optimal vendor selection in a multiproduct supply chain with truckload discounts

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Transportation Research Part E 44 (2008) 684–695

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Optimal vendor selection in a multiproduct supply chainwith truckload discounts

Theodore S. Glickman, Susan C. White *

Department of Decision Sciences, School of Business, The George Washington University, Washington, DC 20052, United States

Received 3 October 2006; received in revised form 11 January 2007; accepted 21 January 2007

Abstract

When products are sold by multiple vendors in various locations, the purchaser must decide what to order from eachvendor and where to send it. To solve this decision problem, a novel optimization model is developed and applied to asituation involving the nationwide wholesale distribution of grocery products. Comparing the model’s solution with theactual record of shipments reveals instances in which the model selected higher-priced vendors in order to capitalize ontruckload cost savings, which are seen to be an important factor in vendor selection. Additional models are developedto reduce computation time and assign shipments to vehicles.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Vendor selection; Supply chain; Truckload discount; Mixed-integer programming; Distribution

1. Introduction

The research discussed here assesses the benefit of using an optimization model to solve a combined vendorselection, product acquisition, and shipment distribution problem. This problem arises, for example, when anational wholesale food distributor has determined the requirements of its regional distribution centers andthen has to decide how much to order from each of its suppliers, depending on purchase and transportationcosts. We explain how the model is formulated, what the theoretically optimal results are for the grocery prod-ucts application, and how those results compare to the record of actual shipments, which was provided to usby an industrial logistics firm. We then introduce a heuristic for improving the initial solution to shorten thecomputation time and discuss procedures to determine which orders to assign to each shipment. The purposeof this research is to show how to handle the computational complexity that arises when accounting for theinteractions involved when simultaneously deciding where to buy, how much to buy, and where to send it.

This decision problem is typical of supply chain scenarios in which retailers place their orders withwholesale food distributors, who then meet the collective retailer requirements by deciding how much of each

1366-5545/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tre.2007.01.007

* Corresponding author. Tel.: +1 202 994 4678; fax: +1 202 994 2736.E-mail address: [email protected] (S.C. White).

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T.S. Glickman, S.C. White / Transportation Research Part E 44 (2008) 684–695 685

product to buy from the various vendors. In this version of the problem, purchase costs and transportationcosts dominate other considerations. In general, however, other factors could also come into play, includingproduct availability and quality and vendor responsiveness and reliability. We assume here that every vendorqualifies in these regards. In addition, we assume that there are no minimum order quantities or purchase dis-counts to consider and no appreciable inventory-related costs to account for. Moreover, demands and pricesare fixed and known. The only wrinkle is the need to account for the differences between truckload (TL) andless-than-truckload (LTL) shipping costs. In this regard, the truckload limitation is assumed to relate toweight only and not to volume; however, one could add a volume constraint to the model readily. Fig. 1 illus-trates the solution to a simple version of this problem, in which three products A–C are purchased from threevendors and shipped to two distribution centers.

2. Related research

The problem of selecting multiple vendors in a supply chain environment has been widely studied using awide variety of formulations. In one of the earliest of these studies, Dickson (1966) conducted a survey of pur-chasing agents to assess the range of different decision criteria used for vendor selection. Weber et al. (1991)later reviewed 74 prominent articles from the research literature and classified them according to the 23 criteriaidentified by Dickson. Ten of these articles reported using mathematical programming with one or moreobjectives to select vendors and choose order quantities. In the earliest of these, Gaballa (1974) usedmixed-integer programming to minimize the total cost of purchasing multiple products from multiple vendors,taking quantity discounts into account. In another, Buffa and Jackson (1983) used the multiobjective tech-nique of goal programming to address three different selection criteria: quality, price and delivery. Othermathematical programming solutions since the Weber review include the chance-constrained mixed-integerprogramming model of Kasilingam and Lee (1996), which minimizes a total cost function based on quality,

Vendor

Vendor

Vendor

DC

A

1 B LTL

TL

LTLC

3

B

TL

TL

LTL

C

2

A

B TL

LTL

1

A

B

C

2

A

B

C

DC

Supplies

Demands

Shipments

Fig. 1. An illustration of vendor selection and transportation decisions for three products.

686 T.S. Glickman, S.C. White / Transportation Research Part E 44 (2008) 684–695

price, and delivery, while taking into account product availability, lead time requirements, and demand uncer-tainty. More recently, multiobjective mathematical programming models that incorporate both transportationand storage costs have been formulated by Ghodsypour and O’Brien (2001) and Aguezzoul and Ladet (2004).

None of the vendor selection research to date, however, appears to distinguish between truckload and less-than-truckload shipping costs, which is a major feature of the approach presented here. In the research liter-ature, the TL vs. LTL distinction arises primarily in the context of (a) optimal vehicle routing, as discussed byFisher (1995) and others, and (b) inbound freight consolidation, as discussed by Russell and Cooper (1992),among others. In the foreseeable future, as oil prices rise and shippers are operating near capacity limits, thecost differential between TL and LTL shipments is likely to become increasingly important.

3. Model formulation

In the wholesale food distributor situation examined here, we are dealing with a network containing 54 ven-dor origins and five distribution center (DC) destinations. Each destination has a set of specified demands forone or more of the 66 unique products that are revealed when the 50 highest-demand products at each of thefive destinations are aggregated. Forty-nine of those products can only be obtained from one vendor, andthose 36 vendors are unique because they do not sell any other products. Hence, the basic problem can bereduced to the 17 products supplied collectively by the other 18 vendors. Every product is transported inmixed-product TL or LTL shipments, each of which travels directly from a vendor to a DC. TL shipmentsare constrained by the trucks’ weight limitation of 45,000 lbs, and any demands not met by those shipmentsare met with LTL shipments.

We make three assumptions for modeling purposes, all of which are characteristic of the wholesale fooddistributor situation. First, when a product is available at a vendor, the level of supply is sufficient for anyorder quantity. Second, all shipping costs are borne by the wholesale food distributor. Third, routing ofTL or LTL shipments from one vendor to another or one distribution center to another is assumed eithernot to occur or not to have any bearing on the selection of vendors. Given the long distances between theDCs in our wholesale food distribution scenario, routing is particularly unlikely, and the distributor didnot consider it a viable option.

For algebraic formulation purposes, we denote the vendors by the index i, the DCs by the index j, and thedifferent products by the index k. The decision variables are defined as follows:

xijk = number of units of product k purchased from vendor i for DC jtij = number of TL shipments from vendor i to DC j

yij = weight of LTL shipments from vendor i to DC j (lbs)

A solution to the decision problem is represented by a choice of values for all of the xijk, tij, and yij variables.We also define the following parameters for the model:

pik = unit cost of purchasing product k at vendor i ($/unit)rij = TL shipping rate from vendor i to DC j ($/truckload)cij = LTL shipping rate from vendor i to DC j ($/cwt)bjk = demand for product k at DC j (units/week)wk = per unit weight of product k (lbs/unit)W = truck weight limit (lbs/truckload)

A set of values for each and every one of these quantities must be determined before a solution to the modelcan be determined.

The problem of selecting the vendors and product quantities to minimize the overall purchase and shippingcost, subject to the demand constraints and truck capacities, can then be written

Min z ¼X

ijk

pikxijk þX

ij

ðrijtij þ cijyijÞ ð1Þ


s:t:X

i

xijk ¼ bjk for all j; k ð2Þ

ð1=W ÞX

k

wkxijk � 1 6 tij 6 ð1=W ÞX

k

wkxijk for all i; j ð3Þ

yij PX

k

wkxijk � Wtij for all i; j ð4Þ

yij P 0 for all i; j ð5Þxijk; tij integer for all i; j; k ð6Þ

We refer to this as the vendor selection and shipment distribution (VSSD) model. The objective function in (1) isthe sum of the total purchase cost plus the total TL and LTL shipping costs. It is this combined cost that is tobe minimized, without regard to the proportion spent on purchasing vs. the proportion spent on shipping. Theinterpretation of each set of constraints is as follows: set (2) ensures that the demand requirements are met foreach product at each destination (i.e., every inbound freight requirement of every DC must be met); set (3)determines the number of TL shipments for each origin-destination pair, based on the number of units pur-chased and their weights (i.e., fill up as many trucks as possible); set (4) restricts the total LTL shipment weightfor each origin-destination pair, based on the total number of TL shipments (i.e., ship the remainder in partialtruckloads).

Although the xijk variables are integer-valued, a simplifying approximation would be to treat them as con-tinuous variables. This would require, however, that the quantities involved are sufficiently large (i.e., in thehundreds or thousands).

We note that the model can be readily modified to account both for truckload weight limitations and vol-ume (‘‘cube’’) limitations by expanding constraint set (3) to include the following constraints:

ð1=V ÞX

k

vkxijk � 1 6 nij 6 ð1=V ÞX

k

vkxijk for all i; j ð7Þ

where vk is the per unit volume of product k and V is the truckload limit on total volume. Coupled with theoriginal constraints in (3), these constraints would ensure that the number of truckloads from vendor i to DC j

is determined by whichever is smaller, ð1=W ÞP

kwkxijk or ð1=V ÞP

kvkxijk. This expression may, of course, be anapproximation, because it does not account for the shape of the product packages, which can also be a limitingfactor.

4. Product-to-truckload assignment

As formulated above, the VSSD model determines the values of three sets of variables: x�ijk, the optimalnumber of units of product k purchased at vendor i for DC j; t�ij, the optimal number of TL shipments fromi to j; and y�ij, the optimal total weight of LTL shipments from i to j. It does not, however, specify the com-position of the full truckloads, i.e., how many units of each product purchased are assigned to each of the TLshipments.

These assignments are determined by solving another optimization problem using the optimal solutionfrom the VSSD model to set the values of the parameters of this problem. We define two new sets of variables,assuming the model contains truckload weight limitations but not volume limitations:

uijkn = number of units of product k assigned to TL shipment n between i and j

sijn = slack weight in the composition of TL shipment n between i and j

The objective is to assign products to the TL shipments for each vendor-DC pair, given the optimal valuesfound for x�ijk and t�ij. The assignment criterion is to minimize the maximum total slack weight among the t�ijtruckloads in each case, where the slack weight for a truckload is the unused portion of the total weight capac-ity (e.g., 45,000 lbs). This criterion strives to equalize the slack weights; but some other assignment criterioncould be used instead, such as simply ensuring that each assignment is feasible, i.e., that its total weight is W orless.


To determine the assignments using the proposed minimax total slack weight criterion, a separate model isrequired for each (i, j) pair with at least one TL shipment, or t�ij > 0. The formulation of this model is as fol-lows, where (i, j) is fixed and the index n ranges from 1 to t�ij:

Min zij ð8Þs:t: zij P sijn for all n ð9Þ

X

k

wkuijkn þ sijn ¼ W for all n ð10ÞX

n

uijkn 6 x�ijk for all k ð11Þ

sijn; uijkn P 0 for all k; n ð12Þuijkn integer for all k; n ð13Þ

We call this the TL assignment model. Constraint set (9) ensures that zij, the slack quantity minimized in theobjective function (8), is the maximum of the slack weights among the TL shipments of concern. Constraintset (10) determines the slack weight for each shipment, given the product assignments represented by the vari-ables uijkn. Constraint set (11) requires that for each product, the total number of units of assigned to all of theTL shipments from i to j does not exceed the total number of units shipped. This model can be viewed as aknapsack problem with multiple knapsacks to be filled (one per truckload) and an upper limit x�ijk on the num-ber of units available of each product, where the objective is to distribute the empty weight equally among theknapsacks.

5. Data and results

The wholesale food distribution industry generated revenues of $402.9 billion in 2001, involving about39,700 distributors, according to the US Census Bureau (2002). The firms involved range from small specialtywholesalers, dealing in gourmet foods, for example, to larger firms that provide a range of services, includingpoint-of-sale merchandising material and product servicing (e.g., stock rotation and product display monitor-ing). Some of the largest wholesalers have integrated vertically to become retailers as well. In a counter-trend,some retailers have become self-distributors by operating their own shipping lines and warehouses. Yet whole-sale food distributors remain the primary supply source for more than 15,000 supermarkets, providing goodsfor nearly one-third of the national supermarket sales, according to Progressive Grocer, an industry publica-tion. The vendors that wholesale food distributors buy from represent the manufacturers and suppliers of anyproduct sold in grocery stores, which include not only traditional grocery products but many other items suchas greeting cards, housewares, and automotive products.

The wholesale food distributor situation we analyzed, with 54 vendors and 66 different products, involvesDCs in these five locations: Gridley, IL; Atlanta, GA; Lewisville, TX; Columbus, OH; and Chester, NY. Table1 lists the vendor codes and locations, with the 18 competitive vendors flagged by an asterisk. Of the 66 prod-ucts, only 17 are carried by more than one vendor, the competitive vendors. While it is tempting to drop theother 43 products from consideration, doing so would eliminate the possibility of improving the utilization oftruck capacity for those products. For the 17 products, Table 2 shows the number of units demanded at eachDC for the period in question. Fourteen of the 17 have two vendors and the others have three vendors.

5.1. Optimization results

The optimal solution to the VSSD model is summarized in Table 3, which shows the optimal total cost z*

and its breakdown by purchase cost, TL shipping cost, and LTL shipping cost. For comparison purposes, thecosts are also shown for the shipments that were actually made in practice. We see that the optimal solutionsaves an estimated $1,092,000, or about 1.5% of the total cost. This is the net saving that results from the com-bination of increasing the purchase cost while reducing both the cost of LTL shipping and TL shipping. Inother words, the optimal solution shows that it is worth paying more for the goods in order to lower thespending on LTL and TL shipments.

Table 1Vendor codes and locations

50635 Salem, OR*52426 Yuba City, CA53505 Gloucester, MA54140 Rochelle, IL54220 Los Angeles, CA

*54585 Los Angeles, CA55175 Denver, PA56045 Atlanta, GA56351 Salisbury, MD56503 Nampa, ID56506 Hamilton, NJ58860 Cambridge, MD59446 Chattanooga, TN

*70635 Clearfield, UT*70637 Jessup, MD*70638 Rochelle, IL73755 Chicago, IL74141 Gadsden, AL74270 Columbus, GA74275 Los Angeles, CA

*75400 Richland, WA*75401 Rochelle, IL*75402 Rochelle, IL76480 Tyler, TX77730 Stafford, TX

*78955 Greeley, CO*78957 Greeley, CO80660 Bedford Hts., OH81546 Van Buren, AR

*81700 Burley, ID*81702 Burley, ID*82315 Dillon, SC83510 Mt. Pleasant, TX

*83512 Mt. Pleasant, TX83602 Badger, WI83850 Waco, TX84215 El Paso, TX86095 Charlotte, NC86881 St Simons, GA86890 Buffalo, NY87436 Forest, MS87475 Omaha, NE87565 Los Angeles, CA88375 Plymouth, WI89040 Chattanooga, TN89995 Los Angeles, CA90235 Milton F’way, OR

*91206 Fort Worth, TX*91208 Fort Worth,TX*94291 Rogers, AR*94292 Springdale, AR94293 Rogers, AR94320 Bellingham, WA99705 Milwaukee, WI


The 1.5% cost reduction may not appear to be very much, but in the wholesale food distribution industry,where a typical value for the net profit margin is around 2.2%, this represents an increase of more than 170% inthat margin. Associated with this cost reduction is a small increase in the number of TL shipments (from 1218

Table 2Distribution center demands for the multi-vendor products (units)

Product code Gridley IL Atlanta GA Lewisville TX Columbus OH Chester NY

790 28,818 – 37,362 – –822 7976 6016 5118 10,843 1793829 29,356 25,294 26,933 31,782 19,266

1069 8424 55,333 3353 61,424 24,0471471 – 86,758 21,336 8905 –7801 38,320 54,019 47,592 459 –

24110 9953 10,465 6701 9648 14,91324112 2225 1473 – 5155 –

100178 1772 2834 6750 – 1350100305 3368 2016 10,383 – 827100330 8735 3246 – – 3752100333 3974 2423 6479 – 980100344 2587 1711 5180 – 759209932 2814 1290 2258 2428 5383211700 1627 986 1054 1609 3557908425 2511 1300 1785 – 6337908600 1685 1015 1421 3775 9853

Table 3Optimized vs. actual costs ($)

Optimized cost Actual cost Absolute change Relative change (%)

Purchase 55,748,765 55,742,860 5904 0.01TL shipping 11,244,188 11,996,819 �752,631 �6.37LTL shipping 6,297,521 6,642,793 �345,273 �5.20Total 73,290,473 74,382,473 �1,092,000 �1.47


to 1223) and a 5.9% decline in the total shipping cost (from $18,639,612 to $17,541,708, amounting to a savingof $1,097,904).

Of the 54 vendors, only 12 are affected by the changes summarized in Table 3. Table 4 identifies these ven-dors and displays the cost impacts for each one. The major shifts underlying the results in this table are these:

(a) In the optimal solution, what was previously an exclusive purchase of product 908600 from vendor 94292is now split between vendors 94292 and 83512, even though vendor 83512 charges roughly one-third moreper unit ($30.80 instead of $23.10). This product is shipped to the DCs in Gridley and Chester.

Table 4Net cost impacts by vendor – optimized less actual ($)

Vendor Purchase TL shipping LTL shipping Total

52426 �47,997 0 �47,997 �95,99454585 47,183 0 54,328 101,51170637 �903,283 �195,663 0 �1,098,94570638 2,017,805 1,325,897 130,360 3,474,06275400 262,197 45,787 12 307,99675401 �260,972 �93,135 3,045 �351,06275402 �2,483 �10,670 19,361 6,20781700 �269,304 �77,437 �19 �346,76181702 275,828 61,293 15 337,13683512 �41,426 �31,468 104,539 31,64594292 31,070 10,463 47,677 89,209


(b) In the optimal solution, some of product 1471, which was previously purchased from vendors 75400 and75402, is now purchased from vendor 75401 at a higher unit price ($11.26 vs. $10.26). This product isshipped to the DC in Atlanta.

(c) In the optimal solution, some of product 211700, which was previously purchased exclusively from ven-dor 54585 at a cost of $29.00 per unit is shifted to supplier 52426 at a cost of $29.50 per unit. This prod-uct is shipped to the DC in Gridley.

Each of these shifts is attributable to a net decrease in total shipping cost that outweighs the higher pur-chase cost. The appendix contains more information, in the form of a detailed table showing every shift,including the vendors and DCs involved and the unit price differentials.

Table 5 shows the cost impacts summarized by DC. Only the DC in Columbus shows no difference betweenthe optimized and actual costs. For two of the other DCs, the purchase cost increased in order to reduce theLTL shipping cost—the total cost of the TL shipments went down in one case and up in the other. Anotherdifference between the optimal and actual solutions is worth noting: of the 54 vendors involved in the actualshipments, only 51 are required in the optimal solution. Such results are always welcome because of the advan-tages of having to interact with fewer suppliers.

Given this optimal solution to the VSSD model, the TL assignment model results for a representative O–Dpair are shown in Table 6, which indicates how many units of each of the products purchased from vendor94292 are assigned to the four TL shipments destined for the DC in Gridley. The unit weights of the threeproducts, which contribute to the slack weights shown, are 11 lbs, 13.3 lbs and 32 lbs, respectively.

Assigning the remaining products purchased to the collective LTL shipments for a particular (i, j) pair isaccomplished by solving the TL assignment model and then subtracting the values in that solution fromthe corresponding values in the optimal solution to the VSSD model. Symbolically, we have

TableChang

PurchaTL shiLTL sTotal

TableRepres

Produc

TruckTruckTruckTruckTotal

TableRepres

Produc

PurchaShippeShippe

v�ijk ¼ x�ijk �X

n

u�ijkn for all k ð14Þ

5es in costs by DC – optimized less actual ($)

Gridley IL Atlanta GA Lewisville TX Chester NY Total

se 7343 �5266 – 3827 5904pping �202,434 �306,205 �245,528 1536 �752,631hipping �216,968 �59,788 �61,813 �6704 �345,273

�412,059 �371,259 �307,341 �1341 �1,092,000

6entative assignment of products to TL shipments (units)

t code 100305 100330 908600 Slack (lbs)

1 0 3292 38 0.42 0 3292 38 0.43 21 2151 505 0.74 3346 0 256 2.0

3367 8735 837 3.5

7entative assignment of products to LTL shipments (units)

t code 100305 100330 908600

sed 3368 8735 837d by TL 3367 8735 837d by LTL 1 0 0


where v�ijk is the optimal value for the total number of units of product k in the LTL shipments from i to j andPnu�ijkn is the optimal number of units of product k assigned to the TL shipments from i to j. The LTL results

for the same vendor and DC analyzed in Table 6 are given in Table 7, which shows that only one unit amongall the units shipped of each product was assigned to a pool of LTL shipments. The entries in this table weredetermined with Eq. (14).

6. Advanced starting solution

The computer time required to solve the VSSD model can be reduced by replacing the standard startingsolution with an advanced starting solution instead. Such a solution can be obtained by omitting the consid-eration of TL shipments from the formulation shown in (1)–(6), which then reduces to the following model,where dijk = pik + cijwk:

Min z ¼X

ijk

dijkxijk ð15Þ

s:t:X

i

xijk ¼ bjk for all j; k ð16Þ

xijk P 0 and integer for all i; j; k ð17Þ

This has the form of a standard transportation problem, in which there is an origin node for every (i, j,k) com-bination and a destination node for every (j,k) combination. The supply is unlimited at the origins but has avalue of bjk at the destinations. An arc connects every origin and destination pair that has j and k values incommon. The unit cost dijk = pik + cijwk applies to each arc, where pik is the unit purchase price, which de-pends only on the vendor and product, and cij is the unit transportation cost, which depends on the vendorand the DC. The computation for this problem goes very quickly and the optimal solution is automaticallyinteger-valued, provided the values of bjk are integer-valued. We call this the transportation initialization model.

Once this model is solved, the initial solution to the VSSD model is determined by (a) adopting the optimalvalues x�ijk from this model and (b) determining the corresponding values for tij and yij from constraint sets (3)and (4). The values that satisfy these constraints are determined by finding a feasible solution to the followingoptimization problem, where constraint sets (19) and (20) restate constraint set (3), which relates tij, the totalnumber of truckloads for each O–D pair, to

Pkwkx�ijk, the corresponding total weight of the shipments. Con-

straint set (21) restates constraint set (4), which determines yij, the total LTL shipment weight for each O–Dpair. The objective function (18) is the total combined weight of the TL and LTL shipments. Whether z isminimized or maximized is immaterial, because its value will turn out to be the same either way

min z ¼X

ij

Wtij þ yij ð18Þ

s:t: Wtij 6

X

k

wkx�ijk for all i; j ð19Þ

Wtij PX

k

wkx�ijk � W for all i; j ð20Þ

Wtij þ yij PX

k

wkx�ijk for all i; j ð21Þ

tij; yij P 0 for all i; j ð22Þ

tij integer for all i; j ð23Þ

We call this the feasible completion model because it provides feasible values of t�ij and y�ij that complete thepartial solution represented by the x�ijk values.

For the problem discussed in Section 5 above, we determined the values of x�ijk, t�ij and y�ij using these twomodels and used them as the advanced starting solution of the VSSD model. Running Premium SolverTM with


a PentiumTM 2.20 GHz processor, the CPU time decreased by only 3%. More experimentation with differentdatasets would be required to determine whether this performance is representative and, if so, how it couldbe improved.

7. Conclusions

This analysis demonstrates the benefit of using an optimization model for vendor selection when multipleproducts are transported via TL and LTL shipments to a number of regional DCs. It contributes to theresearch literature by accounting for the distinction between TL and LTL shipping costs in general and bydemonstrating the importance of that distinction for a particular application involving wholesale food distri-bution. Quantity discounts and inventory costs do not enter into the situation studied here, but these featurescan be incorporated using the results of other researchers. For each vendor-product-DC combination theVSSD model formulated here provides values for the total number of units purchased and transported inthe optimal solution. For each vendor-DC combination, it also provides values for the number of TLshipments and the total weight of all the products transported in LTL shipments. To accelerate thecomputation of these values, we formulated a transportation initialization model and a feasible completion

model, which together generate an advanced starting solution. And to determine a selection of productsand product quantities for each TL shipment, we also formulated a TL assignment model that can be appliedto each vendor-DC combination in the optimal solution to the VSSD model. The selection of products andproduct quantities for all of the LTL shipments can then be determined indirectly based on the results forthe TL shipments.

The suite of models discussed here represents a starting point for developing decision support systemsdesigned for logistical planners and schedulers. At the planning level, the purpose of such a system wouldbe to identify supply chain partners for cooperative relationships and to analyze strategic options concerningtarget markets, DC capacities and locations, carrier selection and contracts, third-party logistics integration,and the implications of future scenarios involving product prices, transportation rates, competitor actions,growth in retail markets, and opportunities for vertical integration.

At the scheduling level, the purpose of the decision support system would be to generate candidate solu-tions for product purchasing and distribution rapidly and economically. Those theoretical solutions couldthen be modified using human judgment to account for factors and eventualities that are not addressed inthe models. With this modification capability, the system would foster resiliency by permitting schedules tobe altered in real time whenever supply chain disruptions or other unforeseen developments affect productsupply and demand or vehicle availability.

Future research should focus on combining the best features of the existing models, including the onesproposed here. Ideally, the models used to select vendors and guide product purchase decisions and trans-portation decisions would be comprehensive, given the interdependence of these decisions. Additionally,they would be capable of accounting for multiple objectives (particularly with respect to vendor selection),as well as uncertainties in the decision parameters (especially cost factors and the timing and volume ofsupplies and demands) and other options such as the routing of trucks among multiple suppliers and mul-tiple DCs, and the inclusion of purchase quantity volume discounts and the inventory holding costsincurred at DCs when products are shipped earlier than necessary in order to capitalize on TL shippingdiscounts.

Appendix. Differences in optimized vs. actual solutions

Item Gridley, IL Atlanta, GA Lewisville, TX Columbus, OH Chester, NY

790 Units shifted 9844 of 28,818 – 8438 of 37,362 – –From/to vendor 75400–75401 – 75400–75401 – –Price increase ($/unit) None – None – –

(continued on next page)

Appendix (continued)

Item Gridley, IL Atlanta, GA Lewisville, TX Columbus,OH

Chester, NY

829 Units shifted – 24,388 of25,294

– – –

From/to vendor – 81700–81702 – – –Price increase($/unit)

– 11.04–11.31 – – –

1069 Units shifted – 55,333 of55,333

– – –


– None – – –

1471 Units shifted – 1258 of 86,758 1500 to 21,336 – –From/to vendor – 75402–75401 75400–75402 – –Price increase($/unit)

– 10.26–11.26 None – –

7801 Units shifted 38,320 of38,320

54,019 of54,019

47,592 of47,592

– –

From/to vendor 70638–70635 70635–70638 70638–70635 – –Price increase($/unit)

None None None – –

24110 Units shifted – 10,645 of10,645

– – –


– None – – –

100178 Units shifted – 1702 of 2834 – – –From/to vendor – 70637–70635 – – –Price increase($/unit)

– None – – –

211700 Units shifted 1627 of 1627 – – – –From/to vendor 54585–52426 – – – –Price increase($/unit)

29.00–29.50 – – – –

908600 Units shifted 848 of 1685 – – – 497 of 9853From/to vendor 94292–83512 – – – 94292–83513Price increase($/unit)

23.10–30.80 – – – 23.10–30.81


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optimal vendor selection in a multiproduct supply chain with truckload discounts

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