 𝑎23𝑚3

3 𝑎31𝑚3 𝑎32

𝑚3 𝑎33𝑚3

𝑝𝑟𝑠𝑚1

𝑝𝑟𝑠𝑚2

𝑝𝑟𝑠𝑚3

𝑟

𝑠

𝑚𝑖

𝑝𝑟𝑠𝑚𝑖 = 1

Where,

r: origin

s: destination

mi: mode I

p: probability


How to estimate the probability of choosing a mode

(𝑝𝑟𝑠𝑚𝑖)

Typically done by random utility maximization

Each mode is a choice given to the commodities to be carried from origin to destination

The attractiveness of each mode can be represented as an utility function

Derived from discrete choice theories

Let’s consider a simple example to get a glimpse of choice models

A Simple Example

6

Mobile Phone Choice

Education

Low(k=1) Medium(k=2) High(k=3)

Smartphone(i=1) 10 100 90 200

Feature phone (i=2) 140 200 60 400

150 300 150 600

25% 50% 25%

• Sample size: N = 600 (Random)

• Mobile phone choice (Smartphone, feature phone)

• Education (Low, Medium, high)

Example: Marginal and Joint Probabilities

• (Marginal) probability of choosing smartphone: P(i = 1)

𝑃 𝑖 = 1 =200

600=

1

3

• (Joint) probability of choosing smartphone and having medium level education: P(i = 1, k =2)

𝑃 𝑖 = 1, 𝑘 = 2 =100

600=

1

6

𝑖=1

2

𝑘=1

3

𝑝 𝑖, 𝑘 = 1

Joint and Marginal Probabilities

Mobile Phone ChoiceEducation Mobile Phone

Choice MarginalLow(k=1) Medium(k=2) High(k=3)

Smartphone(i=1)10

600=

1

60

10

600=

1

60

90

600=

3

20

200

600=

1

3

Feature phone (i=2)140

600=

7

30

200

600=

1

3

60

600=

1

10

400

600=

2

3

Educational Marginal

150

600=

1

4

300

600=

1

2

150

600=

1

4

Example: Model Estimation

• Estimates of the unknown parameters:

𝜋1 = 𝑃 𝑖 = 1 𝑘 = 1 = 𝑃(𝑖 = 1, 𝑘 = 1)

𝑃(𝐾 = 1)=

160

14

=1

15= 0.067

𝜋2 = 𝑃 𝑖 = 1 𝑘 = 2 = 𝑃(𝑖 = 1, 𝑘 = 2)

𝑃(𝐾 = 2)=

16

12

=1

3= 0.333

𝜋3 = 𝑃 𝑖 = 1 𝑘 = 3 = 𝑃(𝑖 = 1, 𝑘 = 3)

𝑃(𝐾 = 3)=

320

14

=3

5= 0.6

Maximum Likelihood Estimation12

Sampling Distribution

• Estimates are not point values, but are distributed

• Hypothetical distribution around the true meanfr

equen

cy

Sampling

distribution

𝜋2 𝜋2

Standard Errors

• Compute the standard error of the estimates

• Since outcomes are Bernoulli random variables

𝑠1 = 𝜋1. (1 − 𝜋1)

𝑁1=

1/15. (1 − 1/15)

150= 0.020

𝑠2 = 𝜋2. (1 − 𝜋2)

𝑁2=

1/3. (1 − 1/3)

300= 0.027

𝑠3 = 𝜋3. (1 − 𝜋3)

𝑁3=

3/5. (1 − 3/5)

150= 0.040

Standard errors

Standard Error of Forecast

• Predicted smartphone share:

𝑃 𝑖 = 1 =

𝑘=1

3

𝜋𝑘 . 𝑃 𝑘

• The estimated standard of the predicted smartphone share is

𝑆 𝑝(𝑖=1) =

𝑘=1

3

𝑃 𝑘 2𝑠𝑘2 ≈ 0.0175 = 1.75%

Discrete Choice Framework

• Decision-Maker

- Individual (person/household)

- Socio-economic characteristics (e.g. age, gender, education, income)

• Alternatives

- Decision-maker n selects one and only one alternative from a choice set

Cn = {1,2,…,i,…,Jn} with Jn alternatives

• Attributes of alternatives (e.g. price, quality)

• Decision Rule

- Dominance, satisfaction, utility etc.

Mobile Phone Choice

• Decision Maker: An individual or a household

• Choice set: Alternative mobile phones

• Decision rule: Utility maximization

• Utility function: Function of attributes of the mobile phone, such as price and quality

Decision Maker Choice

Utility maximization

- Decision maker chooses the alternative that has the maximum utility (and falls within the set of considered alternatives)

If U(smartphone)>U(feature phone), choose smartphone

If U(smartphone)<U(feature phone), choose feature phone

U(smartphone) = ?

U(feature phone) = ?

Constructing the Utility Function

• U(smartphone)= U(pricesmartphone, qualitysmartphone, …)

U(feature phone)= U(pricefeaturephone, qualityfeaturephone, …)

• Assume linearity (in the parameters)

U(smartphone) = 𝛽1 × (pricesmartphone) + 𝛽2 ×(qualitysmartphone) + …

• Parameters represent tastes, which may bary across people

- Include socio-economic characteristics )e.g. age, gender, income)

- U(smartphone) = 𝛽1 × (pricesmartphone/income) + …

+ 𝛽2 × (qualitysmartphone)

Decision Maker Choice

If U(smartphone) - U(feature phone) > 0 , Probability(smartphone) = 1

If U(smartphone) - U(feature phone) < 0 , Probability(smartphone) = 0

1

00

P(smartphone)

U(smartphone) - U(feature phone)

Probabilistic Choice

• Random Utility Model (RUM)

Ui = V(attributes of I; parameters) + ɛi

• What is in the ɛ ? Analysts’ imperfect knowledge

- Unobserved attributes

- Unobserved taste variations

- Measurement errors

- Use of proxy variables

• U(smartphone) = 𝛽1 × (pricesmartphone) + 𝛽2 ×(qualitysmartphone) + … +

ɛsmartphone= V(smartphone) + ɛsmartphone

Probabilistic Binary Choice

1

00

P(smartphone)

V(smartphone) - V(feature phone)

3. The Random Utility Model

• Decision rule: Utility maximization

- Individual n selects the alternative i with the highest utility Uin

among those in the choice set Cn

• Utility: Uin = Vin + ɛin

• Vin: Systematic utility expressed as a function of k observable variables,

e.g. 𝑘 𝛽𝑘𝑥𝑖𝑛𝑘 = 𝛽′𝑥𝑖𝑛

• ɛin : Random utility component

The Random Utility Model (Cont.)

• Choice Probability

P(i|Cn) = P(Uin ≥ Ujn ∀ j ∈ Cn)

= P(Uin - Ujn ≥ 0,∀ j ∈ Cn)

= P(Uin = maxj Ujn ,∀ j ∈ Cn)

• For binary choice,

Pn(1) = P(U1n ≥ U2n)

= P(U1n − U2n ≥ 0)

Example with Attributes

𝑈1 = 𝛽1𝑞1 − 𝛽2𝑝1 + 𝜀1𝑈2 = 𝛽1𝑞2 − 𝛽2𝑝2 + 𝜀2

𝛽1, 𝛽2 ≥ 0

Mobile Phone ChoiceAttributes

UtilityQuality (q) Price (p)

Smartphone(i=1) 𝑞1 𝑝1 𝑈1

Feature phone (i=2) 𝑞1 𝑝2 𝑈2

Example with Attributes(Cont.)

Ordinal utility

- Decision are based on utility differences

- Unique up to order preserving transformation

𝑈1 = (𝛽1𝑞1 − 𝛽2𝑝1 + 𝜀1 + 𝛼)𝜇∗

𝑈2 = (𝛽1𝑞2 − 𝛽2𝑝2 + 𝜀2 + 𝛼)𝜇∗

𝛽1, 𝛽2, 𝜇∗ ≥ 0


𝑈1 =𝛽1

𝛽2𝑞1 − 𝑝1 + 𝜀1

𝑈2 =𝛽1

𝛽2𝑞2 − 𝑝2 + 𝜀2

𝛽 =𝛽1

𝛽2= "𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑞𝑢𝑎𝑙𝑖𝑡𝑦"

𝑉1 =𝛽1

𝛽2𝑞1 − 𝑝1

𝑉2 =𝛽1

𝛽2𝑞2 − 𝑝2

𝑈1 − 𝑈2 = −𝛽1

𝛽2𝑞2 − 𝑞1 − 𝑝1 − 𝑝2 + 𝜀1 − 𝜀2


• Attributes: Describing the alternative

- Generic vs. Alternative Specific

• Examples: Price per call, monthly fee

- Quantitative vs. Qualitative

• Examples: Quality

• Characteristics: Describing the decision-maker

- Socio-economic

Random Terms

• Distribution of epsilons (ε)

• Variance/covariance structure

- Correlations between alternatives

- Multidimensional decision (e.g. mobile phone type and service provider)

• Typical models

- Probit (normal error terms)

- Logit (i.i.d. “Extreme Value” error terms)

4.Binary Choice Models

Choice Set Cn={1,2} ∀ n

Pn(1) = P(1| Cn)=P( U1n ≥ U2n)

= P(V1n + 𝜀1n ≥ V2n + 𝜀2n)

= P(V1n –V2n ≥ 𝜀2n - 𝜀1n)

= P(V1n –V2n ≥ 𝜀n)

= P(Vn ≥ 𝜀n)= F𝜀(Vn)

Binary Probit Model

“Probit” name comes from Probability Unit

𝜀1𝑛 ~ 𝑁(0, 𝜎12)

𝜀2𝑛 ~ 𝑁(0, 𝜎22)

𝜀𝑛 ~ 𝑁(0, 𝜎2) where 𝜎2 =𝜎12+𝜎2

2 − 2𝜎12

𝑓 𝜀 =1

𝜎 2𝜋𝑒−

12(

𝜀𝜎)2

𝑃𝑛 1 = 𝐹𝜀 𝑉𝑛 = −∞

𝑉𝑛 1

𝜎 2𝜋𝑒−

12(𝜀𝜎

)2

𝑑𝜀 = Φ(𝑉𝑛

𝜎)

Where Φ(z) is the standardized cumulative normal distribution

Binary Logit Model

“Logit” name comes from Logistic Probability Unit

𝜀1𝑛 ~ Extreme value(0, 𝜇) 𝐹𝜀 𝜀1𝑛 =exp[-𝑒−𝜇𝜀1𝑛]

𝜀2𝑛 ~ Extreme value(0, 𝜇) 𝐹𝜀 𝜀2𝑛 =exp[-𝑒−𝜇𝜀2𝑛]

𝜀𝑛 ~ Logistic (0, 𝜇) 𝐹𝜀 𝜀𝑛 =1

1+𝑒−𝜇𝜀𝑛

𝑃𝑛 1 = 𝐹𝜀 𝑉𝑛 =1

1 + 𝑒−𝜇𝜀𝑛

Logit vs Probit

• Probit

𝑃𝑛 1 = Φ𝑉𝑛

𝜎=

−∞

𝑉𝑛𝜎 1

2𝜋𝑒−

1

2𝜀2

𝑑𝜀 = −∞

𝑉1𝑛−𝑉2𝑛𝜎 1

2𝜋𝑒−

1

2𝜀2

𝑑𝜀

• Logit

𝑃𝑛 1 =1

1+𝑒−𝜇𝑉𝑛=

1

1+𝑒−𝜇(𝑉1𝑛−𝑉2𝑛) = 𝑒𝜇𝑉1𝑛

𝑒𝜇𝑉1𝑛+𝑒𝜇𝑉2𝑛

• 𝑉1𝑛 = 𝛽′𝑥1𝑛, 𝑉2𝑛 = 𝛽′𝑥2𝑛, 𝑉𝑛 = 𝛽′(𝑥1𝑛 − 𝑥2𝑛)

Why Logit?

• Probit does not have a closed form-the choice probability is an integral

• The logistic distribution is used because

• It approximates a normal distribution quite well

• It is analytically convenient

• Extreme Value distribution can be “justified” because of utility maximization

• Logit does have “fatter” tails than a normal distribution

Summary

• A simple Example

• Discrete Choice Framework

• The Random Utility Model

• Binary Choice Models

• Probit 𝑃𝑛 1 = Φ 𝑉𝑛 = −∞

𝑉𝑛 1

2𝜋𝑒−

1

2𝜀2

𝑑𝜀

(normalize σ = 1)

• Logit 𝑃𝑛 1 =1

1+𝑒−𝑉𝑛=

𝑒𝑉1𝑛

𝑒𝑉1𝑛+𝑒𝑉2𝑛

(normalize μ = 1)

• 𝑉1𝑛 = 𝛽′𝑥1𝑛, 𝑉2𝑛 = 𝛽′𝑥2𝑛, 𝑉𝑛 = 𝛽′(𝑥1𝑛 − 𝑥2𝑛)

Additional Readings

• Ben-Akiva, M. and Lerman, S. (1985), Discrete Choice Analysis: Theory and Application to Travel Demand, MIT Press, Cambridge MA, USA, Chapters 1-7.

Maximum Likelihood Estimation

Log likelihood function:𝐿 𝛽 = 𝑙𝑛𝐿∗ 𝛽 = 𝑛=1

𝑁 𝑙𝑛𝑃 𝑦𝑛 𝑋𝑛, 𝛽 = 𝑛=1𝑁 𝑖∈𝐶𝑛

𝑙𝑛𝑃 𝑖 𝐶𝑛

Where 𝑦𝑖𝑛 = 1if n chose alternative I, 0 otherwise

Logit:

𝑃 𝑖 𝐶𝑛 =𝑒𝜇𝑉𝑖𝑛

𝑗∈𝐶𝑛𝑒

𝜇𝑉𝑗𝑛, 𝜇 = 1

𝐿 𝛽 =

𝑛=1

𝑁

𝑖∈𝐶𝑛

𝑦𝑖𝑛 𝑉𝑖𝑛 − 𝑙𝑛

𝑗∈𝐶𝑛

𝑒𝑉𝑗𝑛

Maximum Likelihood Estimation(cont.)

The maximum likelihood estimation problem:

𝛽 = arg 𝑚𝑎𝑥𝛽𝐿(𝛽1, 𝛽2, … , 𝛽𝑘)

FOC for linear in parameters Logit

𝐿 𝛽 =

𝑛=1

𝑁

𝑖∈𝐶𝑛

𝑦𝑖𝑛 𝑉𝑖𝑛 − 𝑙𝑛

𝑗∈𝐶𝑛

𝑒𝑉𝑗𝑛 𝑉𝑖𝑛 = 𝑘=1

𝐾

𝛽𝑘𝑋𝑖𝑛𝑘

𝜕𝐿(𝛽)

𝜕𝛽𝑘=

𝑛=1

𝑁

𝑖∈𝐶𝑛

𝑦𝑖𝑛 𝑥𝑖𝑛𝑘 − 𝑗∈𝐶𝑛

𝑥𝑖𝑛𝑘𝑒𝑉𝑗𝑛

𝑗∈𝐶𝑛𝑒𝑉𝑗𝑛

= 0

𝑛=1

𝑁

𝑖∈𝐶𝑛

𝑦𝑖𝑛 − 𝑃𝑛 𝑖|𝑥𝑛, 𝛽 𝑥𝑖𝑛𝑘 = 0

Evaluation of Estimation Results

Signs and relative magnitudes of the coefficients For example, we expect the coefficient of price to be negative

Statistical tests

Goodness of fit measures

Statistical tests

Asymptotic t-test

- Used to test if a particular parameter is different from zero or from another known value

- Standard output statistic with most software

𝐻0: 𝛽𝑘 = 𝛽𝑘0

𝑡𝑘 = 𝛽𝑘 − 𝛽𝑘

0

𝑠 𝛽𝑘

- Compare to the critical value of the t distribution at a given level of significance

Statistical tests (cont.)

Likelihood ratio test- Tests nested hypotheses (restrictions in the model)

The statistic −2 𝐿 0 − 𝐿 𝛽

- Used to test the null hypothesis that all parameters are zero

- It is asymptotically 𝜒2 distributed with K (number of parameters) degrees of freedom

The statistic −2 𝐿 𝑐 − 𝐿 𝛽

- Used to test the null hypothesis that all the parameters other than

the intercept are zero

- It is asymptotically 𝜒2 distributed with K-1 (number of restrictions) degrees of freedom

Goodness of Fit

𝜌2 and 𝜌2 are analogous to 𝑅2 and 𝑅2 in least squares.

Likelihood ratio index 𝜌2: measures the fraction of an initial log likelihood that is explained by the model

𝜌2 ≡ 1 −𝐿( 𝛽)

𝐿(0)

𝜌2 is monotonic in the number of parameters K

𝜌2 must lie between 0 and 1.

Goodness of Fit

Adjusted 𝜌2 ( 𝜌2)

- Useful for comparison of models with different number of parameters (i.e., different degrees of freedom)

𝜌2 ≡ 1 −𝐿 𝛽 − 𝐾

𝐿(0)

Extensions of Binary Choice Models44

Classical extensions

Multinomial Logit (MNL)

NL (Nested Logit)

CNL (Cross Nested Logit)

MMNL (Mixed Multinomial Logit)

Logit fixed effect / random effect

Advanced

Latent class

Bayesian

Hybrid

Maryland Freight Mode Choice Model45

Source: Mishra, S., Zhu, X, and Fucca, F. “An integrated framework for Modeling freight mode and route choice” Report for Maryland State Highway Administration. [Download]

http://www.roads.maryland.gov/OPR_Research/MD-13-SP209B4F_An-Integrated-Framework-for-Modeling-Freight-Mode-and-Route-Choice_Report.pdf

Growing awareness of freight system

Thrust at federal, state and local level

Maryland’s freight transportation is estimated

To grow about 105% by 2035

1.4 billion of total tons

4.98 trillion of $ value transfer (108% increase from 2006)

Sustainability of MD corridors to meet the future demand

Background

National Peak Period Congestion-2007 (Freight)

National Peak Period Congestion-2040 (Freight)

Why Freight Mode Choice?

Freight demand by mode varies by

Type of commodity

Value and size of commodity

Travel characteristics near distribution centers

Finer level geometric detail

Detailed Origin-Destination analysis within Maryland

Land use impact on freight flows

LOS identification and project selection

Objectives

Develop methods to forecast freight shipments By rail

By highway

Number of trucks

Time of day

Other

Multimodal

Other

Capable of responding to external changes Fuel price

New distribution centers

Tolling

Freight corridors

Mode Choice Factors

Develop methods to forecast freight shipments By rail

By highway

Number of trucks

Time of day

Other

Multimodal

Other

Capable of responding to external changes Fuel price

New distribution centers

Tolling

Freight corridors

Data

Available from Freight Analysis Framework (FAF)

Annual Macroscopic North American Freight Flow

Tons, Value, Distance, Commodity, Mode

Derive large scale long distance movements

Not available from FAF

Through trips (route)

Short distance internal trips

Cost (fuel price, time)

Just in time delivery

FAF Zones

131 FAF Zones123 nationwide8 international

3 MD FAF Zones Baltimore-MD Washington-MD Remainder-MD

Freight in Maryland

Within

MD

Leaving

MD

Arriving

in MD

Through

(Northeast-

Southeast)

Weight

(million of tons)135 84 91 52

Value (billion$) 92 113 169 177

Value/Weight

(Thousand $/ton)0.7 1.3 1.9 3.4

Northeast: CT, ME, MA, NH, NJ, NY, RI,VTSoutheast: FL, GA, NC, SC

External and Internal Trips By Mode

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

Weight Value Weight Value Weight Value Weight Value

Within Maryland Leaving MD Arriving in MD Through (NE-SE)

Truck Rail Multimode Other

Commodities by Truck(From MD)

Lower Truck Percentage (<40%)

Medium Truck Percentage (41%-80%)

High Truck Percentage (>80%)

From MD

Commodities by Truck (To MD)

To MD




Commodities by Truck (Within MD)

Within MD




Proposed Model Structure

Within MD

Leaving MD

Arriving in MD

Com 1

Com 2

Com 3

4 models for different OD and Commodities

From To From To From To

1 Live animals fish 3 3 15 Coal 3 3 29 Printed prods 1 1

2 Cereal grains 3 3 16 Crude petroleum 3 3 30 Textiles leather 2 2

3 Other ag prods 3 3 17 Gasoline 3 3 31 Nonmetal min. prods 2 3

4 Animal feed 3 3 18 Fuel oils 3 3 32 Base metals 2 2

5 Meat seafood 3 3 19 Coal-n.e.c. 2 2 33 Articles-base metal 1 2

6 Milled grain prods 3 3 20 Basic chemicals 1 2 34 Machinery 2 2

7 Other foodstuffs 3 3 21 Pharmaceuticals 2 1 35 Electronics 2 2

8 Alcoholic beverages 3 3 22 Fertilizers 2 3 36 Motorized vehicles 2 1

9 Tobacco prods 3 3 23 Chemical prods 1 1 37 Transport equip 2 3

10 Building stone 3 3 24 Plastics rubber 2 1 38 Precision instruments 1 2

11 Natural sands 3 3 25 Logs 3 2 39 Furniture 3 2

12 Gravel 3 3 26 Wood prods 3 2 40 Misc. mfg. prods 2 2

13 Nonmetallic minerals 2 2 27 Newsprint paper 1 3 41 Waste scrap 3 3

14 Metallic ores 1 3 28 Paper articles 2 2 43 Mixed freight 2 2

Proposed Method

Aggregated analysis

Using land use as the factor

Logistic Regression Models

𝑃𝑖𝑗 is the probability of Truck Tonnage share

𝑋𝑖𝑗 is the Info of distribution centers,

highway/railway coverage,transportation/warehousing employment.

𝑙𝑜𝑔𝑖𝑡 𝑃𝑖𝑗 = 𝑋𝑖𝑗𝛽𝑗 + 𝜀𝑖𝑗

𝑙𝑜𝑔

𝑇𝑜.𝑑𝑤𝑜.𝑑

1 −𝑇𝑜.𝑑𝑤𝑜.𝑑

= 𝑋𝑖𝑗𝛽𝑗 + 𝜀𝑖𝑗

=𝛽0 + 𝛽1𝐷𝑖𝑠𝑡 + 𝛽2 𝐷𝐶𝑂 + 𝛽3 𝐷𝐶𝐷 + 𝛽4 𝐶𝑜𝑣𝑂 + 𝛽5 𝐶𝑜𝑣𝐷 +𝛽6 𝐸𝑚𝑝𝑂 + 𝛽7 𝐸𝑚𝑝𝐷 … + 𝜀𝑖𝑗

1 2 … 123

…

…

48 𝑤48.1 𝑤48.2 𝑤48.123

49 𝑤49.1

50 𝑤50.1 𝑤50.123

…

Summation of all group 1 tonnage from MD

1 2 … 123

…

…

48 𝑇48.1 𝑇48.2 𝑇48.123

49 𝑇49.1

50 𝑇50.1 𝑇50.123

…

Summation of all group 1 trucktonnage from MD

Proposed Model Structure

The share of truck 𝑃𝑡 =exp(𝑦)

1+exp(𝑦)

y = 0.431 − 0.002𝑋1 + 2.463𝑋2 − 0.164𝑋3 + 0.414𝑋4 − 0.024𝑋5 + 0.286𝑋6 −0.133𝑋7

Parameter Estimates95% CI Lower

95% CI Upper

Wald Chi-Square

Sig.

(Intercept) X0 .431 -2.580 3.442 .079 .779

Highway distance X1 -.002 -.003 -.001 19.315 .000

# Origin zone truck center

X2 2.463 .417 4.508 5.569 .018

# Origin zone rail center

X3 -.164 -.272 -.055 8.766 .003

# Destination zone truck center

X4 .414 .108 .720 7.018 .008

# Destination zone rail center

X5 -.024 -.056 .007 2.265 .132

# Destination zone port center

X6 .286 -.075 .647 2.412 .120

# Destination zone Trans employment

(10K)X7 -.133 -.310 .044 2.160 .142

Example: From MD group1


Parameter Estimate

s

(Intercept) X0 .431

Highway distance X1 -.002

# Origin zone truck center

X2 2.463

# Origin zone rail center X3 -.164

# Destination zone truck center

X4 .414

# Destination zone rail center

X5 -.024

# Destination zone port center

X6 .286

# Destination zone Trans employment (10K)

X7 -.133

• For this group of commodities, the total truck share from MD is less than 40%.

• The truck percentage share decrease with longer distance between the Origin and Destination zone.

• The number of truck-truck centers in MD influence the truck share dramatically.

• More number of rail centers in MD reduce the truck share.

• Truck share is high to the destination zone with more truck and port oriented centers and less rail centers, and less transportation/warehousing employment.


The total group 1 commodity shipped from Baltimore (MD MSA) to Denver (CO CSA) 𝑃𝑡=62.3%

If there is one more port related distribution center in Baltimore

The truck share does not change.

If there is one more truck center in Baltimore 𝑃𝑡=95.1%

If there is one more rail center in Baltimore 𝑃𝑡=58.3%


If the Destination zone is Jacksonville (FL MSA) Distance reduces from 1,591 m to 756m.

Employment reduces from 5.17 to 3.22 10K.

𝑃𝑡=91.9%

With one more port-truck distribution center in Baltimore The truck share does not change.

If there is one more truck center in Baltimore 𝑃𝑡=99.3%

If there is one more rail center in Baltimore 𝑃𝑡=90.6%



95% CI Upper

Wald Chi-

SquareSig.

(Intercept) X0 .689 -.542 1.920 1.204 .273


# Destination zone rail center X2 -.022 -.044 .000 3.676 .055

Destination zone Principal arterialpercentage out of total highway and rail

mileageX3 3.660 .822 6.498 6.388 .011

# Destination zone Trans employment (10K) X4 .112 .013 .210 4.956 .026

For this group of commodities, the truck share from MD ranges from 40% to 80%.

The characteristics in Maryland do not impact the truck share.

The truck share only depends on the destination zone.

The truck is preferred to the zones closer to Maryland, with less rail distribution centers, higher Principal Arterial roadway and more transportation related employments.

Example: To MD group1

Parameter Estimat

es95% CI Lower

95% CI Upper

Wald Chi-Square

Sig.

(Intercept) X0 2.720 2.019 3.421 57.850 0.000

Highway distance X1 -0.001 -0.001 0.000 3.981 0.046

# Origin zone port related distribution center

X2 -0.158 -0.373 0.058 2.060 0.151

Destination zone rail center percentage X3 -2.020 -3.246 -0.794 10.431 0.001

# Origin zone Trans employment (10K) X4 0.040 -0.023 0.102 1.565 0.211

• The percentage of rail oriented distribution centers in Maryland is negative related with the truck share.

• The truck share also depends on the origin zone # port related centers, transportation employments.

• The truck is preferred from the zones closer to Maryland, with less port distribution centers, and more transportation related employments.

Example: To MD group2

• The characteristics in Maryland do not impact the truck share.

• The truck is preferred from the zones closer to Maryland, with more transportation related employments.


95% CI Upper

Wald Chi-Square

Sig.

(Intercept) X0 3.055 1.351 4.760 12.340 .000


Origin zone percentage of rail miles out of total highway and rail mileage

X2 -3.576 -7.274 .123 3.590 .058

# Origin zone Trans employment (10K) X3 .074 .000 .147 3.882 .049

Choice Model for Rail

Parameter B

95% Wald Confidence

Interval

Hypothesis

Test

Lower Upper

Wald Chi-

Square

Group1

Commodity

from MD

(Intercept) 5.525 2.933 8.117 17.46

Truck_dist -0.001 -0.002 0 6.533

D_Port 0.29 -0.002 0.582 3.783

D_PAHwy_P -12.539 -17.422 -7.655 25.324

Group2

Commodity

from MD

(Intercept) 3.822 -0.862 8.506 2.557

Truck_dist -0.002 -0.003 -0.001 23.284

D_truck -0.228 -0.381 -0.075 8.536

D_PAHwy_P -14.252 -20.424 -8.08 20.486

Group1

Commodity to

MD

(Intercept) -2.339 -4.357 -0.32 5.158

Truck_dist -0.001 -0.002 0 6.233

O_truck -0.276 -0.461 -0.091 8.558

O_rail 0.155 0.101 0.209 31.586

D_TC_P -6.958 -12.129 -1.787 6.954

Group2

Commodity to

MD

(Intercept) 7.195 4.799 9.592 34.62

Truck_dist 0 -0.001 -6.50E-05 5.541

O_truck 0.127 0.008 0.246 4.349

O_rail 0.044 0.019 0.069 11.756

D_TC_P -2.173 -3.488 -0.858 10.495

D_RC_P -5.759 -8.147 -3.372 22.361

O_PAHwy_P -8.946 -12.704 -5.188 21.774

Sensitivity Analysis Results

Parameter 48 49 50

Group 1 from MD

# Origin zone truck center X2 1.2314 1.209 1.0761

# Origin zone rail center X3 0.9763 0.9783 0.9904

# Destination zone truck center X4 1.0545 1.0498 1.0213

# Destination zone rail center X5 0.9966 0.9969 0.9986

# Destination zone port center X6 1.0384 1.0351 1.0152

# Destination zone Trans

employment (10K)X7 0.9809 0.9825 0.9923

Group 2 from MD

# Destination zone rail center X2 0.9930 0.9931 0.9928

Destination zone principal

arterial percentage out of total

highway and rail mileage (1%)

X3 1.0115 1.0114 1.0120

# Destination zone Trans

employment (10K)X4 1.0352 1.0349 1.0366

Group 1 to MD

# Origin zone port related

distribution centerX2 0.9474 0.9713 0.9413

Destination zone rail center

percentage (1%)X3 0.9934 0.9964 0.9926

# Origin zone Trans employment

(10K)X4 1.0131 1.0069 1.0147

Group 2 to MD

Origin zone percentage of rail

miles out of total highway and

rail mileage (1%)

X2 0.9883 0.9883 0.9878

# Origin zone Trans employment

(10K)X3 1.0242 1.0240 1.0252

Summary

For Group 1 commodities, number of truck and rail centers will influence the percentage of tonnage carried by truck.

For Group 2 commodities, the percentage of truck tonnage only depends on the characteristics of the opposite zones.

The distance is a dominant variables related to truck share.

The principal arterial highway and rail coverage in the opposite zones are related to truck share for group 2, not group 1.

Number of transportation/warehousing employments in the opposite zones is significant.

Variables such as highway and rail coverage in MD and employment in MD is not related.

Potential Applications

Forecast of Future Freight Demand

Expansion of the Port of Baltimore

Expansion of Panama Canal and Northwest passage

Prevent Infrastructure Bottlenecks

Intermodal Facilities

Truck Distribution Centers

Economic Analysis

Project selection

Dollars lost by not providing infrastructure

Model Extensions

Overall contributing factors (1)

Overall contributing factors (2)

Differences Among Zones

Shipments from Zones

Chicago Freight Mode Choice Model78

Amir Samimia*, Kazuya Kawamurab and Abolfazl Mohammadian. (2011). A behavioral analysis of freight mode choice decisions. Transportation Planning and Technology, Vol. 34, No. 8, p. 857-869.

Data Collection79

Collected 881 domestic shipments in the United States.

A total of 4544 business establishments opened the recruiting email, of which 316 firms participated

A 7% response rate, which is a reasonable rate in such surveys.

Basic information about the following is obtained each establishment

five recent shipments, namely origin, destination, transportation mode, type, value, weight, and volume of the commodity

cost and time of the entire shipping process

Data-Descriptive Statistics80

Modeling Approach81

Used random utility maximization approach

Binary probit and logit

Goodness of fit

AIC

Log-likelihood

Rho-square

Sample validation for both modes

Predicted versus modeled

Model Results82

Marginal Effect and Elasticities83

London Freight Mode Choice Model84

Kriangkrai Arunotayanun , John W. Polak. (2011). Taste heterogeneity and market segmentation in freight shippers’ mode choice behaviour. Transportation Research Part E, 47, pp. 138-148.

Model Form85

MNL

Mixed MNL

Model Results86

Commodity Specific Mode Choice87

Sweden Freight Mode Choice Model88

Gerard de Jong , Moshe Ben-Akiva. (2007). A micro-simulation model of shipment size and transport chain choice, Transportation Research Part B 41, pp.950–965.

Model Summary89

Multinomial logit model for combined shipment size and mode choice

Weight choices

Up to 3500 kg

3501–15,000 kg

15,001–30,000 kg

30,001–100,000 kg

Above 100,000 kg

Nested and mixed models were not significant

Variables90

Results91

lecture-10: freight mode choice - ce.memphis.edu

Documents