Journal of Transportation Management

Volume 26 | Issue 1 Article 4

7-1-2015

Logistics concepts in freight transportationmodelingSubhro MitraUniversity of North Texas at Dallas, Subhro.Mitra@unt.edu

Elvis NdembeNorth Dakota State University, Elvis.ndembe@ndsu.edu

Poyraz KayabasNorth Dakota State University, poyraz.kayabas@ndsu.edu

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Recommended CitationMitra, Subhro, Ndembe, Elvis, & Kayabas, Poyraz. (2015). Logistics concepts in freight transportation modeling. Journal ofTransportation Management, 26(1), 29-42. doi: 10.22237/jotm/1435708980

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LOGISTICS CONCEPTS IN FREIGHT TRANSPORTATION MODELING

Subhro Mitra, Ph.D., P.E.University of North Texas at Dallas

Elvis Ndembe, Ph.D. CandidateNorth Dakota State University

Poyraz Kayabas, Ph.D. CandidateNorth Dakota State University

ABSTRACT

The purpose of this paper is to review logistics concepts used in macro freight transportationmodeling by various planning agencies at the national, state and city level. The chronologicaldevelopment of freight modeling endeavors are studied here and the logistics componentincorporated in the modeling is identified. The key modeling tools are identified and analyzed toidentify the efficacy of the model, ease of use, and data required to implement the model. Theconclusion was that European freight models were more developed than North American freightmodels. The tools most widely used are the aggregate-disaggregate-aggregate model, input-outputmodel, artificial neural network model, matrix estimation method and PCOD model. This paper willgive transportation modelers a better idea of the freight modeling tools available.

INTRODUCTIONMacro freight modeling is an integral part oftransportation planning, undertaken bygovernment agencies and metropolitanorganizations to estimate present and futuretransportation demand. Freight modeling hasundergone major developments andtransformations since its inception to suit thedynamic nature of transport modeling. Asignificant amount of knowledge has been addedover time with the goal of connecting the variousstages of freight transport modeling including:production and consumption, trade (sales andsourcing), logistics, transport, and networkservices (Tavasszy, 2006). Traditionally, the fourstages, in passenger transport modeling havebeen linked to research and studies in freightmodeling. It is generally observed that asignificant number of freight models, bothregional and national, fail to incorporate real lifelogistics dimensions (e.g. distribution centers)into their framework (Jong et al., 2005). The

term logistics includes all activities related toplanning and implementing the movement ofraw materials, inventory and finished goodsfrom origin to final destination. The logisticsdecision making process includes inventorycontrol, material handling, ordering processes,plant and warehouse selection, mode choice, andwarehouse and storage decisions. It isunderstood that all these varied decision can betaken in isolation or may be related to eachother. A review of existing literature on freightmodeling found significant research on modechoice of freight shipments, but not muchresearch on selections of distribution center,warehouse, and in some cases intermodalterminals. Business entities’ logistics decisionsare dynamic and constantly updated based oninput from external agents, including:transportation rates of competing modes, changein demand, price fluctuation, availability of rawmaterials, and numerous other factors in thebusiness environment.

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Observed increases in world population andrapid globalization have fueled growth in U.S.trade from $889 billion to $3.4 trillion between1990 and 2008 (BTS, 2010). This growth intrade is reflected by increased volumes of freightat U.S. freight gateways and correspondingdomestic connections. Considering the economicgrowth witnessed in recent years, it isunreasonable to model future freight demand ina satisfactory manner without incorporatinglogistics dimensions in the freight model (Jin etal., 2005). Freight forecasting models, indeed,need to incorporate logistics factors in themodeling process. However, a review of existingresearch revealed that most of the models needconsiderable development in this area. It iswidely understood that incorporating some ofthese logistics decisions in the modelingframework can be extremely challenging giventhat these factors are specific to individualbusiness entities. The data requirement can beimmense even if a small sample size is used in astudy. In order to implement a logistics model,there is a need to develop a much higherresolution data base for production, attraction,distribution and storage location of individualcommodities or commodity groups. The logisticsmodel will not only determine the origin,destination, and intermediaries, but it will alsoidentify the mode of transport most suitable formoving the freight. In urban freight models,mode choice is not a significant issue since themajority of the freight moves by trucks.

Based on data availability and degree of accuracyrequired, different researchers have used differentmathematical models to predict freight flow. Thispaper aims to present a holistic view of theimportance of incorporating logistics into thefreight modeling process. This is done byreviewing existing logistics concepts, followed byreviewing existing freight logistics models inEurope and the United States. Special attention isgiven to identify mathematical models employedto incorporate logistics concepts into freight

modeling. We have also looked into datarequirements in each of the freight models that doincorporate logistics dimensions.

FREIGHT MODELING CONCEPTS ANDEMERGING ISSUES

Commodity and Trip Based ModelsFreight modeling, can be broadly classified intotwo categories namely trip-based andcommodity-based models (Holguin-Veras andThorson, 2003). In trip-based models truck tripsare estimated from observed parameters like thenumber of employees in an organization, floorarea of the organization, sales volume and otherrelated factors. In the trip-based approach,commodities produced and consumed are notconsidered for estimation purpose. Thecommodity-based approach estimates thequantity of a commodity that is moved betweeneach origin-destination (OD) pair. In the finalstage of the modeling, the commodity flows areconverted into truck trips, based on the type ofvehicle used and the corresponding payload ofthose vehicles. Some modelers prefer the tripbased model, because the trip based model needsfewer data elements compared to the commoditybased model. The data needed for trip basedmodeling is obtained from a survey of trucktrips. The main disadvantage of the trip basedmodel is its disconnection with the economy.This disconnection makes it difficult to forecast,based on economic growth.

Commodity based modeling can forecast trucktraffic based on economic growth and otherparameters of production and consumption ofgoods and services. The principal drawback ofcommodity based modeling is its inability tocapture the behavioral content of freight flows.The other disadvantage is the detailed input-output data requirements to model the flows.

Logistics Cost Optimization and SimulationModelsThere are a number of logistics models whichcan be used for cost optimization to estimate

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freight flows. One of these classes of model isknown as the economic order quantity (EOQ)model. In this model the optimal lot size isdetermined, which in turn will affect the type ofvehicle used for delivery as well as the numberof annual shipments. The EOQ model estimatesthe optimal order quantity as hCDSQ /2=

where Q is the optimal lot size, D is the annualdemand; S is the ordering cost per lot; h isholding cost; and C is the cost per item. Therecan be a number of modifications of this basicEOQ model based on specific businessscenarios. This model can be modified fornumber of items included in one order. The orderfrequency in this case is definedas ShCDhCDhCDn nn 2/)( 2211 +⋅⋅⋅⋅⋅⋅⋅⋅++= where

nD is the demand of nth item, and nC is the costof nth item. The other modification of the baseEOQ model would be to include discounted costbased on the lot size. There are some heuristicsmethods available to estimate the optimalquantity based on the discounted price. Thismodel can be further improved by incorporatinguncertainty in the demand, and then solving thestochastic model to estimate Q.

Another important concept in logistics andfreight modeling is that of network design. Thenetwork design is formulated based on theobjective of maximizing customers’ satisfactionand firms’ competitive position. These modelsdetermine location of logistics facilitiesincluding production centers, warehouses, anddistribution centers. This model also estimatesthe capacity of each of the locations. The choicebetween available transportation services isdetermined by the logistics requirements such asthe availability of vehicles, warehouses,consolidation, and terminal facilities. Boerkampset al., (2000) described the transportationsystems as a collection of supply chain linkages.According to the authors, a supply chain linkageis a trade relationship between the shipper andthe receiver in a network of interconnectedlinkages between raw material suppliers,producers, trading companies, retailers, and end

users. Supply chain linkages may involve anumber of distribution channels, for instancedirect distribution (shipper to receiver) orintermodal distribution (shipper to intermodalfacility, intermodal facility to receiver). SeeFigure 1.

We present here a simple transshipment modelwhich can be used to determine optimal shippingpatterns and shipment sizes for networks with aconsolidation terminal and cost functions. Astandard model formulation of such atransshipment model is given below.

kmj k m

jkmkmi k m

ikmjmj k m

jkm

jmj k m

jkmimj k m

jkmimj k m

jkm

jkmjkj k m

jkmikmiki k m

ikmijmiji j m

ijm

HCXHCXHCX

HCXHCXHCX

CDXCDXCDXMin

×+×+×

+×+×+×

+××+××+××

∑∑∑∑∑∑∑∑∑

∑∑∑∑∑∑∑∑∑

∑∑∑∑∑∑∑∑∑

Subject to:

Indices, decision variables, and parameters usedin the model formulation are presented in Table1. The model objective function (1.1) minimizesthe sum of total transshipment and handlingcosts in a given freight network involvingproduction, consumption and intermediatefacilities. The model output determines theoptimal shipping patterns and shipment sizes forthe networks and the number and location ofintermediate facilities to operate.Cijm, Cikm and Cjkm, which are the unit cost ofshipment for different legs of the shipment.These depend on the type of shipment andwhether it is truck load (TL), less than truck load

Journal of Transportation Management32

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(LTL) or small package shipment. For TLshipment the truck configuration will have a bigimpact on the cost. Some of these rates areavailable from published rate sources fordifferent shipment types. More specificinformation is obtained by surveying shippersand carriers. In many instances, there is ratenegotiation between shippers and carriers, andmost often it is difficult to get these negotiatedrates due to issues related to confidentiality.

Constraint sets (1.2) and (1.3) are the productionand attraction constraints, which ensure thatdemand at consumption points are satisfied withthe supply generated at production points.Constraint (1.4) is the capacity constraint forintermediate facilities, which limits the amountof total inflow to the intermediate facilities;ensuring available transshipment capacities arenot exceeded. Constraint set (1.5) is the flowconservation constraints in the transshipmentnetwork, which ensures that the sum of inflow toany intermediate facility is equal to the sum ofthe outflow from that intermediate facility.Finally, the nature of decision variables isdefined in (1.6); all decision variables are non-negative real number values. The proposedmodel can easily be improved by introducing thefollowing system design aspects to the modelformulation: inventory, modes of transportation,shipment size, shipment unit, and multipleplanning periods.

Many distribution networks are influenced bythird-party logistics (3PL) providers. A 3PL is athird party company that manages the delivery oflogistics services (Hertz and Alfredsson, 2003).More and more firms are outsourcing their logisticsactivities to 3PL companies. Tian et al. (2009) haveundertaken research to understand the relationshipbetween a 3PL and its customer firms. Thisresearch found that 3PL’s significantly improve thelogistics process of customer firms. Distributionnetwork design by a shipper differs considerablyfrom a network design by 3PL service providers.3PL service providers would consolidate shipmentsfrom suppliers and direct it to manufacturing plants

based on the available consolidation center of the3PL providers (So el al, 2007).

The other concept, which is becoming increasinglyimportant, is reverse logistics. Reverse logisticshas a shorter product lifecycle and also a moredemanding customer (Daugherty et al., 2001).Reverse logistics needs an efficient network designto minimize the cost of transporting returned goodsunder new sets of supply, demand and capacityconstraints. This network design is much morecomplex, because of the higher degree ofuncertainty (Lieckens and Vandaele, 2007).

Two other concepts which are increasinglybecoming important in logistics network designare “lean” supply chains and “green” supply chains.Lean supply chains aim at reducing waste andelimination of non-value added activities whichincludes time, labor, equipment, and inventory(Corbett and Klassen, 2006). Green supply chainstrategy tries to minimize the negative impact ofsupply chains on the environment. Participationof suppliers, customers; and internal operations andprocesses managers, is required to make the supplychain green (Corbett and Klassen, 2006;Mollenkopf, 2010).

LITERATURE REVIEW OF MACROFREIGHT LOGISTICS MODELS

Chronological Development of FreightLogistics Models

Tavasszy (2006) emphasized the integration oflogistics factors into freight models. He traced earlydevelopments in the Netherlands in the first halfof the 1990s, which took more than a decade beforebeing recognized elsewhere. Tavasszy alsoindicated that development in freight logistics ingeneral can be directly linked to local priorities infreight policy. He also points out that freightmodeling has taken different directions in differentcountries and continents. For example, freightmodeling development in Europe has taken adifferent course compared to that of the U.S. Thechronological development of various freightlogistics models are shown in Table 2.

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European Macro Freight Models

Traditionally most freight models were developedin Europe, probably due to the interconnectivityof European nations and the need to accuratelyportray rising freight costs associated with shippingfreight within and across national borders. Someprominent and widely used European freightmodels are:

SAMGODS ModelSAMGODS was developed by the SwedishInstitute for Transport and CommunicationsAnalysis (SIKA) in 2001. The Aggregate-Disaggregate-Aggregate (ADA) modeling tool inSAMGODS is also used in NEMO, which is thefreight model developed for Norway. NEMO andSAMGODS incorporated logistics aspects into thefreight modeling process (Jong et al., 2005).

SMILE ModelSMILE (Strategic Model for Integrated Logisticsand Evaluations), originally initiated in 1998 inthe Netherlands, and was the initial aggregatefreight model developed to estimate freight flowsvia distribution centers using discrete choicemodeling (Tavasszy et al., 1998). SMILE is appliedon a national scale, with the principal objective ofmodeling future freight flows on the transportnetwork by precisely modeling a path from oneregion to the other (Friedrich and Liedtke 2009).The path of freight flow and mode choice isanalyzed jointly based on logistics costs andwarehouse costs. Another model similar to theSMILE is the SLAM (Spatial Logistics AppendedModule), which is a European level transportmodel, defining supply path choices similar to thatin SMILE.

GOODTRIP ModelThe GOODTRIP model closely followed thedevelopment of the SMILE model and has thepotential of determining the costs, performance,and impacts of long term transportation policymaking and implementation (Tavasszy, 2006).GOODTRIP was initially intended to assess thegeneral logistical performance and environmental

impacts of alternatives policies. This laternarrowed down to the food, retail, and bookstoressector because of potentially larger differences indistribution structure of various products andconsumer behavior (Boerkamps and Binsbergen1999). As a disaggregate model, GOODTRIPaimed at evaluating changes in supply chainnetworks, consumption and distribution patterns,delivery requirements, mode choices, andenvironmental impacts. The GOODTRIP modelis different from the SMILE model in two ways(Yang et al., 2009). In the GOODTRIP model,activities and vehicle tours are estimated from landuse. In the case of the SMILE model, activitiesand vehicle flows are generated from commodityflows.

EUNET2.0 ModelEUNET2.0 is a regional economic and freightlogistics model that was developed in 2003 as apilot model, to enhance the understanding ofexisting and ongoing research in logistics usingspatial input-output modeling in the UnitedKingdom (Jin et al., 2005). In this model, freightflow is segmented into a number of logistics stages,according to commodity type.A significant number of origin-destination (O-D)matrices are divided into commodity type, andvarious distribution phases, which includedistribution centers, ports and local depots. Thismodel captured the effect of logistics centers andthe national economy on freight movement (Jin etal., 2005).

PCOD ModelHolmblad (2004 proposed the PCOD freighttransport model. This PCOD model illustrates theinterrelationship between the spatial distributionof freight and transportation patterns emanatingfrom an existing transport network. The PCODmodel converts the PC matrix into an O-D matrix.The PC matrix contains information on amount ofgoods produced at the production zone and theamount of goods consumed at the consumptionpoint. Logistics nodes are introduced in betweenthese terminal points to model the actual flow anddevelop the O-D matrix. With the incorporation

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of indirect transport, Holmblad (2004) predictedthat the transport of goods through logistics nodeswould be more cost efficient, owing to the fact thatlogistics operators would have the choice ofscheduling their transport needs to optimizeexisting transportation resources.

North American Macro Freight Models

In general, the evolution of freight modeling in theUnited States can closely be linked to passengertravel modeling. A significant number of modelsdeveloped are simplistic adaptations of urban traveldemand models. Hamburg (1958) indicated thatattempts to formulate truck freight models can betraced back to Detroit. Subsequent initiatives havebeen made to adapt passenger travel forecasts totruck modeling. Some metropolitan authorities andstates have customarily overlooked freight modelsor have used rudimentary estimates of truckmovement in their modeling process (RANDEurope et al. 2002). However, in recent years, therehas been a shift towards more elaborate modelswith improved data granularity (e.g. commodityflow survey). The United States has two distinctfreight models: commodity flow models and truckflow models developed at the urban, state andnational levels (RAND Europe et al. 2002). Thedichotomies between these two models areattributed to the difference in priorities at each level(Tavasszy, 2006). Presently, there is lack ofinformation about the number of existing truckmodels in the United States. It is generalobservation that most freight models do notrepresent the existing strategic link between theeconomy and the transportation network (RANDEurope et al. 2002).

Some of the most promising freight models in theUnited States are the Seattle FASTrucks Mode, theNew York City Best Practice Model, the OregonTLUMIP Commercial Travel Model, and the LosAngeles County Metropolitan TransportationAuthority (MTA) freight transportation planningmodel. The vast majority of U.S. models are basedon the four-stage passenger modeling frameworkand lack logistics dimensions. The MTA model forLos Angeles is promising in terms of incorporation

of logistics factors and does so by applyingmethodologies similar to that in SMILE and theGOODTRIP model (Fischer et al., 2005).

REVIEW AND ANALYSIS OF MODELTYPES

Aggregate-Disaggregate-Aggregate ModelAggregate-Disaggregate-Aggregate modelsinvolve a number of demand matrices, which arespecific for a particular commodity, and show thequantity of goods transported from one zone toanother. As discussed by Ben Akiva et al. (2008),aggregate models tend to be based on costminimization behavior of firms, while disaggregatemodels include more detailed policy-relevantvariables for firms’ decision making. In practice,disaggregate models have several drawbacks. Oneof these is the need for more detailed data, whichis difficult to generate because of cost andconfidentiality (Winston, 1983 and Oum, 1989).Although difficult in practice, disaggregate modelsproduce more accurate individual mode choiceforecasts by representing the cause and effectrelationships in firms’ decision making processes.However, aggregate and disaggregate approachesshould be considered complementary, notcompeting (Ben Akiva et al. 2008). Integratedaggregate-disaggregate modeling approachesbenefit from aggregate data when representingcollective behavior, and from disaggregating whenthe data represents the behavior of individualdecision making processes (Ben Akiva et al. 2008and Samimi et al. 2009).

The disaggregate logistics model is undertaken ina series of steps. The first step is the disaggregationof flows from one firm to another firm. The secondstep is the logistics decisions by firms, and finallyaggregating freight to O-D flows for networkassignment (Jong et al. 2005). The logistics modelhelps to determine shipment size and transportchain (e.g. mode, vehicle and terminal types, andloading unit utilized). The ultimate decisionmaking process at the firm level is theminimization of total logistics costs. The total

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yearly logistics costs are estimated by the equationbelow

Grskmnql=Okq+Trskql+Dk+Yrskl+Ikg+Kkq+Zrskq

Where, G is total yearly logistics costs; O is theorder cost; T is the transport, consolidation anddistribution costs, D is cost of deterioration duringthe hauling process; Y is capital cost of goods intransit; I is inventory costs; K is cost of inventoryand Z is the stock out costs.

Input-Output ModelsInput-output models provide an overview of theflow of goods and services to analyze the economicprogress and show intermediate transactionsbetween producers and customers. Input-outputtables show goods and services produced in a yearthrough domestic production, imports,consumption of goods by customers, and exports.The demand generated by domestic industries andimports is disaggregated by different industries.Input-output coefficients represent the amount ofinput required to generate one unit of outputnecessary to satisfy the demand generated bydomestic industries and imports. Input-outputmodels can be used to represent single-region andmulti-region commodity flows. According to Ben-Akiva et al. (2008), multi-region input-outputmodels usually perform better than single-regioninput-output flows. Ben-Akiva et al., (2008)pointed to major multi-region input-output modelsundertaken by Chenery (1953), Moses (1955),Leontief (1936), Bon (1984) and Cascetta (2001).The main difference among these models is theway in which the effects of technical coefficientsand trade flow coefficients are estimated in themodeling structure. In freight demand modeling,changes in transportation infrastructure can directlyaffect the amount of transportation serviceavailable and can affect trade flows. Therefore,changes in freight movement networks haveinevitable impacts on input-output coefficients.

Using Leontief ’s Input-Output model, ageneralized form of the EUNET2.0 model showstotal consumption, demand, and the total amount

of a given commodity m that is used for producingcommodities as

Where:Dm is total consumption of commodity m, Ymo isthe quantity of final demand of commodity m Xn ,is the quantity of production of commodity m and,

is the quantity of commodity m that is

used for producing all commodity n.

Artificial Neural NetworksThe artificial neural network (ANN) is a type ofnetwork structure in which the nodes are the“artificial neurons” and the edges connecting thesenodes are the “synapses”. In the ANN model thecomputation is done replicating the way the brainhandles information. The input and the output ofthe computational information process is receivedand sent via synapses from and to the other artificialneurons, respectively. The order of input and outputtransfers is performed according to the informationprocessing state of the artificial neuron in theartificial neuron network. The informationprocessing structures of artificial neurons mayvary; artificial neurons can be designed to performvery simple operations (i.e. adding to input values)or very complex operations (i.e. there can be sub-artificial neuron networks within an artificialneuron). It is also possible to group artificialneurons in different layers. In such a case, artificialneurons are typically organized in three layers: theinput layer which accepts the model inputs; theoutput layer which provides the final model output;and the hidden layer which functions as thecomputational information processing structure(Bilegan et al. 2007).

There has been a variety of artificial neural networkapplications in the area of transportation. Acomprehensive review of artificial neural networkapplications in transportation is presented byDougherty (1995). It is observed that in the areaof freight demand modeling, the use of artificial

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neural networks is relatively new. According toBilegan et al., (2007), artificial neural networkapplications in freight demand modeling havepotential to improve the performance of predictivemodels.

Matrix Estimation MethodsProduction-consumption (P-C) and origin-destination (O-D) matrices are the basic tripmatrices for freight planning and management. TheP-C matrix represents the economic trade patternsbetween zone pairs; primary producers to finalcustomers. The origin-destination (O-D) matrixrepresents the actual physical movements in thetransportation infrastructure, from productionzones to consumption zones. In short, the O-Dmatrix represents the actual freight movement ofthe P-C matrix (Williams and Raha 2002).

There is a compromise between modelcomplexity and data accuracy in choosing anadequate representation of transportationdemand. The reason for the compromise is thatthe detailed description of trip data, betweenorigin and destination pairs, is not alwaysavailable. The feasibility of collecting trip data,including the origin, the destination, allintermediate stops (warehouses, intermodalfacilities), the exact time, the route, and thepurpose of the trip is a challenging task. Even ifthe data collection process is feasible, theamount of information would be unmanageable.Therefore, reasonable representation of demandshould be somewhere in between these twoextremes (Williams and Raha 2002).

The O-D and P-C matrices are reproduced data.The following are the important points to considerwhen generating O-D matrices from original datasources (Williams and Raha 2002):• All of the available observed data resources

like prior matrix and traffic counts should beused efficiently.

• Data from different sources like differentsampling fractions and inaccurate data maynot be consistent.

• Use of data sources can be weighted basedon the data source reliability, accuracy ofmeasurements, and sampling errors.

• Matrix estimation procedures shouldconsider trends in different commoditycategories, economic and industry trends

• Future changes in transportationinfrastructure and transportation costs shouldbe considered including logistics cost.

Our review indicates that a critical improvementhas taken place in freight modeling is the inclusionof logistics dimensions. In the next section of thisarticle we present a discussion of the mathematicaltools used to incorporate logistics aspect in freightmodels.

PCOD ModelsThe principal objective behind the inclusion ofdistribution centers in a supply chain or goodsflow network is to reduce overall transportationcosts. The PCOD model proposed by Holmblad(2004) is an effort to model freight flow througha network using distribution and consolidationcenters. Certain assumptions are required tointroduce logistics in transforming the P-Cmatrix into an O-D matrix. This is evidenced inHolmblad (2004) who indicated thattraditionally, due to potential complexities,logistics structure in the production-to-consumerchain is generally approximated. Contrary toexisting and most recent advances in transportlogistics models, which undertake the bottom upmodeling approach with an extensive treatmentof modes and networks, the PCOD modelingapproach applies a top to bottom modelingframework. This is characterized by meso-economic, aggregate transport logisticsmodeling, using regional transport centers withtransport decision making at the micro andmacro levels (Holmblad 2004). Holmblad (2004)indicated that the PCOD model has twoprincipal features that make it suitable for freightmodeling. In general, the modeling of freightmovement in the transport system can beundertaken using a heuristic technique, in whichthe unit cost of transport is dependent on thevolume of transport.

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First, as previously mentioned, the PCOD modelfollows a cost minimization approach using theheuristics framework. It converts the regionaltrade flow to regional transport flow, therebyproviding better modeling results relative to amacroscopic approach. Second, by representingthe transport system and network by a limitednumber of parameters, the PCOD modelformulation provides a simplistic and easy tounderstand approach to freight transport usingdistribution centers. To begin with, the PCODmodel divides the general area of interest intozones that have both production output (Pr ) inzone r and final consumption (Cs ) in zone s.This main level of the model building process isreferred to as the P-C land or level 1.

The second level, described as distribution-consumption (D-C) land, is characterized as atransport only zone with no likely production orconsumption. Transport is not restricted withinD-C land, but in P-C land it can be directtransport only (l=r and m=s). The connectionbetween P-C and D-C land can be denoted by amatrix element PCODw

rslm, which is a depictionof transport between the zone r and the zone s(PCrs ) that constitutes the total transport ODw

lmfrom l to m. The matrix element representing theconnection between P-C and D-C land(PCODw

rslm) corresponds to transport from zone lto zone m. The matrix representing theconnection between levels in the PCOD model isas followsPCrs: (PCODw

rslm ) , where

PCODwrslm=PCrs or PCODw

rslm = 0

The entire system is formulated as a system oflinear equations; however, a method at arriving atthe cost of transportation and handling at thedistribution centers is necessary so as to minimizethe system costs.

CONCLUSIONS

This paper illustrates that freight modeling effortsare not fully realized, without considering logisticscomponents in the modeling process. The majority

of freight models have closely followed traditionalfour stage passenger travel demand models. Theneed to improve and incorporate logistics conceptsis understood by transportation modelers both inEurope and the United States, but incorporationof these dimensions into models has been slow.This slow development might be explained partlyby the lack of data needed to incorporate logisticselements in freight models, and partly by theinability of existing modeling tools to incorporatethese dimensions. In this paper we have tracedthe emergence of freight models in different partsof the world and the chronological order of thisdevelopment. We have focused on themathematical tools used in these models as well.In many modeling endeavors, the key obstacle isto adapt the right mathematical tool. This papershould assist modelers in adapting the right toolbased on the modeling objectives.

We have categorized the modeling endeavor intoEuropean freight models and North Americanfreight models. We suggest that European freightmodels seem to be more developed, as far asinclusion of logistics aspects in freight modelingis concerned. We have identified that SAMGODS,SMILE, GOODTRIP, EUNET2.0, PCOD arepioneering freight models which have incorporatedlogistics dimensions into the modeling process.The modeling technique used in many of thesefreight models are varied, but the prime modelingtools used are aggregate-disaggregate-aggregatemodels, input-output models, artificial neuralnetwork models, matrix estimation methods andthe PCOD model. Based on the objectives and dataavailability, these modeling tools are implementedand various additions and alternations areundertaken to arrive at more realistic results forsuccessful implementation.

Logistics decisions, in a business entity, aredynamic and are reshaped constantly by changingbusiness needs. These decisions play major rolesin the direction of freight movement within andbeyond the domestic boundaries of a country. Someof the logistics concepts like reverse logistics; 3PLand green supply chains were not observed in mostof the logistics concepts introduced to macro

Journal of Transportation Management40

freight models. The learning curve for freightmodeling is improving, and it can be anticipatedthat newer concepts in logistics will be adapted infreight modeling. Finally, it should be recognizedthat more work can be done in this area.

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BIOGRAPHIES

Subhro Mitra is Assistant Professor of Business - Logistics and Supply Chain Management atUniversity of North Texas at Dallas. He holds a Ph.D. in Transportation and Logistics from NorthDakota State University. His Research interests include freight flow modeling, security in supplychain, asset management and life-cycle cost, optimizing logistics network and facility location. Hehas published in reputed journals like journal of Transportation Research Record, TransportationJournal, the Journal of Transport and Land Use, International Journal of Operations Research andInformation Systems and Journal of Transportation Research Forum.Email: Subhro.Mitra@unt.edu

Elvis Ndembe is a Ph.D. Candidate in Transportation and Logistics at North Dakota StateUniversity. He holds a Masters’ degree in Agribusiness and Applied Economics from North DakotaState University. His research interests include transportation economics, freight transportationdemand, food and agricultural marketing, and supply chain management. He has written severalreports and published in Agribusiness an International Journal, and Choices Magazine a peer-reviewed Magazine published by the Agriculture and Applied Economics Association (AAEA). Hewas joint 2010 outstanding research award recipient for Agribusiness an International Journal.Email: Elvis.ndembe@ndsu.edu

Poyraz Kayabas is a Ph.D. student in Transportation and Logistics Program at North Dakota StateUniversity. He holds a Masters’ degree in Industrial Engineering and Management from NorthDakota State University. His research interests include freight transportation demand, agriculturallogistics, supply chain management, and traffic safety.Email: poyraz.kayabas@ndsu.edu