European Journal of Operational Research 237 (2014) 1133–1141

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European Journal of Operational Research

journal homepage: www.elsevier .com/locate /e jor

Innovative Applications of O.R.

Operational transportation planning of freight forwarding companiesin horizontal coalitions

http://dx.doi.org/10.1016/j.ejor.2014.02.0560377-2217/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +49 421 218 66920.E-mail address: kopfer@uni-bremen.de (H. Kopfer).

Xin Wang a, Herbert Kopfer a,⇑, Michel Gendreau b

a Chair of Logistics, University of Bremen, Bremen, Germanyb Département Informatique et recherche opérationnelle and Interuniversity Research Centre on Enterprise Networks, Logistics, and Transportation (CIRRELT), Université de Montréal,Montréal, Canada

a r t i c l e i n f o

Article history:Received 21 January 2013Accepted 25 February 2014Available online 4 March 2014

Keywords:LogisticsDistributed decision makingTransportation planningSubcontractingCollaborative planningRequest exchange

a b s t r a c t

In order to improve profitability, freight forwarding companies try to organize their operationaltransportation planning systematically, considering not only their own fleet but also external resources.Such external resources include vehicles from closely related subcontractors in vertical cooperations,autonomous common carriers on the transportation market, and cooperating partners in horizontalcoalitions. In this paper, the transportation planning process of forwarders is studied and the benefitof including external resources is analyzed. By introducing subcontracting, the conventional routing ofown vehicles is extended to an integrated operational transportation planning, which simultaneouslyconstructs fulfillment plans with overall lowest costs using the own fleet and subcontractors’ vehicles.This is then combined with planning strategies, which intend to increase the profitability by exchangingrequests among members in horizontal coalitions. Computational results show considerable costreductions using the proposed planning approach.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

The increasing pressure on modern freight forwarding compa-nies to improve profitability has strongly influenced their fleetmanagement and transportation planning strategies. In order toutilize resources more efficiently, it is no longer sufficient forforwarders to optimize the usage of their internal resources, butthey also have to improve the management of external relationswith other carriers. Forwarders can fulfill their acquired customerrequests by applying the following options: (1) keeping the execu-tion in-house using their own fleet (self-fulfillment), (2) forward-ing requests to other carriers (subcontracting), and (3)exchanging requests with partners in horizontal cooperations(collaborative planning). Using all three options may result inconsiderable cost-savings. However, due to the high heterogeneityof these different options, forwarders have to apply new planningschemes to realize the embedded potential. In this paper, we studythe operational transportation planning under consideration of allthree fulfillment options.

Besides self-fulfillment, forwarders can subcontract somerequests to subcontractors in vertical cooperations and to commoncarriers to reduce their fleet size. Due to the high fixed costs of

vehicles, many forwarders strongly downsize their own fleet. Thisenables them to do ‘‘cherry-picking’’, i.e., assigning the most prof-itable tours to their own vehicles and filling the gap between theown fleet capacity and customer demand by using capacities ofother carriers. As a consequence, the process of forwardingrequests to subcontractors has to be integrated into the traditionalvehicle routing and scheduling. Krajewska and Kopfer (2009) referto this extension as the integrated operational transportationplanning (IOTP).

In addition to subcontracting, the operational efficiency can beimproved further by building up horizontal coalitions enablingcollaborative planning. According to Stadtler (2009), collaborativeplanning can be understood as a joint decision making processfor aligning plans of individual coalition members with the aimof achieving coordination in light of information asymmetry. Wangand Kopfer (2014) refer to the joint decision making process forfulfilling transportation requests in a horizontal coalition as collab-orative transportation planning (CTP). CTP aims to reach a realloca-tion of requests among the coalition members through requestexchange, with total costs less than the sum the partners’ individ-ual costs would be without cooperation.

The main differences between the cooperations in IOTP and CTPis that CTP is performed on the basis of an equal partnership, whilein IOTP the players are in a hierarchical relation with the forwarderbeing the client of carriers acting as subcontractors. In IOTP,

1134 X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141

forwarders plan independently for their internal and externalcapacities without explicitly coordinating with their subcontrac-tors. In CTP, all partners plan for themselves (i.e., for their own fleetand, if applicable, for their subcontractors either) and try to harmo-nize their plans with those of other coalition members.

Although both approaches, IOTP and CTP, have been investi-gated in literature, a systematical integration of both approachesinto vehicle routing strategies has not been discussed yet. In thispaper, we study how the operational planning of the forwardersshould be performed taking subcontracting and collaborative re-quest exchange into account. The purpose is to develop an appro-priate mechanism to realize the cost-saving potential at thehighest level, which is embedded in the integration of IOTP and CTP.

The remainder of this paper is organized as follows. Relatedliterature is reviewed in Section 2. Different planning strategiesare formally described in Section 3. The solution approaches forthe IOTP problem are presented in Section 4 and integrated intoa collaborative planning framework in Section 5. Section 6 showsthe computational results. Section 7 concludes this paper.

2. Literature review

2.1. Combining vehicle routing and subcontracting

The idea of using external resources for the fulfillment of trans-portation requests is not new in transportation planning. Due tothe high fixed costs related to trucks and the low profit margin, for-warders have to keep a very high utilization rate of their own fleetto generate acceptable profits. Introducing subcontracting enablesforwarders to do ‘‘cherry-picking’’ for their reduced fleet and thus,to ensure a high utilization rate of own vehicles, even in case ofstrongly fluctuating demands for transportation volume.

‘‘Cherry-picking’’ is often performed by forwarders in practice,in spite of the fact that it implements a sequential planningapproach, which may lead to inferior solutions regarding the totalfulfillment costs. Thus, simultaneous planning approaches havebeen proposed in transportation planning literature. The resultingplanning problems, i.e., variations of the IOTP, have attracted inter-est of researchers for some decades.

Ball, Golden, Assad, and Bodin (1983) investigate the problem ofsimultaneously generating routes for own vehicles and subcon-tracting single requests to common carriers. The underlying rout-ing problem can be seen as a multi-depot full-truckload (FTL)pickup and delivery problem (PDP). Klincewicz, Luss, and Pilcher(1990) study a variation of the IOTP which is based on the vehiclerouting problem (VRP) with stochastic customer demands. Thewhole area to be served is divided into several sectors assignedeither to an own vehicle route or to common carriers. A static ver-sion of this problem on the operational level is proposed andsolved many years later by Chu (2005), who discusses the problemwhere only a fixed number of heterogeneous trucks with limitedcapacity are available in the own fleet and the demands of custom-ers are known. After that, this problem and its variation with ahomogeneous fleet are investigated in Bolduc, Renaud, and Boctor(2007), Bolduc, Renaud, Boctor, and Laporte (2008), and Côté andPotvin (2009). Based on the analysis of a German mid-sized freightforwarder, Krajewska and Kopfer (2009) introduce a variation ofthe IOTP while considering several different tariff structures forfreight charges, and propose a tabu search heuristic to solve thisproblem.

2.2. Integrating collaborative transportation planning

Small and mid-sized forwarders face greater difficulties intaking advantage of both economy of scope and economies of scale,

due to their relatively limited business size. The commonly esti-mated achievable cost reduction through CTP amounts to 5–15%(Cruijssen & Salomon, 2004; Krajewska, Kopfer, Laporte, Ropke, &Zaccour, 2008). The attained cost-savings represent the joint ben-efits of the coalition that cannot be achieved individually. Theycan then be shared among the coalition members.

In order to exploit the cost-saving potential embedded in CTP,appropriate request exchange mechanisms, which are simple andimplementable, yet effective in terms of generating high joint ben-efits have to be developed. Such mechanisms must be able to dealwith distributed information and decision-making competencesWang and Kopfer (2014). Some approaches have been proposedin literature to tackle this challenging task. These approaches differnot only in the solution methodologies but also in the scenarios(e.g. underlying routing problems) to which CTP is applied.

Krajewska and Kopfer (2006) propose a request exchangemechanism using a combinatorial auction (CA), which is basedon the idealized assumption that the fulfillment costs for any bun-dle of requests can be exactly evaluated. Schwind, Gujo, andVykoukal (2009) propose two auction mechanisms for a scenariowith several warehouses supplying single commodity goods tocustomers, which can be modeled as the VRP with time windows(VRPTW) (Cordeau, Desaulniers, Desrosiers, Solomon, & Soumis,2002). Due to the characteristics of the VRP, only requests locatedbetween neighboring profit centers are exchanged. For the PDPhowever, it is impossible to simply choose candidate requests forexchange on the basis of their geographical locations. Berger andBierwirth (2010) deal with the CTP of a coalition, where each mem-ber has to solve a PDP without capacity restriction. Schönberger(2005) proposes a CA-based approach for a similar problem, inwhich also time windows of requests have been considered. Özen-er, Ergun, and Savelsbergh (2011) solve the CTP problem by usingbilateral exchanges for forwarders doing FTL business. Wang andKopfer (2014) propose a route-based request exchange mechanismfor the exchange of less-than-truckload (LTL) requests. The basicrouting problem is the pickup and delivery problem with time win-dows (PDPTW) with a fixed homogeneous fleet.

The approaches proposed by Berger and Bierwirth (2010) andÖzener et al. (2011) depend on the calculation of the marginalcosts for single requests. The basic idea is to choose those requestswith the highest marginal costs and offer them for exchange. If anexchange resulting in a better solution for all parties is found, itwill be accepted and the exchange process continues. Otherwisethe process ends. This idea suffers from the fact that the underlyingprocess resembles a hill-climbing strategy, which does not acceptany declined solution and thus cannot escape from local optima.The mechanisms in Berger and Bierwirth (2010) realize an averagecost-saving potential of 18.2–64.8% for different test sets, and theapproach in Özener et al. (2011) of 30% in the test setting relevantfor CTP as discussed in this paper.

Schönberger (2005) and Wang and Kopfer (2014) solve the CTPproblem by following the decomposition principle proposed byDantzig and Wolfe (1960). This decomposition scheme is suitablefor decentralized decision making (with distributed information)since each member decides for his part without regard to whetherit is feasible for any other part (Dantzig & Wolfe, 1960), and with-out having to expose private information. In both approaches, theCTP problems are decomposed into several subproblems reflectingthe routing decisions of single participants and a coordinatingproblem. Schönberger (2005) assumes an extremely high pricelevel for forwarding requests to common carriers and tries toincrease the degree of self-fulfillment. Wang and Kopfer (2014)use an iterative route generation process and realize almost thecomplete cost-saving potential which is determined by solvingthe centralized problem using effective heuristics for vehiclerouting.

X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141 1135

3. Extending operative transportation planning

In this section, the operative transportation planning problemsare formally described. We begin with the PDPTW as the initialsituation and extend it gradually to the combined collaborativeintegrated planning.

3.1. From PDPTW to ‘‘Cherry-picking’’

Suppose a horizontal coalition of m independent freight for-warders. Each member i comes along with a request portfolio Ri

containing ni; i ¼ 1; . . . ;m, LTL requests. Each request r 2 Ri withload lr P 0 must be transported from its pickup location to a deliv-ery location. Let Pi ¼ Ri ¼ f1; . . . ; nig be the set of pickup nodes andDi ¼ fni þ 1; . . . ;2nig the set of delivery nodes. The origin–destina-tion pair of request r ¼ u 2 Pi is ðu;ni þ uÞ. Let lu ¼ lr and lniþu ¼ �lr .Each forwarder i has an own fleet K1

i available on the first mode,i.e., self-fulfillment (SF). Each vehicle k 2 K1

i has the capacity Qk, afixed cost ak, and a variable cost rate bk for each distance unit.All vehicles are stationed at the depot oi. Let oi denote the start de-pot and oi0 the end depot which is a duplicate of oi. Member i’sPDPTW can be defined on a graph Gi ¼ ðVi;AiÞ, whereVi ¼ Pi [ Di [ foi; oi0 g is the node set and Ai ¼ Vi � Vi is the edgeset. For each edge ðu;vÞ 2 Ai, a distance duv and a travel time d0uvare given. The service at node u 2 Vi must be started within a timewindow ½bu; eu�, and the duration of the service is given by su. Thebinary variable xuvk; ðu;vÞ 2 Ai; k 2 K1

i , is one if vehicle k travelsover edge ðu;vÞ. If vehicle k serves node u; Tuk defines the timewhen the service starts and Luk the load after the service is com-pleted. The PDPTW can be modeled based on Desrosiers, Desaul-niers, Erdmann, Solomon, and Soumis (2002) and Ropke andPisinger (2006) as follows.

min Ci ¼Xk2K1

i

ak þXk2K1

i

Xðu;vÞ2Ai

bkduvxuvk ð1Þ

subject toXk2K1

i

Xv2Vi

xuvk ¼ 1 8u 2 Pi ð2Þ

Xv2Vi

xuvk �Xv2Vi

xv;niþu;k ¼ 0 8k 2 K1i ; u 2 Pi ð3Þ

Xv2Pi[foi0 g

xoi ;v;k ¼X

u2Di[foigxu;oi0 ;k

¼ 1 8k 2 K1i ð4Þ

Xu2Vi

xuvk �Xu2Vi

xvuk ¼ 0 8k 2 K1i ; v 2 Vi ð5Þ

xuvk Tuk þ su þ d0uv � Tvk� �

6 0 8k 2 K1i ; ðu;vÞ 2 Ai ð6Þ

bu 6 Tuk 6 eu 8k 2 K1i ; u 2 Vi ð7Þ

Tuk þ d0u;niþu;k 6 Tniþu;k 8k 2 K1i ; u 2 Pi ð8Þ

xuvkðLuk þ lv � LvkÞ ¼ 0 8k 2 K1i ; ðu; vÞ 2 Ai ð9Þ

lu 6 Luk 6 Q k 8k 2 K1i ; u 2 Pi ð10Þ

0 6 Lniþu;k 6 Q k � lu 8k 2 K1i ; u 2 Pi ð11Þ

Loi ;k ¼ 0 8k 2 K1i ð12Þ

xuvk 2 f0;1g 8k 2 K1i ; ðu; vÞ 2 Ai ð13Þ

Suppose that the forwarder i downsizes its own fleet and sub-contracts a subset of the acquired requests to external carriers.Krajewska and Kopfer (2009) identify three modes of subcontract-ing. The first two modes are applied to subcontractors who are fre-quently engaged by the forwarder and are nearly exclusivelyemployed by him. Complete vehicle routes starting from and end-ing at the forwarder’s depot are outsourced to these subcontrac-tors. A subcontractor’s vehicle will be paid either on a tour basis(TB) or on a daily basis (DB) for executing a route. The paymentfor mode TB is calculated by multiplying the route length with

an agreed cost rate per distance unit, which is higher than thecorresponding cost rate of an own vehicle to compensate subcon-tractors’ fixed costs. For mode DB, a predefined flat-rate is paidto a subcontractor for a complete day, without violating the agreedlimits for travel distance of the route. For these two modes TB andDB, it is necessary that forwarders plan these routes in advancewhich they pay for because the freight to be paid depends on thecharacteristics of the planned routes. The third mode is appliedwhen requests are shifted to common carriers. In this case, an indi-vidually agreed charge will be paid to a subcontractor for fulfillinga request or a bundle of requests.

Let K2i and K3

i denote the sets of vehicles hired on modes TB andDB, respectively. The set of vehicles available for forwarder i isKi ¼ [3

g¼1Kgi . Let payr denote the customer payment for request r.

The binary variable zsr ¼ 1; r 2 Ri, indicates that request r should

be selected for self-fulfillment.‘‘Cherry-picking’’ can be modeledas a two-phase optimization problem. First, requests that mayresult in highest payoffs are selected for the own fleet. The remain-ing requests are then assigned to subcontractors. In the first phase,the objective function of the model (1)–(13) is replaced by

maxXr2Ri

payrzsr �

Xk2K1

i

ak �Xk2K1

i

Xðu;vÞ2Ai

bkduvxuvk ð14Þ

As Ri ¼ Pi, we can use index u instead of r. The selection of requestsfor self-fulfillment causes that (2) is replaced byXk2K1

i

Xv2Vi

xuvk ¼ zsu 8u 2 Pi ð15Þ

Assume that the set of not assigned requests in the first phase is

Rsubi � Ri. Define the graph Gsub

i ¼ Vsubi ;Asub

i

� �in analogy to Gi

according to Rsubi . Suppose that the charge of outsourcing a request

r 2 Rsubi to a common carrier is cr . The binary variable zd

k; k 2 K3i ,

indicates if a vehicle of mode DB is used. The binary variable

zcr ; r 2 Rsub

i , indicates if request r should be given to a commoncarrier. The customers’ payments will be held by the forwarderand the objective in this phase is to minimize the total subcon-tracting costs.

minXk2K2

i

Xðu;vÞ2Asub

i

bkduvxuvk þXk2K3

i

akzdk þ

Xr2Rsub

i

crzcr ð16Þ

Constraint (2) has to be reformulated asX

k2K2i [K3

i

Xv2Vsub

i

xuvk þ zcu ¼ 1 8u 2 Psub

i ð17Þ

and the following two constraints must be added into the model(3)–(13).X

v2Psubi

xoivk ¼ zdk 8k 2 K3

i ð18Þ

Xðu;vÞ2Asub

i

xuvk 6 RLk 8k 2 K3i ð19Þ

Eq. (18) ensures that a vehicle k 2 K3i will be paid if it is used.

Constraint (19) restricts the maximal route length for k 2 K3i to RLk.

3.2. Integrated operational transportation planning

Although ‘‘cherry-picking’’ can help achieving a very highprofitability of the own vehicles, it may result in expensive routesfor subcontracting and thus lead to inferior solutions compared tothe IOTP which simultaneously minimizes the total fulfillmentcosts of all four modes. The IOTP problem consists of two stronglyinterdependent subproblems. The first one is the mode-selectionproblem, which assigns requests to different modes. The second

1136 X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141

one is the routing problem, which has to be solved for modes SF, TB,and DB. As the customer payments are constant, the problem ofIOTP aims at minimizing the total fulfillment costs and can bemodeled as

min Ci ¼Xk2K1

i

ak þX

k2K1i [K2

i

Xðu;vÞ2Ai

bkduvxuvk þXk2K3

i

akzdk þ

Xr2Ri

crzcr ð20Þ

subject to constraints (3)–(13) and (17)–(19) by replacing Psubi and

Vsubi with Pi and Vi, respectively.

3.3. Combining integrated and collaborative transportation planning

Suppose now that the m independent members of the coalitionwant to reduce their total costs by exchanging requests. It isassumed that all requests Ri; i ¼ 1; . . . ;m, can be offered forexchange in the coalition and fulfilled by any available vehicle ofany partner in the coalition.

The request portfolio Ri of each forwarder i can be divided intotwo parts. The first part is the set of requests R0

i # Ri that have beenoffered but not transferred to other partners. The transferredrequests constitute the set R�i ¼ Ri n R0

i . The new request portfolioafter the exchange is R0i ¼ R0

i [ Rþi , while Rþi is the set of requestsacquired from other partners. The execution costs for the newrequest portfolio R0i according to a plan P0i are denoted as C0i. TheCTP can be modeled as the following optimization problem

min TCCTP ¼Xm

i¼1

C 0i ð21Þ

subject to R0h \ R0i ¼£ 8h; i ¼ 1; . . . ;m; h – i ð22Þ[m

i¼1R�i ¼ [mi¼1Rþi ð23Þ

In order to evaluate the efficiency of a CTP approach, two refer-ence scenarios, isolated planning and centralized planning, aredefined.

In the scenario of isolated planning, each member i has to fulfillhis customer requests either by using his own vehicles or by sub-contracting. An execution plan Pi with total costs Ci as defined in(20) can be obtained by solving the IOTP problem. The total costs ofall coalition members are then given by the sum of costs of all part-ners’ individual plans TCIP ¼

Pmi¼1Ci.

In the scenario of centralized planning, a notional planningauthority would plan for the entire coalition. This planning author-ity would have to be able to access all private information and tobe provided with all decision-making competences. Let R ¼ [m

i¼1Ri

be the set of all customer requests and K ¼ [mi¼1Ki the set of all

available vehicles of the coalition. Specifically, K1 ¼ [mi¼1K1

i ;

K2 ¼ [mi¼1K2

i , and K3 ¼ [mi¼1K3

i . The IOTP for the centralized planningcan be defined on a new graph G ¼ ðV ;AÞ with V ¼ [m

i¼1Vi andA ¼ ðV � VÞ. The objective function minimizes the total fulfill-ment costs TCCP for the entire coalition. Similar to (20), it canbe defined as

min TCCP ¼Xk2K1

ak þX

k2K1[K2

Xðu;vÞ2A

bkduvxuvk þXk2K3

akzdk þ

Xr2R

crzcr ð24Þ

4. Solution approaches for the isolated and centralized planning

In order to solve the IOTP for both isolated and centralizedplanning, two heuristics have been developed. The first one is anadaptive large neighborhood search (ALNS) heuristic, which isbased on the ALNS proposed in (Ropke & Pisinger, 2006) for thePDPTW. The second approach improves the solution qualityfurther. The IOTP problem is modeled as a set partitioning problem(SPP) or a set covering problem (SCP). Then, promising partial solu-tions are iteratively looked for using ALNS, and are finally recom-bined into better solutions.

4.1. Adaptive large neighborhood search

The ALNS proposed by Ropke and Pisinger (2006) is embeddedin a simulated annealing (SA) metaheuristic, while in each iterationa removal and an insertion operator are chosen and used. Theremoval or insertion operators are selected based on a probabilityvector which is altered and adapted to the current situation duringthe search process.

In the ALNS proposed in Ropke and Pisinger (2006), two kinds ofinsertion operators and three removal operators are used. The firstinsertion operator is called basic greedy heuristic. For all requestsnot scheduled in any route, this operator evaluates the insertioncost, Dcrk, defined as the increment of route cost after request r isinserted into route k at the best possible position. The request withthe minimum Dcr ¼mink2KfDcrkg is then inserted at its bestposition overall. The process is repeated until no more insertionsare possible. The other insertion operators called regret heuristicsadditionally estimate the consequential cost of not inserting arequest in the current iteration. The request with the highest con-sequential cost is then inserted. The three removal operators areworst removal, Shaw removal, and random removal. Worst removaliteratively removes the request with the highest marginal cost,that is the cost difference with and without this request. Shaw re-moval iteratively removes some similar requests at a time. Randomremoval randomly chooses requests and removes them from vehi-cle routes.

In order to make the heuristic suitable for IOTP, we modified theheuristic. Instead of calculating the insertion cost Dcrk, the cost-savings cr � Dcrk that is achievable by inserting request r into routek is calculated. Here, cost-savings refer to the amount of cost thatcan be reduced if a request is inserted into a route instead of beingforwarded to a common carrier. Requests with positive cost-sav-ings are automatically considered as candidates for insertion. Butalso requests with negative cost-savings can be inserted intoroutes if Dcrk � cr 6 fTit is applicable, where f is a threshold param-eter and Tit is the SA temperature in iteration it. At the beginning ofthe search process, while Tit is still large, the heuristic tries to in-sert all requests into vehicle routes. In later phases, Tit becomesmuch smaller and the heuristic becomes more and more selective.Requests will only be (re-)inserted into vehicle routes if the inser-tion will reduce the overall objective value (at least at the momentwhen the insertion is done).

For the vehicles paid on mode DB, the cost function for thesearch process has to be changed, because otherwise the insertioncost for any request in an empty route would be the flat-rate, andafter that, the insertion cost would be zero for further requests. Wethus calculate a fictive variable cost for this mode by dividing theflat-rate by a route length that is slightly shorter than the maxi-mum agreed route length and use it for calculating insertion costs.

4.2. Heuristic II: An iterative approach

In this section, a sophisticated approach, given by HII, is pro-posed. It uses the ALNS heuristic iteratively to find efficient vehicleroutes and recombines them to generate IOTP solutions. In general,HII is similar to the column generation technique used for solvingvehicle routing problems.

The IOTP problem can be modeled as an SPP. Let X1i ; X2

i , and X3i

represent the sets of feasible routes for modes SE, TB, and DB,respectively. Xi ¼ [3

g¼1Xgi represents all feasible routes in all fulfill-

ment modes. Denote the fulfillment costs of a route j 2 Xi as cj. Forown vehicles, only the variable costs are considered. If a route canbe executed in more than one mode, it will be represented as dif-ferent routes in Xi, because the route costs may vary in differentmodes. f g

j 2 f0;1g; g ¼ 1;2;3, specifies the mode of route j.arj ¼ 1 indicates that a request r is served in route j and arj ¼ 0

X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141 1137

otherwise. The binary variable yj; j 2 Xi, indicates if a route is cho-sen for request fulfillment. Furthermore, we also use cr to denotethe charge for outsourcing request r 2 Ri to a common carrierand zc

r ¼ 1 to indicate this. The IOTP problem can be defined asto choose some requests for outsourcing and to choose a set ofvehicle routes for the execution of the rest of requests in such away, that the total fulfillment costs are minimized. This decisionproblem, which is the so-called master problem, can be modeledas follows

min Ci ¼Xk2K1

i

ak þXj2Xi

cjyj þXr2Ri

crzcr ð25Þ

subject toXj2Xi

arjyj þ zcr ¼ 1 8r 2 Ri ð26Þ

Xj2Xi

f gj yj 6 jK

gi j 8g ¼ 1;2;3 ð27Þ

yj 2 f0;1g 8j 2 Xi ð28ÞThe objective function (25) minimizes the total costs including

the fixed costs of the own fleet, the total costs of routes, and thecharges for outsourcing requests to common carriers. Constraint(26) ensures that every request must be executed by exactly oneroute or alternatively be outsourced to a common carrier. Con-straint (27) is the fleet size restriction. This model is valid for a sin-gle forwarder. The model for the coalition’s centralized planningcan be derived by considering all requests, routes and vehicles ofall members.

The problem of finding feasible routes is defined as the subprob-lem. As it is impossible and not necessary to enumerate all feasibleroutes, only a subset of X0i � Xi will actually be generated. To im-prove the solutions obtained by using X0i, an iterative process isapplied, in which only promising routes that can improve theobjective value are searched and added into X0i. In particular, HIIstarts with solving the IOTP problem heuristically using the ALNSheuristic. The routes in the best solutions found by ALNS arerecorded to generate a meaningful X0i.

In each iteration of the iterative process, the master problem isrelaxed to a linear programming (LP) problem by relaxing yj 2 X0i toa continuous variable and the relaxed problem is solved. The objec-tive function value of this relaxed problem can be improved byadding new columns, i.e., vehicle routes, with negative reducedcosts into X0i. The reduced cost of a column j is defined as�cj ¼ cj �

Pnir¼1prarj �

P3g¼1rgf g

j , where p and r are the dual multi-pliers related to constraints (26) and (27), respectively. We replacej with k to get the reduced cost of a route for vehicle k as�ck ¼ ck �

Pr2Ri

prark �P3

g¼1rgf gk . A common way to find new routes

is to solve the problem of minimizing �ck. However, HII uses twooptions to find a set of complimentary routes at a time, even ifsome of them may have non-negative reduced costs.

Option one is to solve the IOTP problem using the ALNS heuris-tic with the objective of minimizing the total reduced costs of all itsroutes.

minXk2Ki

�ck ¼Xk2Ki

ck �Xk2Ki

Xr2Ri

prark �X3

g¼1

Xk2Ki

rgf gk ð29Þ

The first term on the right-hand-side calculates the total routecosts of the solution. The second term sums up the pr values forthose requests chosen for the vehicles and can be rewritten asP

r2Riprð1� zc

rÞ, while zcr ¼ 1; r 2 Ri indicates that request r is out-

sourced to a common carrier and zcr ¼ 0 that it is planned in some

vehicle route. As the last term is a constant, (29) is equivalent to

minXk2Ki

ck �Xr2Ri

prð1� zcrÞ ¼

Xk2Ki

ck þXr2Ri

przcr �

Xr2Ri

pr ð30Þ

We can omit the constant termP

r2Ripr again, and reformulate this

objective function by substituting the total route costs in a moreconcrete form

minX

k2K1i [K2

i

Xðu;vÞ2Ai

bkduvxuvk þXk2K3

i

akzdk þ

Xr2Ri

przcr ð31Þ

This is the same objective function as (20), except that the constantterm of fixed costs

Pk2K1

iak is omitted and the charge for common

carriers is replaced by the dual variable p. That is why we candirectly use the ALNS heuristic to generate new routes. Since theIOTP problem with heterogeneous fleet is solved here, we denotethe heuristic using this option as HII-HET.

Instead of solving the IOTP problem for the entire fleet Ki, thesecond option is to solve several subproblems for every vehiclemode, i.e., for the vehicle sets Kg

i ; g ¼ 1;2;3, respectively. Thus,each IOTP instance solved here has a homogeneous fleet. Wedenote this variation as HII-HOM.

As both options solve the corresponding subproblems in a heu-ristic manner, a set of different sub-optimal solutions can beobtained. The routes in these solutions are then added into X0i.The iterative process of generating new routes ends when somestopping criterion is satisfied.

After the route generation process, the master problem is solvedagain while the constraint (26) is replaced by

Xj2Xi

arjyj þ zcr P 1 8r 2 Ri ð32Þ

(25), (32), (27), and (28) constitute the SCP-based model of themaster problem. A feasible solution to this model may be infeasibleto the original problem since some requests may be assigned morethan once. More precisely, some requests may be assigned to morethan one vehicle. In this case, the solution to the SCP-based modelwill be repaired. The solution repair routine first removes allrequests that have been assigned to several vehicles from therelated routes. Then it tries to reinsert them into vehicle routesat the best position while keeping the remaining part of the resultunchanged.

The entire heuristic consists of 5 steps:

Step 1: Solve the original IOTP problem using ALNS and recordthe best h solutions found. Add all routes derived from therecorded solutions into X0i.Step 2: Solve the LP relaxation of the master problem. Checkwhether the objective value has been improved more than�%. If so, go to Step 3, otherwise go to Step 5.Step 3: Substitute cr with pr for all r 2 Ri. Add the fixed termsinto the IOTP model. Solve the IOTP problem with updated val-ues using ALNS and record the best h solutions found. Add allroutes derived from the recorded solutions into X0i.Step 4: Check if the given number of maximal iterations hasbeen reached. If so, go to Step 5, otherwise go back to Step 2.Step 5: Solve the SCP-based model of the master problem.Repair the solution using ALNS if necessary.

Each time when the ALNS is used, up to h best solutions foundduring the search process are recorded. Subsequently, each routein these solutions is reviewed for feasibility in other fulfillmentmodes. A route may be added into X0i more than once with differentroute costs calculated for different modes. This operation can beunderstood as an special form of the swap operator, which changestwo vehicle routes of different types. Our tests show that it canlead to considerable improvements, especially for HII-HET.

Further mentionable is that in Step 2, the SCP-based model ofthe master problem can also be used by replacing (26) with (32).Computational results show no difference in performance betweenthe two formulations.

1138 X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141

5. Solution approach for collaborative planning

In this section, the iterative heuristic approach HII is adjusted toa heuristic for CTP. This approach represents an extension of theroute-based request exchange mechanism proposed for CTP inWang and Kopfer (2014) by considering a heterogeneous fleetand subcontracting. The collaborative problem can be consideredas m IOTP problems that have to be solved by individual membersof the coalition and a coordinating problem in form of an SPP or anSCP that has to be solved by an ‘‘agent’’ who technically could justbe a computer.

The whole process begins with a preprocessing phase, in whichparticipating forwarders propose their customer requests forexchange in a request pool. After that, all partners solve their indi-vidual IOTP problems and the resulting costs are denoted as inter-nal price Ci. The generated routes are reported to the agent in formof request bundles. For each bundle, the route cost is revealed tothe agent as the cost of this bundle but the concrete order of cus-tomer nodes in the corresponding route needs not to be reported.The agent solves the coordinating problem for the entire coalitionby choosing the most promising bundles, i.e., by solving the SPP orSCP, to minimize the total costs of the coalition. In order toimprove the solution quality, the agent solves the LP-relaxed SPPand sends the dual values associated with the requests and vehi-cles back to the members so that they can generate new routes,and thus, bundles using the feedback information. When a fairlywell improved solution (compared to the isolated scenario) isfound, the chosen bundles are declared as winning bundles andtheir costs will be paid by the agent. Finally, the differencebetween the total internal prices paid to the agent and the totalcosts of winning bundles paid by the agent will be determined asjoint benefits of the coalition. The major difference between thisapproach and the HII presented in Section 4.2 is that the IOTP prob-lems in the collaborative scenario are solved simultaneously by allpartners, who only generate routes for their own disposablevehicles.

5.1. Preprocessing

In this step, all members initially offer their request portfoliosRi; i ¼ 1; . . . ;m, for exchange. As a result, R ¼ [m

i¼1Ri is the entireset of requests in the request pool. For each request r 2 R, the infor-mation about the pickup and delivery locations, the time windows,and the load to be transported is also transferred to the agent andare generally accessible. However, the customer payments remainconcealed.

After that, collaborating partners have to specify the internalprices for their own request sets Ri by solving their individual IOTPproblems. The sum of internal prices of the request portfolios of allpartners corresponds to the total fulfillment costs of the isolatedplanning TCIP . The internal prices are only necessary for the deci-sion of the coalition on the acceptance of CTP solutions ifTCCTP 6 TCIP , and for the determination of the collaborative profitTCIP � TCCTP . Apart from that they remain concealed.

5.2. Route generation process

The first step of applying the decomposition scheme proposedby Dantzig and Wolfe (1960) is to generate a meaningful set of col-umns, i.e., vehicle routes in our case. This step is called initial routegeneration and it is similar to Step 1 of HII in Section 4.2. After that,the iterative process of route generation starts and it is similar toSteps 2 and 3 of HII in Section 4.2.

5.2.1. Initial route generationPurpose of this step is to generate a meaningful set of vehicle

routes to start the iterative process of route generation. One strat-egy to achieve this is to encourage each partner to do ‘‘cherry-pick-ing’’ for his own vehicles and all his available subcontractors, whileleaving the remaining requests to common carriers. Thus theobjective function for initial route generation can be defined asmaximizing the reduction of external freight charges for subcon-tracting requests to common carriers by ‘‘cherry-picking’’.

maxXr2R

crð1� zcrÞ

�Xk2K1

i

ak þX

k2K1i [K2

i

Xðu;vÞ2A

bkduvxuvk þXk2K3

i

akzdk

0@

1A ð33Þ

The first term calculates the amount of freight charges for therequests chosen for the fleet in case they are outsourced tocommon carriers. The rest part calculates the route costs for fulfill-ing these requests with available vehicles. Their difference is thenthe reduction of external freight charges through ‘‘cherry-picking’’.This is equivalent to

minXk2K1

i

ak þX

k2K1i [K2

i

Xðu;vÞ2A

bkduvxuvk þXk2K3

i

akzdk þ

Xr2R

crzcr

�Xr2R

cr ð34Þ

This objective function (34) is actually the same as (20) becausethe last term in (34)

Pr2Rcr is a constant term and can be ignored.

The only difference is that the request set Ri is substituted by theentire request set R of the whole coalition. We can use the ALNSheuristic presented in Section 4.1 to solve this problem. Again,we record the best solutions found during the search process forthe route generation.

As we want to guarantee that the winning bundles chosen bythe agent do not exceed the fleet capacities available to theforwarders, each partner has to report the maximum number ofwinning bundles he is able to fulfill in each single mode (SF, TB,DB). Additionally, we split the modes into vehicle types becausethe fleet of a single mode could be heterogeneous as well. Allvehicles of a single type are identical with respect to capacityand cost parameters. If a route is feasible for one vehicle of aspecific type, then it is feasible for all vehicles of that type atthe same cost.

5.2.2. Temporary winner determinationAfter all members have submitted their bundles, the agent

temporarily solves the current winner determination problem(WDP). The idea is almost the same as solving the master problem(25)–(28).

Suppose a set R ¼ f1; . . . ;ng with n requests is offered forexchange. Each member i has submitted xi bundles. For eachsingle request r 2 R, a single-request bundle with its outsourcingprice cr as its bundle cost is also added into the bundle set. Thecost of a bundle cj is identical to the route cost if it is derivedfrom a vehicle route or to the outsourcing price if it is a single-request bundle. The total number of bundles is x ¼

Pmi¼1xi þ n.

Let arj ¼ 1 indicate that request r 2 R is contained in bundle jand arj ¼ 0 otherwise. Denote the number of all vehicle typesreported by all carriers as s. Let fgj ¼ 1 represent that bundle jis proposed for type g; g ¼ 1; . . . ; s and fgj ¼ 0 otherwise. Thereported maximum acceptable number of winning bundles fortype g is jg . The WDP can be modeled as an SPP while the binaryvariable yj; j ¼ 1; . . . ;x, takes value 1 if bundle j is chosen as awinning bundle.

X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141 1139

min TCCTP ¼Xxj¼1

cjyj ð35Þ

subject toXxj¼1

arjyj ¼ 1 8r 2 R ð36Þ

Xxj¼1

fgjyj 6 jg 8g ¼ 1; . . . ; s ð37Þ

yj 2 f0;1g 8j ¼ 1; . . . ;x ð38Þ

Denote this SPP-based WDP model as WDP-SP. An LP relaxationof WDP-SP is given by relaxing yj to be a continuous variable.Denote the relaxed problem as WDP-LP. Then, the dual values ofconstraints (36) and (37) can be used for generating new routes.The route generation problem is to build new routes with negativereduced costs �cj, which can be calculated for a variable yj as�cj ¼ cj �

Pr2Rprarj �

Psg¼1rgfgj, where p and r are the dual vari-

ables corresponding to the constraints (36) and (37), respectively.To improve the objective function value of WDP-LP, new routeswith �cj < 0 have to be found. Values of p and r are read by theagent and sent back to forwarders while pr is given in a revisedform of p0r ¼ maxf0;prg; r 2 R.

5.2.3. Iterative route generationGiven the values of p0 and r, forwarders can generate new

routes. In order to reduce the number of iterations needed for routegeneration, i.e., rounds of communications between the agent andforwarders, a bunch of routes are generated at a time instead ofsearching for a route with the minimal reduced cost �cj. Analoguesto the options presented in Section 4.2, this can be done by solvingIOTP instances. Again, two options can be chosen. Each membercan either solve an IOTP instance for his entire heterogeneous fleetKi (including vehicles of his subcontractors) or solve a set of IOTPinstances each only for a homogeneous vehicle set of a specificvehicle type. We use CTP-HET and CTP-HOM to differentiate thesetwo options, respectively.

Applying the CTP-HET option means to search for a set of vehicleroutes, which can be fulfilled using the entire fleet Ki of a singlepartner i. We can formulate the objective function of this optimiza-tion problem by using index k instead of j in cj for emphasizing thevehicles

minXk2Ki

�ck ¼Xk2Ki

ck �Xk2Ki

Xr2R

p0rark �Xk2Ki

Xs

g¼1

rgfgk ð39Þ

Analogues to (29), this objective function is equivalent to

minXk2K1

i

ak þX

k2K1i [K2

i

Xðu;vÞ2Ai

bkduvxuvk þXk2K3

i

akzdk þ

Xr2R

p0rzcr ð40Þ

Thus, the iterative route generation problem has exactly thesame structure as the original IOTP problem and we can use thesame heuristic to solve it. During the search process, a number ofsolutions will be recorded for generating new bundles. For theoption CTP-HOM, the objective functions for each vehicle typecan be formulated directly in the same way as (40).

This strategy helps find not only ‘‘good’’ routes that willimprove the WDP-LP objective values, but also routes that arecomplementary to those good ones. Computational results showthat the gap between the WDP-LP and the final integer WDP-SPsolutions is quite small (for almost all instances, the gap is smallerthan 2%), so that it is unnecessary to call a branch-and-bound(B&B) routine after the column generation phase. This effect isespecially favorable for CTP, as such B&B routine would cause alot of communications between the agent and forwarders, andthus, a lot of transactional costs.

The new routes are added to the existing bundle set. The Stepstemporary winner determination and iterative route generation arerepeated until some stopping criterion is met. The route generationphase is then concluded.

5.3. Final winner determination and flow of payments

In this phase, the agent solves another relaxation of the WDP-SP. Now, the constraint (36) is replaced by

Xxj¼1

arjyj P 1 8r 2 R ð41Þ

This model, defined by (35), (41), (37), and (38), is the SCP-basedmodel of the WDP. We denote it as WDP-SC.

If the WDP-SC solution is also feasible to WDP-SP, the requestseach winning bundle pursued, will be assigned to the forwarderwho won this bundle. If a bundle representing the choice ofoutsourcing only one request to a common carrier wins, it willbe returned to the member who proposed it for exchange.

If the WDP-SC solution is infeasible to WDP-SP because somerequests are assigned to several winning bundles, the agent canrepair this solution simply by assigning such a multi-assigned re-quest r to that partner who has won more multi-assigned requeststhan all other partners competing for r and removing it from allother bundles. Finally, the agent inquires the total costs for thenew request portfolio R0i for all partners i; i ¼ 1; . . . ;m, and getsthe collaborative result.

The total costs of the CTP solution, including both the winningbundles’ costs and the possible costs for subcontracting, will becompared with the results of the isolated planning. The CTP solu-tion will only be accepted if positive joint benefits are realized.

If a collaborative solution has been accepted, the flow of pay-ments among the coalition members can be determined. First, allforwarders have to pay the amount of the internal costs Ci to theagent. These are the costs that would result from the situationwithout collaboration. As an outcome of WDP, requests will be as-signed to forwarders according to the winning bundles, and theircosts will be paid to the members by the agent. Any request thathas been assigned to a single-request winning bundle representingthe option of common carriers will be returned to the partner whooffered it for exchange. The freight charge for outsourcing a requestr to common carriers is given by cr and also paid by the agent tothe corresponding forwarder. The difference of the incoming pay-ments acquired by the agent, and the total payments paid out byhim is then determined as joint benefits of the collaboration. Theyhave to be shared among all participating members.

The difference between the model WDP-SP and the masterproblem of the IOTP presented in Section 4.2 is that the fixed costsof own vehicles are no more a component of the objective function(35). Instead, they are considered indirectly in the route costs. As aresult, if a forwarder cannot win any bundles for some of his ownvehicles, he must pay the fixed costs for these vehicle on his own.For the winning bundles, the costs will be compensated by the cor-responding payments from the agent. This effect gives forwardersmore incentive to generate efficient routes, especially for theirown vehicles.

6. Computational experiments

In order to analyze the cost-saving potentials by performingboth IOTP and CTP and to evaluate the efficiency of the proposedCTP mechanism, new theoretical instances are generated. In total,29 IOTP instances are derived from the PDPTW instances generatedby Li and Lim (2001) and 24 CTP instances are generated using thenew IOTP instances (see Appendix A). As it is obvious that the IOTP

Table 1Results for IOTP instances.

Ins. ALNS HII-HET HII-HOM

Cost Time Cost Time Cost Time

lc 2832.82 11.06 2791.88 8.90 2791.72 9.87lr 4008.98 13.50 3966.38 10.27 3966.38 14.34lrc 4294.03 15.64 4224.65 12.11 4224.65 14.21all 3722.61 13.33 3673.13 10.35 3673.08 12.92

Table 2Results of centralized planning for CTP instances.

Ins. ALNS HII-HET HII-HOM

Cost Time Cost Time Cost Time

C 9478.84 137.2 8765.16 115.9 8765.03 749.6R 13710.64 133.7 12073.23 388.5 12073.39 3444.8RC 14098.77 150.4 12702.17 141.1 12714.57 2293.6all 12429.41 140.4 11180.18 215.1 11184.33 2162.7

1140 X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141

is superior to ‘‘cherry-picking’’ regarding the overall fulfillmentcosts, we exclude the experiment of ‘‘cherry-picking’’.

6.1. Results for isolated and centralized planning

The heuristics presented in Section 4 are used for solving theIOTP problem for both the isolated and centralized planning sce-narios. For the ALNS, we use the same parameter setting for theoperators as suggested in Ropke and Pisinger (2006). The temper-ature Tit of the SA process in iteration it is determined asTit ¼ Tit�1 � cr where cr is the cooling rate. The start temperaturefor each instance is set individually such that a solution which is10% worse than the current solution is accepted with a probabilityof 0.5. The cooling rate cr is determined such, that after the maxi-mal number of SA iterations the temperature is reduced to 5% ofthe start niveau. The heuristic stops after 25,000 iterations or25,000/3 iterations without any improvement of the best solutionfound so far.

For HII, the ALNS heuristic is used iteratively for route genera-tion. For both HII-HET and HII-HOM, the ALNS runs up to 10,000iterations in the first step and only 2500 iterations in the followingsteps. The whole process is stopped after the iterative route gener-ation process has been repeated five times or after three consecu-tive abortive attempts to improve the objective function value ofthe LP-relaxed master problem by at least 5%. Each time, up to1000 best solutions found during the search process are recorded.The routes contained are added to the route set X0. If a route can beexecuted by vehicles of different modes, it will be added into X0 asdifferent routes with different costs. We use IBM ILOG CPLEX tosolve the LP-relaxed master problems and the SCP-based modelof the master problem. All instances are solved using both heuris-tics 10 times on an Intel i7 PC with 8 cores à 3.4 GHz. The aggre-gated results for the IOTP instances and the CTP instances ofcentralized planning are shown in Tables 1 and 2, respectively.

Table 3Result of collaborative planning.

Ins. Isolated planning Centralized planning Collaborative

CTP-HET

TCIP TCCP DTC1 /1 TCCTP

C 9669.61 8759.09 910.52 8.68 8932.70R 13722.76 12066.90 1655.87 11.08 12191.37RC 14597.59 12699.27 1898.32 11.76 12811.03all 12663.32 11175.08 1488.24 10.51 11311.70

Detailed results can be found in Appendix B. The cost values aregiven as the average cost of the best solutions found for theinstances. The time values are given as the average time in seconds(seconds) used to solve an instance in this set.

HII-HET and HII-HOM obviously outperform the simple ALNS.For small IOTP instances (100 customer nodes), the iterativeapproaches can achieve on average an improvement of 1.33% withregard to solution quality compared to ALNS. HII-HOM performsslightly better than HII-HET. The improvements of HII for largerCTP instances (up to 500 customer nodes) amount to 10.05%(HII-HET) and 10.02% (HII-HOM), respectively. Considering thecomputational time, the approach HII-HET appears to be favorablein comparison to the other two heuristics. For the three CTP in-stances R105, R107 and R108, it took quite a long time for CPLEXto optimally solve the WDP-SC. However, if the the relative MIPgap tolerance (MIP-Gap) is reduced to 0.01, this time can bereduced by up to 71.2% with an average decline of the solutionquality of 0.2%. The computational time of HII-HOM increasesdramatically with the number of customer nodes.

6.2. Results for collaborative planning

During CTP, all forwarders call in parallel the ALNS heuristic tosolve their IOTP problems and generate routes. In the Step initialroute generation, the heuristic is allowed to run up to 10,000 itera-tions and the computational time is restricted to 2 minutes (min-utes). Each forwarder records up to 1000 best solutions foundduring the search process and derives bundles from the routes inthese solutions. After that, the Step iterative route generation is re-peated five times. The time limit to run ALNS is reduced for CTP-HET to 30 seconds each time. For CTP-HOM, the IOTP problem ofeach vehicle type is solved within 20 seconds by running the ALNSup to 2500 iterations, while up to 350 solutions are recorded forroute generation, i.e., 1 minute and up to 1050 solutions for threevehicle types in total. We do not set a time limit for CPLEX to solvethe WDP-LP, since this can be done in less than 1s for all instances.For the WDP-SC however, the MIP-Gap is set to 0.01. A time limit of2 minutes is also set for CPLEX. As a result, the total time for CTP islimited to 6.5 minutes for CTP-HET and 9 minutes for CTP-HOM.The time given for running ALNS is generally sufficient and thetime limits are primarily used for synchronizing the parallel com-puting of several forwarders.

We simulated the collaborative planning of the coalition foreach CTP instance once and got 24 samples to evaluate theperformance of the proposed request exchange mechanism. Theresults can be found in Table 3. The total costs for the isolated plan-ning TCIP are calculated by summing up the costs of all IOTP solu-tions. DTC1 ¼ TCIP � TCCP and /1 ¼ 100 � DTC1=TCIP (%) are theabsolute and relative cost-saving potential through centralizedplanning. Similarly, DTC2 ¼ TCIP � TCCTP and /2 ¼ 100 � DTC2=TCIP

(%) show the absolute and relative cost reduction through CTP.Parameter g ¼ 100 � DTC2=DTC1 (%) shows the realized percentageof cost-saving potential and thus how efficient the reqeustexchange mechanism is. Both variations of collaborative planning

planning

CTP-HOM

DTC2 /2 g TCCTP DTC2 /2 g

736.92 7.19 82.53 8921.01 748.61 7.17 80.971531.40 10.32 94.55 12293.39 1429.37 9.75 90.181786.57 11.10 94.38 12822.13 1775.48 11.11 95.451351.63 9.54 90.49 11345.51 1317.82 9.34 88.87

X. Wang et al. / European Journal of Operational Research 237 (2014) 1133–1141 1141

can realize the cost-saving potential to a great extend within thesame predefined time limit.

7. Conclusion

The highly volatile conditions in the transportation market havestrongly influenced the resource management and the operationalplanning of modern freight forwarders. To improve the operationalefficiency, forwarders have to reorganize their internal processesfor a better management of external relations to partners in bothvertical and horizontal cooperation. In this paper, the operationaltransportation planning of forwarders in road haulage is discussedtaking own resources and those of partners into account. The tworelated topics for transportation fulfillment, i.e., subcontracting invertical and request exchange in horizontal cooperations, areintegrated into conventional routing problems for the first timein literature. New solution approaches for operational transporta-tion planning that can help forwarders realizing the cost-savingpotential embedded in a systematical consideration of subcon-tracting and request exchange are proposed. Compared with justcombining routing and subcontracting, computational resultsbased on theoretical instances show that the costs can be furtherreduced more than 10% on average by introducing request ex-change. The proposed decentralized planning approach can aver-agely realize over 90% of these potentials, while privacy andautonomy of members in horizontal coalitions remain protected.

Acknowledgement

This research was supported by the German Research Founda-tion (DFG) as part of the project ‘‘Kooperative Rundreiseplanungbei rollierender Planung’’.

Appendix A and B. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.ejor.2014.02.056.

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