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On Transport Service Selection in IntermodalRail/Road Distribution NetworksChristian Bierwirth, School for Economics and Business, Martin-Luther-University Halle-Wittenberg, Germany, E-mail:[email protected] Kirschstein, School for Economics and Business, Martin-Luther-University Halle-Wittenberg, Germany, E-Mail:[email protected], School for Economics and Business, Martin-Luther-University Halle-Wittenberg, Germany, E-Mail: [email protected]

Abstract

Intermodal rail/road freight transport constitutes an alternative to long-haul road transport for thedistribution of large volumes of goods. The paper introduces the intermodal transportation problemfor the tactical planning of mode and service selection. In rail mode, shippers either book train capacityon a per-unit basis or charter block trains completely. Road mode is used for short-distance haulage tointermodal terminals and for direct shipments to customers. We analyze the competition of road andintermodal transportation with regard to freight consolidation and service cost on a model basis. Theapproach is applied to a distribution system of an industrial company serving customers in easternEurope. The case study investigates the impact of transport cost and consolidation on the optimalmodal split.

JEL-classification: R41, M11, L92

Keywords: intermodal transportation problem, service selection, transport cost rates, sustainabletransport chain

Manuscript received April 23, 2012, accepted by Karl Inderfurth (Operations and InformationSystems) July 25, 2012.

1 IntroductionIntermodal freight transport reflects the combina-tion of two or more modes of transport (e.g., road,rail, water) within a single transport chain. It isgenerally assumed that the moved goods are con-tainerized and, thus, allow a standardized hand-ling during the transfer between any two modesinvolved in the transport. Intermodal freight trans-port is receiving increasing attention in the Euro-pean transport economy as it is considered away toincrease traffic safety, and to reduce road conges-tion and air pollution at the same time (EuropeanCommunities 2002).In this paper we concentrate on intermodalrail/road transport from the viewpoint ofa large shipper organization. Today, manyshippers consider intermodal transportation asan alternative for delivering goods to customers

instead of long-haul road transports from theshipper’s door to the customer’s door. However,several prerequisites must hold in order to makethe intermodal transport of goods profitable.

1. The cost rate per transport unit and kilometermust be significantly smaller in rail transporta-tion than in road transportation. Otherwise,the intermodal transport costwould exceed theroad transport cost because the traveling dis-tance of an intermodal chain is always longerthan the direct distance from door to door.

2. The hauling distance between the shipper’sdoor and the customer’s door must be abovea certain break-even distance. This is becausethe cost incurred by an intermodal transportincludes additional fees which are charged byintermodal terminal operators for transferringa transport unit from road to rail or from rail to

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road. The cost advantage of rail transport canonly compensate the additional fees beyond acertain distance covered by rail carriage.

3. The transport is not time critical as it is knownthat intermodal transport usually takes con-siderably more time compared to direct roadtransport.

Shippers must have a model for intermodal trans-port planning which is different from models usedfor planning the long-haul road transports. Sucha model aims at deciding on the transport facil-ities to use and on the capacity that needs to beprovided by carriers on each transport mode inorder to realize a cost-effective flow of cargo. Thecontribution of this paper is to provide such amodel for the tactical transportation planning. Itincorporates the selection of modes of transport,transport services, and the consolidation of cargoflows. Scalable cost functions for road and railtransport are included in the model in order toconsider realistic cost rates for the transshipmentand movement of goods. This way, economies ofscale and consolidation effects are captured in themodel.It is shown by a real-world case study how optimaltransport decisions can be made in a distributionnetwork with competing rail and road transportservices. For this purpose, we consider a com-pany which produces a certain good in a coupleof sites located within one region. The demandregion where the customers reside is far from thesupply region. There are three distinct servicesavailable for the transport of goods. In the firstservice, called door-to-door (D2D), a transportunit is moved directly from a production site to acustomer’s location by means of a road transport.In both other transport services, the goods are firstmoved by truck to an intermodal terminal locatedin the origin region, then moved by train to anintermodal terminal of the destination region, andfinally moved by truck from the destination ter-minal to the customer. The rail transport, whichtakes most of the transport distance, can eitherappear in less-than-train load (LTL) mode wherea company pays a charge for each unit of load, orin full-train-load (FTL) mode where the companycharters a block train as a whole.The paper is organized as follows. In section 2,we briefly review the relevant literature and showthat our approach takes a new perspective not yet

investigated. In section 3, a tactical transportationplanning model is presented which can be used byshippers to decide on serving customers by road,intermodal rail/road transportation, or a mixturethereof. This includes also identifying realistic costfunctions and freight consolidation effects, whichare incorporated in a mathematical optimizationmodel. Section 4 illustrates the model by a smallproblem instance to shed light on the impact of costand the structure of optimal decisions. Section 5presents a case study for a company that serves cus-tomers in eastern Europe from production sites inwestern Europe. The paper is concluded in section6.

2 LiteratureThe growing interest in sustainable (or green) lo-gistics has also given rise to the rapid progressof scientific literature on intermodal transporta-tion. A framework classifying the diverse contri-butions in this field was proposed by Macharisand Bontekoning (2004) and Caris, Macharis, andJanssens (2008). In these survey papers the au-thors employed a classification which contains 12categories combining (i) the type of operator thatfaces an operations problem in the intermodaltransportation chain and (ii) the time horizon ofthe problem. It is distinguished between

• drayage operators, who move goods by truckbetween intermodal terminals and the ship-pers and receivers,

• terminal operators, who transship goods fromroad to rail and from rail to road,

• network operators, who carry goods within therailway network, and,

• intermodal operators, who represent the usersof the intermodal infrastructure.

Intermodal operators are either shippers or re-ceivers themselves, or freight forwarderswhoorga-nize the carriage of goods on behalf of the shippersor the receivers. The length of the time horizonof a problem assigns it to the strategic, tacticalor operational level. Long-term decisions in inter-modal transportation are for instance the locationand layout planning of intermodal terminals, andthe railway network design. Medium-term or tac-tical problems deal with the capacity planning of

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equipment and the development of consolidationand pricing strategies. Short-term problems ad-dress the routing and scheduling of trucks, theload planning of trains, and the redistribution ofcontainers and railcars.Basically, thementioned problems are faced eitherby drayage, terminal or network operators, whilethe intermodal operator is only concerned with theoperational problem of selecting transport routesand services as offered by other operators. Only afew papers addressed the category of operationalproblems faced by an intermodal operator.Min (1991) considered an international supplychain connecting suppliers in Japan with a re-ceiver in the US. The shipper can decide on usingvarious intermodal chains, combining road, rail,air and deep-sea transportation, where both, costand time, are of concern. A goal programmingapproach is proposed which allows model solu-tions and their response to be analyzed regardingchanges of freight rates, charges for loading andstorage, and transit times. In order to achieveminimum cost routes and schedules in generalorigin-destination networks, Barnhart and Ratliff(1993), Boardman, Malstrom, Butler, and Cole(1997), and Ziliaskopoulos and Wardell (2000)as well as Chang (2008) and Verma, Verter, andZufferey (2012) adapted concepts of shortest pathsalgorithms. This streamof research aims at provid-ing operational assistance to intermodal operatorsto identify the optimal path for an individual ship-ment in a network with various transport modesavailable. Verma, Verter, and Zufferey (2012) pro-posed an intermodal routing problem in a rail-road network for containerized hazardous mate-rials. Here, the objective is not only to minimizetransportation cost but also to reduce the expectedrisk inherited by a specific mode of transportation.A more holistic view was taken by Erera, Morales,and Savelsbergh (2005). These authors consideredan intermodal operator managing a homogeneousfleet of tank containers. The containers are movedbetween shippers and customers in a global trans-port network. An integrated model is proposedfor routing containers and repositioning emptycontainers, which is solved as a multi-commoditynetwork flow problem.In contrast to the above research, our paper focuseson the question of how intermodal transportationcan be put in competition with road transporta-tion. Thereby we concentrate particularly on large

shipper organizations residing at multiple loca-tions and producing large volumes of output. If alarge shipper acts as an intermodal operator, alsotactical transport decisions come into the fore.Those decisions comprise, for example, the alloca-tion of a production site to an intermodal terminaland the freight consolidation of shipments in therailway network. Papers dealing with strategic andtactical issues of intermodal operators are as yetunknown. In the framework of Macharis and Bon-tekoning (2004), tactical operation problems areonly assigned to the other types of operators. Thisis because a perspective of small and medium-sized shippers is taken, who delegate the tacticaldecisions to drayage and network operators. Therelevant literature of these categories is briefly re-viewed below.The assignment problem of shipper and customerlocations to a terminal’s service area is referredto as the intermodal ramp selection or intermodalterminal location problem (Taylor, Broadstreet,Meinert, andUsher 2002). This problemwasmod-eled as a binary linear program by Arnold, Peeters,andThomas (2004) and solvedby aheuristic calledIntermodal Terminal Location Simulation System(ITLSS) for a real-world case observed in Spain.In a recent paper, Sörensen, Vanovermeire, andBusschaert (2012) addressed the same problem bytwo meta-heuristics, namely a Greedy Random-ized Adaptive Search Procedure (GRASP) and anAttribute-Based Hill Climber (ABHC). For a set ofrandomly generated test instances, both methodsare able to discover solutions nearby the optimalsolution. Ishfaq and Sox (2010) provided a modelfor intermodal terminal location that also allowsdirect shipments by road transports. Economies ofscale are reflected by non-linear transport costs.They propose a tabu search procedure which isable to find near-optimal solutions for networkswith up to 20 terminals. This branch of litera-ture is still growing with focus, e.g., on the in-corporation of different service types, see Ishfaq(2012), or on different transport units, see MengandWang (2011). However, all approaches assumea set of predefined transport orders with given ori-gins and destinations. In contrast, in this paper weare given production quantities and customer de-mands where the flow and consolidation of goodsis the subject of the optimization.Closely related with the intermodal terminallocation problem is the freight consolidation

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problem faced at an intermodal terminal.Obviously, the more shipment volume is allocatedto a certain terminal, the better a network operatorcan consolidate the inbound and outboundtransport operations. At the tactical level, networkoperators have to decide about the frequencyof a service, the assignment of equipment andcapacity to services, the lengths of trains, and thelike (Nozick and Morlok 1997). These decisionsbasically influence the cost contribution of the railcarriage in the intermodal transport and thus havea strong impact on competitiveness. Spasovic andMorlok (1993) estimated that rail contributesbetween 60% to 75% of the total origin-destinationcost in the intermodal transportation. Kim andVan Wee (2011) provided a thorough survey onthe cost of intermodal transports. By means ofsimulation, the relative importance of the variouscosts of an intermodal transport is studied. Itis found that the costs of long-haul road andrail transports have the highest impact on thecost-effectiveness of intermodal transports. In theabsence of realistic cost information, Sörensen,Vanovermeire, and Busschaert (2012) determinedtransport cost by the Euclidean distance betweenorigin and destination and incorporate a raildiscount through dividing the covered raildistance by two. Estimate functions for true costrates in road and rail traffic were provided byJanic (2007, 2008).

In this paper, we take the position that the men-tioned tactical problems are in the responsibility ofthe shipper. We investigate the selection problemof terminals in the origin and in the destinationarea together with the freight consolidation prob-lem for the rail transport. The latter problem alsoincludes choosing LTL, FTL, and D2D transportservices. The cost effects of these decisions are in-cluded in a function used for estimating the totalcost of all considered transport services.

3 The Intermodal TransportationProblem

In this section,we formally describe the consideredplanning problem, identify realistic cost functionsand freight consolidation effects, and provide amathematical optimization model. The notationused for modeling the problem is summarized inTab. 1.

Figure 1: Network representation of theclassical transportation problem

3.1 Notation and assumptionsIn the intermodal transportation problem (ITP),a set of customers C and a set of production sitesS are given. The production sites produce a cer-tain product that is demanded by customers. Thedemand of customer c ∈ C, measured in transportunits (TUs), is denoted by nc. The production out-put of site s ∈ S,measured in TUs, is denoted by qs.It is assumed that the company’s productionplan issuch that total output equals total demand. Gener-ally, shipments can be sent on a per-TU basis fromproduction sites to customer locations by a D2Droad transport service. The corresponding trucktravel distance between nodes s ∈ S and c ∈ C inthe network is denoted by dsc and the correspond-ing cost rate per TU and kilometer (km) is denotedby cD2D. Suppose the shipper aims at minimizingthe total cost of transportation using exclusivelyD2D services, then the resulting problem resem-bles the classical transportation problem, Dantzigand Thapa (1997). This situation is illustrated inFig. 1 for a network with two production sites andthree customers.In the ITP, shippers are also given the oppor-tunity to ship goods by rail. In general, next toproduction sites and customer locations, so-calledintermodal terminals are available in the logisticsnetwork, enabling the transfer of TUs from roadto rail or vice versa. In the following, it is assumedthat the shipper has already preselected a set ofterminals to be potentially used for intermodaltransportation, leading to a network that containstwo subsetsO andD of intermodal terminals. Ter-minals o ∈ O are located in the origin area wherethe production sites reside. They receive goodsfrom the production sites and distribute them to

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Figure 2: Network representation of theITP

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terminals d ∈ D in the destination area, wherethe customers reside. Fig. 2 shows a simple inter-modal network consisting of two origin terminalsand two destination terminals. In order to performan intermodal rail/road transport, a pre-carriagefor shipping goods from production sites to termi-nals o ∈ O and a post-carriage for shipping goodsfrom terminals d ∈ D to customers is done byroad transportation while transportation betweenterminals o and d is bridged by a long-haul railtransportation. In this logistics network, the set ofnodes is given byN = S∪O∪D∪C. The set of roadconnections is defined byA = S×C ∪ S×O ∪ D×Cand the set of rail connections is represented byB = O×D.Typically, rail operators provide twodifferent typesof services to shippers. InFTL service, the shippingcompany charters a complete block train, whichprovides a capacity of capFTL TUs. For this service,the shipper has tomeet a cost rate of c̃FTL, which ismeasured in e per kilometer traveled by the blocktrain. In LTL service, train capacity is booked byshippers on a per-TU basis. Here, the shipper hastomeet a cost cLTL per TU-km. In practice, the costfor FTL transportation allows a saving over LTLtransportation cost provided a sufficiently largenumber of TUs can be consolidated within onechartered block train.Given the output volume of the production sites,the ITP is to decide on the usage of D2D, FTL,and LTL services such that customer demand isfulfilled at minimum total transportation cost. Inparticular, this problem includes deciding on thenumber of block trains to be chartered, on thenumber of TUs sendbyLTL service, and, finally, on

Table 1: Notation

Network:C set of customersS set of production sitesO set of terminals in the origin areaD set of terminals in the destination areaN set of nodes,N = S ∪ O ∪ D ∪ CA set of road transport arcs,

A = S×C ∪ S×O ∪ D×CB set of rail transport arcs, B = O×Ddij distance between nodes i ∈ N and j ∈ NServices:D2D direct door-to-door road transportFTL full-train-load rail serviceLTL less-than-train-load rail serviceQuantities and capacities:qs quantity provided at site s ∈ Snc demand of customer c ∈ CcapFTLload capacity of a block train (in TU)capFTLbreak-even capacity (in TU)Cost rates:cD2D D2D cost rate per TU-kmcpre pre-carriage cost rate per TU-kmcpost post-carriage cost rate per TU-kmc̃FTL FTL cost rate per train-kmcFTL FTL cost rate per TU-km, cFTL = c̃

FTL

capFTL

cLTL LTL cost rate per TU-kmwith cLTL≥cFTL

Decision variables:xij flow of TUs on arc (i, j)∈A ∪ BxLTLod LTL flow of TUs on rail arc (o,d) ∈ Byod number of chartered block trains on rail

arc (o,d) ∈ Bzod binary, 1 iff a block train is chartered for

a shipment volume above capFTL andbelow capFTL on rail arc (o,d) ∈ B

roadshipments forpre-carriage, post-carriage, andD2D services. To summarize, the ITP consideredin this paper is characterized as follows:

• All input data is known and deterministic. Vol-ume of goods is measured in transport units(TUs), distance is measured in kilometer (km),and cost is measured in Euro (e).

• The truck load capacity is given by one TU andthe train load capacity is given by a fixedmulti-

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ple of TUs. This enables a straight transforma-tion of truck shipments into train loads whenconsolidating cargo in an intermodal terminal.

• Production output, transport flow, anddemand of goods consider a single type ofcommodity. The total output of productionsites equals the total customer demand.

• The production sites are clustered in onegeographical area (called the origin area). Thecustomer locations constitute a second cluster(the destination area). Rail links connect theintermodal terminals in both areas. Such a net-work structure is observed, for instance, whenan industrial region serves a foreign market.

• In the ITP, schedules for truck and traintravels as well as handling times at theintermodal terminals are out of scope.

3.2 Modeling cost and freightconsolidation effects

Inorder to generate reliable solutions fromthe ITP,realistic cost rates for road and rail transportationaswell as freight consolidation effectsmust be con-sidered in the planning model. Typically, in roadtransportation, vehicle cost per traveled kilometerobeys economies of scale, i.e. cost decrease withthe length of the hauling distance. The total travel-ing cost of a vehicle contains fixed cost, including,e.g., loading and stop cost, and variable cost de-pending on the distance traveled. Since fixed costsare shared among the traveled distance units, adecrease in the total cost per traveled kilometeris observed. Furthermore, short-distance trips areoften performed at lower average speed comparedto long-distance trips. Hence, costs incurred ona time basis, like salary of truck drivers, have astronger impact on the cost per kilometer in short-distance transport.Several studies provide models for capturing theseeffects within cost functions for road transportoperations, e.g., Forkenbrock (2001), Smart andGame (2006), Janic (2007, 2008). The model ofJanic (2007) describes these effects for road trans-portation within the EuropeanUnion. It quantifiesthe average cost per vehicle-kilometer croad by aninverse exponential function of the haulage dis-tance d as

(1) croad(d) = e5.46 · d−0.278

Figure 3: Road and rail cost functionsbased on Janic (2007)

00.250.500.751.001.251.501.752.002.25

0 250 500 750 1000 1250 d [km]

cost rate[e/TU-km]

crailTU

croad

per vehicle-km. Since we define the load capacityof a truck by one TU, the vehicle cost function (1)can be used to determine the cost per TU-km at thesame time. The function croad(d) is depicted in theupper curve of Fig. 3. To simplify the formulationofthe ITP, we derive individual cost rates from thisfunction for the pre-carriage, the post-carriage,and for theD2D service. Cost rate cpre is calculatedfrom the average distance between all productionsites and all terminals in the origin area. Cost ratecpost is obtained in the same way from the aver-age distance between terminals in the destinationarea and the customer locations. This simplifica-tion is justified by the fact that freight carriersusually charge the same cost rate for services thattake place within a same region. Finally, the costrate cD2D is obtained from the average door-to-door distance between the production sites andcustomer locations.Decreasing cost per traveled kilometer is also ob-served in rail transportation. Janic (2007) spec-ified average train travel cost per kilometer as afunction of train gross weight w and the haulingdistance d. It is calculated by

(2) crail(d,w) = e0.58 ·w0.74 · d−0.26

per train-km. The author also reported the averagegross weight ofw = 1560 tons for freight trains inEurope. Corresponding information for Australiaand the US is provided by Forkenbrock (2001) andSmart and Game (2006).In order to derive the cost per TU-km for railtransportation, the load capacity of a block traincapFTL must be taken into consideration. Becauseof technical limits regarding the maximal grossweight and the maximal overall length of trains,capFTL = 38 TUs is observed in western Europe

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Figure 4: Cost function for consolidatedrail transports

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(DB Netz AG 2009). With this value and assuminga fully utilized train, the cost function (2) results ina corresponding function crailTU(d) which measuresthe average cost per TU-km over a train traveldistance d by

crailTU(d) =1

38· e0.58 · 15600.74 · d−0.26

= e3.52 · d−0.26(3)

per TU-km. As expected, crailTU(d) is clearly belowcroad(d), see Fig. 3.To derive transport cost rates applicable in theITP model formulation, we transform (2) and (3)into rates for FTL and LTL transportation. Thecost per train in FTL transportation is calculatedfrom (2) by c̃FTL = crail(d,1560), where d is setto the average travel distance between the termi-nals in the origin area and the terminals in thedestination area of an ITP instance. The cost perTU in FTL rail transportation is calculated from(3) by cFTL = crailTU(d). Finally, the cost per TU inLTL transportation is calculated by cLTL = ε ·cFTL,where ε ≥ 1 reflects the surcharge that has to bemet by the shipper when rail transport capacity isbooked on a per-TU basis.Having determined the service cost for D2D, LTL,FTL, pre-carriage, and post-carriage, the total costfor serving a customer exclusively from one pro-duction site and with one transport service is com-posed as shown in Tab. 2.When selecting services for rail transportation, afurther effect has to be taken into consideration.Since cost per TU are lower in FTL service thanin LTL service (cFTL < cLTL), selecting FTL ser-vices can be economically useful even if the blocktrain capacity is not fully exploited by the shippedvolume. The break-even load capFTL, at whichchartering a block train at cost rate c̃FTL is less ex-

Table 2: Transportation cost for relation(s, c) under exclusive service selection

cost

service pre-carriage main-carriage post-carriageD2D - nc ·cD2D ·dsc -LTL nc · cpre · dso nc ·cLTL ·dod nc · cpost · ddcFTL nc · cpre · dso � nccapFTL �·c̃FTL ·dod nc · cpost · ddc

pensive than shipping in LTL service on a per-TUbasis, is computed by

(4) capFTL =cFTL

cLTL· capFTL =

c̃FTL

cLTL.

It results as the ratio of cost per TU in FTL andLTL servicemultiplied by the load capacity of a fullblock train. Any shipment volume above capFTL

justifies chartering a block train to save cost overthe LTL service. The resulting cost function forconsolidated rail transports is shown in Fig. 4.The consolidation of cargo that is shipped on a railarc (o,d) ∈ B is performed in three steps: First,the number of block trains yod to be chartered andfully used for FTL services is determined by

(5) yod =⌊

xodcapFTL

⌋,

where xod denotes the number of TUs that theshipper projects to send via rail link (o,d). Second,for the rest of the shipment, which is computedby xod − yod · capFTL, FTL service is booked if itexceeds the break-even capacity, and LTL serviceotherwise. This decision is reflected by the binaryvariable zod defined as

(6) zod =

{1, if xod −yod · capFTL > capFTL.0, otherwise.

Having determined yod and zod, the number of TUssend in LTL service is finally calculated by

(7) xLTLod = max{0, xod − (yod + zod) · capFTL}.

3.3 Optimization modelNext to the decision variables introduced for mod-eling the flow of TUs on rail arcs (xod) and thefreight consolidation for FTL and LTL services(yod, zod, xLTLod ), we also define variables xij for theflow of TUs on road arcs (i, j) ∈ A. With these de-cision variables, the ITP is formulated as a mixed-

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integer programming (MIP) model as follows.

[ITP] min → Z =∑s∈S

∑c∈C

xsc · dsc · cD2D

+∑s∈S

∑o∈O

xso · dso · cpre

+∑d∈D

∑c∈C

xdc · ddc · cpost

+∑o∈O

∑d∈D

(yod + zod) · dod · c̃FTL

+∑o∈O

∑d∈D

xLTLod · dod · cLTL(8)

subject to∑j∈O∪C

xsj = qs ∀s ∈ S(9)

∑s∈S

xso =∑d∈D

xod ∀o ∈ O(10)

∑o∈O

xod =∑c∈C

xdc ∀d ∈ D(11)∑

i∈S∪Dxic = nc ∀c ∈ C(12)

yod ≥xod

capFTL− 1 ∀(o,d) ∈ B(13)

M · zod ≥ xod − yod · capFTL − capFTL(14)∀(o,d) ∈ B

xLTLod ≥ xod − (yod + zod) · capFTL(15)

∀(o,d) ∈ Bxij, xLTLod ≥ 0 ∀(i, j) ∈ A ∪ B, (o,d) ∈ B(16)

yod ∈ N ∀(o,d) ∈ B(17)zod ∈ {0,1} ∀(o,d) ∈ B(18)

The objective function (8) minimizes the totaltransportation cost. It comprises the cost of D2D,FTL, and LTL services together with the cost ofpre- and post-carriages. Constraints (9) ensurethat the total production volume of site s is shippedto customers directly or to the intermodal termi-nals. Constraints (10) and (11) represent the in-flow/outflow conditions for the terminals. Here,(10) ensures that all goods sent from produc-tion sites to a terminal in the origin area leavethis terminal for terminals in the destination area.From (11), it is ensured that all goods arriving ata terminal in the destination area are shipped tocustomers. Constraints (12) ensure that customerdemand is fulfilled. Constraints (13) to (15) affect

the consolidation of cargo on rail links (o,d) ∈ Bby setting decision variables yod, zod, and xLTLod .These constraints represent the MIP formulationof Equations (5) to (7) . In detail, Constraints (13)determine the number of used block trains thatare fully loaded. Constraints (14) decide whether afurther block train is chartered for the remainingTUs (zod = 1). Here,M refers to a positive numberequal or larger than capFTL. Finally, Constraints(15) determine the number of TUs for which LTLservice is booked. The domains of the decisionvariables are defined in (16) to (18). Note that nointeger condition is required for the flow variablesin (16). These variables inevitably take integer val-ues provided that production quantities, customerdemands, and train capacity parameters are allintegers.It can be taken from model (8)-(18) that the ITPis a generalization of the classical transporta-tion problem. Actually, it reduces to this prob-lem if rail transportation is omitted by enforcingxLTLod = yod = zod = 0. Nevertheless, the general-ized problem remains a linear flow problem thatis solvable by standard solvers even if the pro-duction sites, customers, and terminals composean intermodal network with several hundred loca-tions. Therefore, the MIP-solver ILOG Cplex 12.1(ILOG 2012) can be used to solve ITP instances ofpractical size.

4 Illustrative exampleAn example is provided for gaining insight into thestructure and diversity of ITP solutions. We inves-tigate the selection of services and the transportflows that are found by the optimization modelfor a very simple network structure under vari-ous cost parameter constellations. The network ischaracterized by two production sites, three cus-tomers, exactly one intermodal terminal o in theorigin area, and one intermodal terminal d in thedestination area. Locations of the network nodesare chosen such that the rail distance betweenthe intermodal terminals is dod = 1000 km. Thedoor-to-door road distances between productionsites s ∈ S and customers c ∈ C, the pre-carriagedistances between production sites and terminalo as well as the post-carriage distances from ter-minal d to the customers are shown in Tab. 3(gray cells). Note that, for each combination of sites ∈ S and customer c ∈ C, the total distance for

205


an intermodal transport (dso + dod + ddc) is strictlylarger than the corresponding direct door-to-doordistance dsc. This is because intermodal transportsrequire a detour for visiting the intermodal ter-minals. Furthermore, road traffic networks are farmore dense and, thus, usually approximate an air-line distance closer than rail traffic networks can.Additionally, the customers’ demands and produc-tion sites’ outputs are given in the last row and lastcolumn of Tab. 3, respectively. The values havebeen chosen such that total production outputequals total customer demand.

Table 3: Example parameters: Transportdistances, demand & production quantities

customer c term. qs1 2 3 o

site s1 1200 900 1100 150 150

2 1100 1000 900 50 50

term. d 300 150 50 1000 -

nc 110 70 20 - 200

Table 4: Experimental setting: Cost ratiointervals

cFTL

cD2Dcdray

cD2D

lower bound 0.1 0.1upper bound 1.5 3.0step size 0.0025 0.0025

We first investigate the impact of changes of thecost rates on the selection of transport services.For this purpose, cost rates cFTL, cLTL, cpre, andcpost are varied within certain intervals. The D2Dcost rate cD2D is determined as described in section3.2. It is kept fixed and serves as a reference valuewhen varying the other rates. To limit the numberof possible parameter variations, we consider afixed ratio between LTL transport cost and FTLtransport cost per TU. We assume that LTL cost is25%aboveFTL cost, i.e. we set ε = 1.25 and derivecLTL = 1.25 · cFTL. We also assume that the pre-and post-carriage cost rates are equal and jointlyrefer to them as the drayage cost rate cdray = cpre =cpost. In the experiment, the cost ratios c

FTL

cD2D andcdraycD2D are considered.These ratios are systematicallyvaried as specified inTab. 4. Fromthis full-factorialexperimental design,weobtainmore than300000

parameter combinations.Model ITP is solved oncefor each combination using ILOG Cplex 12.1.Figure 5 illustrates the percentage of the totaltransport volume that is shipped in intermodalrail/road transportation under each combinationof cost ratios. This measure is also referred to asthe intermodal share of transports. It can be seenthat ten differently structured solutions turn out tobe optimal with respect to specific constellations ofthe cost ratios. The intermodal shares of these tensolutions differ strongly. They range from a pureintermodal transport (solution 1), where all TUsare shipped on the rail link, to a pure D2D service(solution 10) where no customers are served byintermodal transport. The modal split of the tensolutions, i.e. the percentage of the total transportperformance (measured in TU-km) carried out inthe distinguished service modes, is shown in Fig.6.Further details about the ten solutions, includingthe number of chartered block trains (yod + zod)and the number of TUs sent in LTL service (xLTLod )as well as in pre-carriage, post-carriage, and D2Drelations are provided in Table 5.The cost ratios c

FTL

cD2D = 1 andcdraycD2D = 1 subdivide

Fig. 5 into four quadrants. In the upper quad-rants, cFTL is larger than cD2D makingD2D servicethe cost-efficient option for the very most con-stellations. Only if the drayage cost rate cdray ismuch lower than cD2D, the saving in pre- and post-carriage can compensate the higher rail transportcost, leading to a few intermodal transports (solu-tions 4 and 6). However, in practice, FTL cost perkilometer is usually lower than long-haulD2D costper kilometer. This means that the constellationshown in the upper quadrants is rather unrealistic.Similarly, short-distance drayage cost per kilome-ter is usually above long-haul D2D cost per kilo-meter. Hence, also the constellation of the two leftquadrants is hardly met in practice. Realistic costconstellations, where cdray ≥ cD2D ≥ cLTL ≥ cFTL

holds, fall into the lower-right quadrant of the fig-ure. It is worth mentioning that all ten solutionsare met in this quadrant. From this observation, itis found that already a very small instance of theITP can show a variety of different solutions beingoptimal under specific transportation cost rates.Using Fig. 5, we further investigate the change ofthe solution structure following from the varia-tion of one cost parameter under ceteris paribusconditions. Starting from solution 1, where all cus-

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Figure 5: Intermodal share of transports under varied cost

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tomers are served by intermodal transport, theincrease of cFTL causes a gradual decrease in theintermodal share, see solution sequence 1-2-3-4-6-8-10. Interestingly, such change-overs often com-prise shifting a number of TUs from one service toanother, but not necessarily a shift of a completecustomer demand between services. For example,as can be taken from column xd2 in Tab. 5, the so-lution sequence 1-2-3-4 corresponds to a stepwisedecrease in the fraction of demand of customer2 that is served by rail. Gradual decreases in theintermodal share and the exchange of customer de-mands on the rail link are caused by the restrictedproduction volumes of production sites and theconsolidation effects in the intermodal transport.For these reasons, optimal solutions can bring outthat customers are served by a combination of twoor more services. We even observe two solutions(5 and 7) where the shipper makes use of all threeservices.The analysis reveals the mechanism that deter-mines whether LTL orD2D service is selected for acustomer. A prerequisite for choosing LTL serviceis that c

LTL

cD2D < 1 holds. This is because an LTLservice causes additional detour cost for the pre-and post-carriages to and from the intermodal ter-minals. Hence, considering a customer c that is

projected to be served by site s, the shipper facesthe question of whether the detour cost stays be-low the cost saving that results from rail haulage.In other words, the shipper needs to determinethe maximum pre- and post-carriage distance upto which serving customer c by site s in LTL ser-vice is profitable. This question can be answeredby assuming cost equality for the LTL and D2Dtransport cost functions in Tab. 2.

(19) cD2D · dsc = cpre · dso + cLTL · dod + cpost · ddc

If cdray = cpre = cpost holds, Equation (19) can bereformulated as

(20) dsc =cdray

cD2D· (dso + ddc) +

cLTL

cD2D· dod.

Given certain cost rate ratios cdray

cD2D andcLTLcD2D as

well as the door-to-door distance dsc and the trainhaulage distance dod, the right-hand side of Equa-tion (21) then delivers an upper bound for thedrayage distance up to which LTL is economicallypreferable compared with D2D service.

(21) dso + ddc <cD2D

cdray· dsc −

cLTL

cdray· dod.

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Table 5: Detailed results for all solutions

sol.intermodal share rail transport pre-carriage post-carriage door-to-door

% # TU yod+zod xLTLod x1o x2o xd1 xd2 xd3 x11 x12 x13 x21 x22 x23

1 100 200 5 10 150 50 110 70 20 0 0 0 0 0 02 95 190 5 0 140 50 110 60 20 0 10 0 0 0 03 76 152 4 0 102 50 110 22 20 0 48 0 0 0 04 57 114 3 0 80 34 110 0 4 0 70 0 0 0 165 45 90 2 14 40 50 0 70 20 110 0 0 0 0 06 38 76 2 0 26 50 0 56 20 110 14 0 0 0 07 25 50 1 12 0 50 0 30 20 110 40 0 0 0 08 19 38 1 0 0 38 0 18 20 98 52 0 12 0 09 10 20 0 20 0 20 0 0 20 80 70 0 30 0 010 0 0 0 0 0 0 0 0 0 80 70 0 30 0 20

For example, with cost rates cdray = 5, cD2D = 2,cLTL = 1, a given door-to-door distance dsc =d23 = 900 km, and a given rail haulage distancedod = 1000 km, the upper bound for the drayagedistance is 160 km. With the drayage distanced2o+dd3 = 100km for serving customer 3 fromsite2, LTL service is less expensive than D2D serviceunder the considered cost rates. The describedparameter constellation leads to solution 9, wherecustomer 3 is served in LTL service. If, however,the LTL rate increases to cLTL = 1.5, the upperbound for the drayage distance changes to 60 km.Now, the actual drayage distance of production site2 and customer 3 exceeds the upper bound and,consequently, customer 3 is served by a door-to-door transport.The conducted analysis allows to decide whichservice to choose (LTL or D2D) for a certainsite-customer relation. Still, the complexity of theITP, involvingmultiple sites, customers, terminals,and FTL consolidation hinders solving the entireproblem through consideration of individual site-customer relations.

5 Real-world case studyIn this section, we present a case study of a largecommodity-producing company that resides inwestern Europe. In the next subsection we mo-tivate the case study. Afterwards, we describe theproduction and distribution network that is usedby the company. Finally, the cost drivers of the dis-tribution system are subject of an analysis that isbased on solving the ITP in different settings. The

results are discussed and recommendations re-garding the future development of the company’sdistribution system are drawn.

5.1 MotivationWe consider a company which is currently themarket leader for a chemical product used in theconstruction industry. This good is produced atproduction sites located in Germany, Belgium, andthe Netherlands. The sites produce the good forthe entire European market. In the case study,we focus only on a part of the eastern Europeanmarket, in particular Ukraine. Currently the com-pany faces a strong growth of demand in thiscountry. However, since places for production andconsumption are far away from each other, a signi-ficant logistical effort arises to serve the customers.At the moment, the production and distribution isorganized as follows. Customers order the goodson a monthly basis. From this data, the companygenerates a master production schedule specifyingthe monthly output of the production sites. Af-terwards, each customer is informed which of thesites handles its order. Typically, goods are pro-vided at the production sites and the customersorganize truck transportation for each single TU.This policy for the distribution and payment ofgoods follows the incoterm ′Ex Works′ (EXW),ICC (2010). It means that it is the customer’s re-sponsibility to organize and pay for the shipmentof TUs from the providing site to their own frontdoor. Next to the distribution cost, the customeralso bears the risk involved in the transportationprocess. To get rid of the diverse risks involved in

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Figure 6: Modal split as a percentage oftotal TU-km

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eastern Europe transportation, the company hasfavored the sketched trading conditions in the past.As a consequence of the behavior of the producerand the customers, the distribution of goods reliesalmost completely on D2D road transportation.On the other hand, the company faces increas-ing expectations of governmental authorities andNGOs regarding product responsibility and sus-tainable logistic processes. For these reasons, thecompany is thinking about insourcing the distri-bution process, by switching the EXW policy tothe conditions of the ′Delivered at place′ (DAP)incoterm. Here, the customer specifies the point ofdelivery in their home country, which is usually thecustomer’s front door, and the producer has to pay

the cost and to bear the risk of the transportation.On the other hand, the company can control theflow of goods by selecting the used transportationservices.In the following study it is investigated whetherintermodal transportation is a viable option forserving customers. Our analysis is based only ontransportation cost rates where further costs likeinsurance and duties are beyond its scope. In along-term perspective, the company is also inter-ested in knowing the impact of changes in trans-portation cost on the optimal distribution policy.This is motivated by an expected increase of roadtransport cost (e.g., through emission fees, roadtolls, and energy cost) and a possible decreaseof rail transport cost (through infrastructural de-velopment of railway networks, subsidies for in-termodal transport, and growing efficiency of railtransport providers). To investigate these ques-tions, the distribution system of the company ismodeled as an intermodal transportation problemand solved to optimality under various parameterconstellations.

5.2 DataThe case study considers eleven production sitesin western Europe and 35 customer locations inUkraine. Somecustomers refer to a single companywhereas others refer to local markets. The averagedistanceofdirectD2D transportationbetweensitesand customers is 2213 km. According to (1) thiscorresponds to the cost rate cD2D = 0.64 e perTU-km.We consider two different scenarios for the railtransport network, one scenario with only two in-termodal terminals and the other scenario withfive intermodal terminals. In the 2-terminal sce-nario, one terminal is located in the origin areaand one is located in the destination area. The ter-minal in the origin area lies in central Germany. Itis attractive for intermodal transportation as it isclosely located to one of the production sites. Fur-thermore, the terminal lies in the eastern part ofthe origin area, which eases consolidation of cargothat is sent from other production sites eastwardsto the customers in Ukraine. The terminal in thedestination area is located near Kiev. This locationconstitutes more or less the center of the destina-tion area. The rail link connecting both terminalshas a length of 1765 km.

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Table 6: Distances of rail links for5-terminal scenario

terminal o1 2

term

inal

d 1 1765 2360

2 1130 1800

3 2180 2850

In the 5-terminal scenario, two terminals are lo-cated in the origin area and three terminals arelocated in the destination area. Next to the termi-nal in central Germany, a second terminal in theorigin area is at Rotterdam. This facility is chosenbecause it is close to the westernmost productionsites and it is capable of handling large volumesof chemical products. In Ukraine, two more termi-nals are selected in industrial centers, namely inLviv and in Dnipropetrovsk. The terminals in the5-terminal scenario are connected by six rail linkswith distances shown in Tab. 6. The further termi-nals promise shorter drayage distances, which isexpected to make intermodal transportation moreattractive. We consider both scenarios to assessthe benefit gained from a denser transportationnetwork.The average distances for pre-carriage and post-carriage are givenwith462kmand368km, respec-tively, in the 2-terminal scenario. In the 5-terminalscenario, the average distance for pre-carriage tothenearest terminal is 313kmand forpost-carriageit is 178 km. Corresponding cost rates cpre and cpost

are computed as described in section 3.2. Thereby,the post-carriage rate is reduced by one third torepresent the lower cost level in Ukraine. Thisreduction expresses the current difference in pur-chasing power between Ukraine and the EuropeanUnion, see Worldbank (2012). In the 2-terminalscenario the cost rate for chartering a block trainover the distance of 1765 km is calculated by c̃FTL =19.15e per train-km.According to the regulationsof western European railways, the block train ca-pacity is limited to capFTL = 38 TUs, see DB NetzAG (2009) and Fiedler (2005). Although, regula-tions in eastern Europe are less strict, cross-borderrail transport to eastern Europe is not allowed toexceed capFTL, see Vogel (2000). Hence, we ob-serve a corresponding cost in FTL transportation

Table 7: Cost rates used in the case study

2-terminal 5-terminal

cD2D 0.64 e per TU-kmcpre 0.99 e per TU-km 1.11 e per TU-kmcpost 0.70 e per TU-km 0.86 e per TU-kmc̃FTL 19.15 e per train-km 18.50 e per train-kmcFTL 0.50 e per TU-km 0.49 e per TU-kmcLTL 0.55 e per TU-km 0.54 e per TU-km

of cFTL = 138

· c̃FTL = 0.50e per TU-km. From thiswe estimate the LTL cost rate cLTL = 0.55 e perTU-km, including a 10% surcharge (ε = 1.1). Inthe 5-terminal scenario the cost rate for charteringa block train over an average distance of 2014 kmis calculated by c̃FTL = 18.50 e per train-km withcorresponding cost per TU-km of cFTL = 0.49 eand cLTL = 0.54 e in FTL and LTL transporta-tion, respectively. All cost rates are summarizedin Tab. 7. Furthermore, the case data consist ofproduction quantities and customer demands for aone-month period as well as of traveling distancesfor road transports, see Tab. 9-11 in Appendix A.

5.3 ResultsThe company is interested in knowing the effi-ciency of the current way of distribution, which isbased completely on direct D2D truck transporta-tion. To answer this question, an ITP instanceis created with the data reported above and railtransportation is suppressed by fixing the decisionvariables xLTLod = yod = zod = 0. This way, a clas-sical transportation problem is solved which leadsto a transportation plan of total cost e541 900 anda total transportation performance of 844214 TU-km. The solution is visualized in Fig. 7a where thewidth of a line reflects the intensity of the TU flow.This solution serves as a reference solution in thefollowing study.Solving the ITP instances for the 2-terminal sce-nario and the 5-terminal scenario, we obtain thesolutions shown in Figs. 7b and 7c, respectively.Here, the bold lines depict the flow of TUs alongrail links. The dashed green lines refer to roadtransportation in pre- and post-carriage. In thesolution of the 2-terminal scenario, 22% of TU-km are performed in rail mode, leading to totalcost of e 531 568, see Tab. 8. This represents a2% saving realized by economies of scale in the

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Table 8: Case study results for differentproblem settings

setting interm.share

total cost

ref. sol. (100% D2D) 0% e541 9002-terminal scen. 22% e531 568 (-2%)5-terminal scen. 32% e516802 (-5%)

rail transportation compared with the referencesolution. In the 5-terminal scenario, rail transportaccounts for 32% of TU-km. This is explained bythe shorter distances in the pre- and post-carriageand by the longer distances between rail terminalsin the origin and destination area. The total costof this solution is e 516802, which is another 3%saving compared with the optimal solution of the2-terminal scenario. In this scenario, customerslocated in the western Ukraine are still served byD2D service. For these customers, the drayage costof intermodal transport would exceed the savingsgenerated through the rail transport. It is also in-teresting to see that only two of the three terminalsin the destination area are used in the optimal solu-tion. Obviously, customers of western Ukraine canbe served at relatively short D2D distances, whiledrayage distances exceed the upper bound (21).In consequence, the westernmost rail terminal ofUkraine cannot be used profitably for intermodaltransportation at the assumed cost rates.Although the cost savings of intermodal trans-portation are noteworthy in both scenarios, theyalone do not justify to switch about 30% of TUvolume from EXW to DAP terms because of theaccompanying risk and administrative expense.However, since the company is facing an increas-ing public interest in climate protection, it con-siders changing the distribution system in order toreach a desired percentage of intermodal transportperformance. In the following, we investigate howthe optimal transport plan changes if a certain per-centage of intermodal transports is enforced. Forthis end, restriction (22) is added to the ITPmodelwhich assures that at least p%of the total transportperformance accounts for the rail mode.

(22)∑

(o,d)∈Bxod · dod ≥ p ·

∑(i,j)∈A∪B

xij · dij

To assess the impact of this additional constraint,the ITP is solved for both scenarios under values of

p ranging from 0% to 65%. Note that shares largerthan 65% cannot be enforced in the consideredscenarios because road transportation is not com-pletely avoidable due to the drayage operationsrequired in intermodal transportation.The observed optimal distribution cost are shownin Fig. 8. It is found that the distribution cost isconstant for p38% total cost exceeds the cost of thereference solution, i.e. the intermodal transportno longer provides an economic advantage for thecompany. A similar observation is made for the5-terminal scenario, where total costs are constantup to p=32%. They are below the cost of the ref-erence solution for p


Figure 7: Solutions for the case study(a) Optimal network flow - reference solution (only D2D transports).

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Figure 8: Total cost under varied values of p

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13 and 17 e per train-km. We take from Fig. 9that observing the market for rail services care-fully is a good recommendation for large shipperorganizations. With their high transport volumesthese companies have the power to negotiate lowerrates and, thus, can generate a substantial savingof transportation cost that would justify switchingincoterms.Moreover, comparing the 2- and 5-terminal sce-narios, it can be recognized that total transporta-tion cost are always lower in the 5-terminal sce-nario, i.e. in the denser railway network. Of course,this effect diminishes the less rail transportation isinvolved in the distribution system as is caused byexpensive train cost rates above 22e per train-km.On the contrary, for cheap train cost rates below 17e per train-km, the difference in total cost of bothscenarios is almost constant. This is striking, asit means that a dense network cannot take higheradvantage from very cheap train cost comparedwith a sparse network.Finally, we analyze the interplay of LTL and FTLservices to consolidate the rail transportation be-tween western Europe and Ukraine. Here, the aimis to verify whether LTL transportation is an at-tractive alternative for the considered companygiven that per-TU transportation cost is usually

larger than FTL cost per TU-km. For this end, weconsider three selected FTL train cost rates. Foreach of these rates, we derive two LTL cost rates,namely cLTL = ε · cFTL with ε = 1.0 and ε = 1.1,respectively. Note that with ε = 1.0, no incentiveis created for the shipper to consolidate full blocktrain loads. The resulting six ITP instances havebeen solved for both terminal scenarios.For the 2-terminal scenario, the transport per-formance (measured in TU-km) achieved in theoptimal solutions is depicted in Fig. 10. It indicatesthat the modal split clearly favors rail transporta-tion, the lower the train charter rate c̃FTL is. At thesame time, the total transport performance mea-sured over all modes of transportation grows witha decline of the train charter rate. This is explainedby the growing influence of detours that are causedby the drayage operations in the intermodal trans-port chain. It is also observed in this figure thatthe LTL service is used by the company only, ifthe per-TU cost of LTL is equal to the per-TU costof FTL (ε = 1.0). LTL service is not used if itscost are higher than the cost of the FTL service(ε = 1.1). Two different ways are observed to cir-cumvent LTL services. In the first way (observedunder c̃FTL = 19.15 and c̃FTL = 10.00), LTL iseliminated by chartering an additional block train

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Figure 9: Sensitivity of intermodal share and total cost

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and filling it up with further TUs that are shiftedfromD2D service intoFTL service. In other words,the shipper is given an economic incentive to con-solidate cargo and intensify the use of intermodaltransportation. In the other way (observed underc̃FTL = 15.00), the shift of TUs happens fromLTL service to road transportation. This optionis chosen, if the LTL shipment is very small and,thus, cannot be filled up to block train load cost-efficiently.The corresponding results of the 5-terminal sce-nario are shown in Fig. 11. In this scenario, theoriginal block train charter rate is c̃FTL = 18.5e per train-km, see Tab. 7. In this network, LTLservice is involved in the distribution also undera surcharge (ε = 1.1), at least for c̃FTL = 15 andc̃FTL = 10. This is because the transport volumeshipped by rail is distributed among several ter-minals and rail links where some relations do notshow enough volume for consolidating a completeblock train. At the same time, drayage distancesare shorter compared with the 2-terminal scenariowhich particularly favors LTL over D2D serviceeven for small shipments.To summarize the experiments, we draw the fol-lowing findings. Under the assumed cost rates, acomplete D2D service of customers is not the eco-

nomically best option for the company. However,the cost saving that is possible by shifting ship-ments from road to rail is rather limited. On theother hand, enforcing high percentages of inter-modal transportation, e.g., by legislative regula-tions, will increase distribution cost significantly.We also found that LTL service is not that im-portant for shippers generating enough transportvolume to consolidate rail carriage into full blocktrains. The density of the rail network has a con-siderable impact on the service selection of a com-pany. A denser network enables shorter drayagedistances which, in turn, causes that a higher per-centage of rail transports is recommended not onlyfrom the environmental perspective but also fromthe economic perspective.Moreover, in such a net-work, the shipments split up into smaller volumessuch that unconsolidated LTL shipments receive acertain relevance even for large shippers.

6 ConclusionThe paper generalizes the classical transportationproblem to the intermodal transportation problem(ITP) by capturing decisions for selecting transportmodes, transport services, and intermodal termi-nals. It is shown that this tactical planning problem

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Figure 10: 2-terminal scenario: Transport performance per service under varied cost

D2DprepostLTLFTL

transport performance [TU−km]0 200000 400000 600000 800000 1000000

ε=1.0

ε=1.1c~FTL = 10

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ε=1.1c~FTL = 15

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ε=1.1c~FTL = 19.15

Figure 11: 5-terminal scenario: Transport performance per service under varied cost

D2DprepostLTLFTL

transport performance [TU−km]0 200000 400000 600000 800000 1000000

ε=1.0

ε=1.1c~FTL = 10

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ε=1.1c~FTL = 15

ε=1.0

ε=1.1c~FTL = 18.5

yields a variety of solutions being optimal underspecific constellations of the transport cost rates.To determine the optimal modal split for a com-pany’s distribution system, an ITP instance can besolved with cost rates estimated close to reality.Furthermore, the impact of expected changes oftransport cost can be assessed in order to adaptthe distribution system of a company in futuretime. In the case study, we have verified that inter-modal transportation is a profitable alternative tolong-haul road transportation for the consideredcompany. In contrast to smaller companies, thisshipper can influence the tactical planning of anintermodal network because of its large transportvolume. Smaller companies typically outsource the

tactical planning to logistics service providers. Us-ing our approach, companies can implement sus-tainable transport chains with a declining per-centage of road transport and low transportationcost. The definition of the intermodal transporta-tion problem comprises rail transportation fromterminals in the origin area to terminals in thedestination area. If a problem instance containsmultiple terminals in one or both of these areasand if rail transportation is possible between ter-minals located within the same area, multi-stageconsolidation as well as rail-based drayage oper-ations come into the play. The development ofmodels and solution methods for such problems issubject of future research.

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Appendix

Table 9: Case study parameters: Road transport distances, demand & productionquantities

production site s nc1 2 3 4 5 6 7 8 9 10 11

custom

erd

1 2298 2170 2389 2315 2673 2363 1922 2297 2601 2207 2374 12 2576 2398 2617 2633 2940 2680 2196 2610 2876 2422 2649 13 2067 1912 2132 2112 2436 2160 1688 2091 2369 1943 2141 14 2179 2044 2263 2204 2552 2252 1802 2185 2481 2079 2254 55 2477 2346 2566 2495 2852 2543 2102 2477 2780 2382 2554 26 2503 2373 2592 2519 2878 2567 2127 2501 2805 2408 2579 47 2807 2674 2893 2822 3182 2870 2432 2805 3110 2708 2883 118 2022 1886 2105 2052 2395 2100 1645 2032 2325 1922 2098 19 1729 1636 1852 1731 2107 1779 1361 1714 2031 1681 1806 110 2087 1940 2160 2124 2458 2172 1708 2104 2389 1973 2162 111 1884 1766 1984 1902 2260 1950 1510 1883 2187 1806 1960 712 2527 2357 2576 2577 2893 2625 2147 2556 2828 2384 2601 213 1777 1667 1885 1790 2153 1838 1404 1772 2079 1709 1853 3914 1685 1594 1809 1687 2063 1735 1317 1670 1987 1640 1763 315 2030 1878 2098 2073 2400 2120 1651 2052 2332 1910 2104 6216 2244 2126 2344 2254 2620 2302 1870 2237 2546 2164 2320 117 2119 1988 2207 2142 2493 2190 1743 2123 2422 2024 2195 118 2698 2562 2782 2717 3073 2765 2322 2699 3001 2596 2774 119 1427 1321 1537 1451 1803 1498 1054 1431 1730 1366 1504 420 2517 2399 2618 2523 2894 2571 2145 2507 2820 2437 2594 321 2269 2179 2395 2255 2648 2303 1903 2241 2570 2223 2347 18822 2066 1927 2146 2098 2439 2146 1689 2078 2369 1961 2142 1423 2244 2177 2389 2212 2623 2260 1886 2200 2542 2224 2322 324 1558 1448 1665 1579 1934 1627 1184 1560 1860 1491 1634 125 2496 2412 2627 2473 2875 2521 2133 2461 2796 2456 2574 326 2627 2453 2673 2680 2993 2727 2248 2658 2928 2479 2701 127 2569 2439 2658 2584 2944 2632 2194 2567 2872 2474 2645 328 2045 1866 2085 2111 2407 2157 1665 2087 2345 1892 2117 729 2030 1878 2098 2073 2400 2120 1651 2052 2332 1910 2104 430 2413 2230 2449 2476 2775 2523 2033 2453 2713 2254 2485 131 1649 1556 1771 1653 2027 1701 1280 1636 1950 1601 1726 132 2013 1865 2084 2053 2383 2101 1634 2032 2315 1898 2088 433 2206 2112 2328 2197 2584 2245 1839 2182 2507 2155 2284 134 2024 1867 2087 2071 2392 2118 1644 2049 2326 1898 2098 135 2519 2394 2613 2530 2895 2578 2145 2513 2822 2430 2595 2

qs 49 54 11 26 73 7 34 66 18 19 28 385

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Table 10: Case study parameters: Roadtransport distances (pre-carriage)

terminal o1 2

pro

ductionsite

s

1 379 3262 349 4793 525 2964 507 5585 750 1096 545 5667 1 6798 473 5239 680 13510 421 50011 453 277

Table 11: Case study parameters: Roadtransport distances (post-carriage)

terminal d1 2 3

custom

erc

1 320 876 1832 566 1172 3463 42 634 4964 190 758 3125 479 1022 376 507 1074 157 799 1332 2748 93 552 5339 418 260 80910 68 636 44411 232 427 63212 506 1137 25113 331 287 77314 451 201 87315 1 609 51216 314 805 26117 162 684 38118 687 1268 21219 625 2 105720 553 1063 11921 470 876 36122 85 618 47623 575 813 50524 503 123 95025 667 1050 33226 609 1198 33527 571 1114 5528 167 666 59329 1 609 51230 424 1008 35631 470 178 89332 26 595 51733 407 772 37534 31 611 52235 535 1100 88

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BiographiesChristian Bierwirth is Professor of Productionand Logistics at Martin-Luther-University, Halle-Wittenberg, Germany. He holds a Diploma Degreein Mathematics from the University of Heidelbergand a Ph.D. in Business Administration from theUniversity of Bremen. His research focuses on de-veloping heuristics for complex scheduling prob-lems from the fields of production and logistics.His work has been published in international jour-nals like the Journal of Scheduling, OR Spectrum,Evolutionary Computation, the European Journalof Operational Research, the International Journalof Production Economics, Transportation Scienceand others.

Thomas Kirschstein holds a Diploma Degreein Business Economics from Martin-Luther-University Halle-Wittenberg.

He is currently working as a research assistant atMartin-Luther-University. His research interestsinclude integrated planning of logistical processesin complex production networks and geometry-based robust statistical methods.

Frank Meisel holds a Diploma Degree inTransportation Engineering from the TechnicalUniversity of Dresden and a Ph.D. in BusinessAdministration from Martin-Luther-UniversityHalle-Wittenberg. He is currently workingas a researcher and teaching assistant atMartin-Luther-University. His research interestsinclude supply chain management, transportationplanning, and container terminal operationsplanning. He has published in the Journal ofScheduling, OR Spectrum, the European Journalof Operational Research, Transportation Scienceand others.

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1 Introduction2 Literature3 The Intermodal Transportation Problem3.2 Modeling cost and freight consolidation effects3.3 Optimization model

4 Illustrative example5 Real-world case study5.1 MotivationFigure 6:Modal split as a percentage of total TU-km5.2 Data5.3 Results

6 ConclusionAppendixReferencesBiographies

Documents

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