Less-Than-Truckload carrier collaboration problem: modeling framework and solution approach

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  • J HeuristicsDOI 10.1007/s10732-013-9229-7

    Less-Than-Truckload carrier collaboration problem:modeling framework and solution approach

    Selvaprabu Nadarajah James H. Bookbinder

    Received: 17 September 2012 / Revised: 13 June 2013 / Accepted: 18 June 2013 Springer Science+Business Media New York 2013

    Abstract Less-Than-Truckload (LTL) carriers generally serve geographical regionsthat are more localized than the inter-city line-hauls served by truckload carriers. Thatlocalization can lead to urban freight transportation routes that overlap. If trucks aretraveling with less than full loads, there typically exist opportunities for carriers tocollaborate over such routes. We introduce a two stage framework for LTL carriercollaboration. Our first stage involves collaboration between multiple carriers at theentrance to the city and can be formulated as a vehicle routing problem with timewindows (VRPTW). We employ guided local search for solving this VRPTW. Thesecond stage involves collaboration between carriers at transshipment facilities whileexecuting their routes identified in phase one. For solving the second stage problem, wedevelop novel local search heuristics, one of which leverages integer programming toefficiently explore the union of neighborhoods defined by new problem-specific moveoperators. Our computational results indicate that integrating integer programmingwith local search results in at least an order of magnitude speed up in the second stageproblem. We also perform sensitivity analysis to assess the benefits from collaboration.Our results indicate that distance savings of 715 % can be achieved by collaboratingat the entrance to the city. Carriers involved in intra-city collaboration can further save315 % in total distance traveled, and also reduce their overall route times.

    S. Nadarajah (B)Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh,PA 15213-3890, USAe-mail: snadaraj@andrew.cmu.edu

    J. H. BookbinderDepartment of Management Sciences, University of Waterloo, Waterloo, ON N2L 3G1, Canadae-mail: jbookbinder@uwaterloo.ca


  • S. Nadarajah, J. H. Bookbinder

    Keywords LTL collaboration Vehicle routing Constraint programming Integer programming Integrated methods

    1 Introduction

    Competitive pressures, economic volatility and increased service expectations haveforced companies to look outside their own operations for efficiency gains (Lynch2001). This has involved collaboration with potential competitors, and optimizingjoint operations to eliminate costs that cannot be individually controlled.

    Collaboration is a strong relationship between multiple parties, with the goal ofa mutually beneficial outcome for all collaborating members. This paper focuseson operational collaboration (Sutherland 2006) between Less-Than-Truckload (LTL)transportation carriers. LTL carriers are concerned with delivery of small shipments(between 500 and 15,000 lbs on average) by truck to multiple consignees, ultimatelyover a limited geographical region. Figure 1 is a schematic showing the inter-cityline haul to the distribution network of the destination city and the subsequent localdeliveries. The distribution network includes distribution centers and vehicle depots,and is typically located away from the city center. Goods are received at this locationfrom their line haul journey and prepared for their local routes.

    Shippers can also enter into operational collaboration, where they bundle lanesbefore their submission to a carrier. A lane is a contiguous portion of highway or road,considered by the carrier as a single link for routing purposes.

    Carriers prefer bundled lanes, as they may lead to what are termed continuousmoves. Continuous Move Routes are ones in which we would ideally have zero dead-head miles and no asset-repositioning costs. The latter costs are incurred when atruck travels empty between two stops. This reduction in cost allows carriers to offermore competitive rates to the shipper, thereby providing an incentive for shippers tocollaborate.

    The present paper deals with the specific problem of collaboration between LTLcarriers, whose loads are small in size and unpredictable. We consider the typical casewhere LTL carriers deliver loads within urban regions. In this setting, time windowsfor deliveries are usually tight. This leads to routes that are highly inefficient in termsof distance traveled, which our method aims to improve through collaboration.

    We term the collaborative solution to the above stated problem as LTL col-laboration. LTL collaboration aims at designing efficient routes which minimize

    Fig. 1 Line haul and localdelivery


  • Less-Than-Truckload carrier collaboration problem

    asset-repositioning cost, total distance traveled, and maximizes truck asset utiliza-tion. Reduction in asset repositioning costs can lead to large savings for carriers, sincetrucks in the USA travel empty 20 % of the time on average (Wilson 2007). Localintra-city trucking costs were a staggering annual 435 billion United States dollars in2006 (Wilson 2007). The 2008 Canadian state of logistics report showed that truckingrepresented over 14 billion Canadian dollars, which was about 8 % of the Canadiangross domestic product (Industry Canada, 2008). These high costs also mean that smallimprovements through LTL collaboration will translate to large savings in real costsin both countries.

    The main contributions of this paper are:

    1. A two-stage framework for collaboration between LTL carriers. The first stageinvolves exchange of (partial) loads between carriers at the entry to the city, whiletrucks make such exchanges at transshipment points during local delivery in thesecond stage.

    2. Novel heuristics that solve the mathematically complicated problem that resultsfrom the second stage of our collaborative framework. We develop a planningheuristic based on quadtree search to assist the decision maker in choosing trans-shipment points. For constructing collaborative routes using these transshipmentfacilities, we develop a local search heuristic based on new move operators andleverage integer programming to efficiently explore the union of the neighborhoodsdefined by these moves. Our computational tests indicate that our integration ofinteger programming with local search results in at least an order of magnitudespeed up when constructing collaborative routes.

    3. Computational sensitivity analysis on a rectangular region with parameters cal-ibrated to the city of Toronto to assess the benefits to carriers from engaging incollaboration at the city entrance and in collaboration at transshipment points whileexecuting local routes. Our results indicate that collaboration at the city entranceresults in distance savings between 715 % over all carriers, and increases vehicleutilization by 45 %. Intra-city collaboration leads to route distance savings of315 % over collaborating carriers, and also reduces route times.

    The remainder of this paper is organized as follows. We review the relevant liter-ature in Sect. 2. Definition of the carrier collaboration problem, and the hierarchicalframework for its study, are presented in Sect. 3. A high-level description of our solu-tion approach is given in Sect. 4; details of each heuristic are discussed in Sects.57. The evaluation procedure is described in Sect. 8, and computational results arepresented and discussed in Sect. 9. Concluding remarks and suggestions for futureresearch appear in Sect. 10.

    2 Literature review

    Carrier collaboration has received increased attention in recent years. A major part ofthis literature focuses on truckload collaboration; see Ergun et al. (2007), Liu et al.(2010), zener et al. (2011) and references therein. There are also several referencesthat concern the allocation of profits from carrier collaboration among partners using


  • S. Nadarajah, J. H. Bookbinder

    game theoretic methods. Examples include Houghtalen et al. (2011) and zener et al.(2011).

    Our emphasis in this article is rather on LTL collaboration, and Cruijssen andSalomon (2004), Krajewska and Kopfer (2006, 2009) are recent articles on this topic.Cruijssen and Salomon (2004) consider collaboration between multiple carriers, wherecollaboration involves the sharing of orders between transportation companies. Theyassess the benefit from collaboration by solving a capacitated vehicle routing problemfor each individual carrier (non-collaborative case) and compare this solution withthe solution from solving a single capacitated vehicle routing problem that combinesorders from all carriers (collaborative case). Krajewska and Kopfer (2006, 2009) alsostudy the problem of carriers sharing orders but they solve a pick up and deliveryproblem with time windows to determine when collaboration is beneficial. In additionto assessing the cost savings from collaboration, they use game theoretic mechanisms,namely core and Shapley value, to divide the savings among the coalition of carriers.A distinguishing feature of our work is the second stage of collaboration, collaborativerouting, which is absent in Cruijssen and Salomon (2004) and in Krajewska and Kopfer(2006, 2009). Thus we extend this literature in a significant manner, and our extensionprovides additional opportunities for LTL carriers to reduce travel distance and time.

    The optimization problems that arise in our LTL collaboration framework are chal-lenging. Our first stage of collaboration at the entrance to the city involves solving avehicle routing problem with time windows (VRPTW). There is an extant literature onsolving VRPTW; see Brysy and Gendreau (2005a,b) for a review of exact methodsand metaheuristics for its solution. We employ guided local search (GLS) (Voudourisand Tsang 1998, 2002) for solvin


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