Price planning for time-definite less-than-truckload freight services

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  • Logistics 2009 Elsevier Ltd. All rights reserved.


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    its prots. Price planning has yet to be well studied and incorporated into the overall marketing strategy by the time-deniteLTL freight delivery industry. In practice, prices are simply set at a constant percentage above costs across the market. Thisensures that the carrier will earn at least that percentage of prot.

    Studies of pricing strategies and capacity allocation in revenue management have been carried out for perishableasset industries, such as airline and liners (Feng and Xiao, 2006; McGill and van Ryzin, 1999; Subramanian et al., 1999;

    1366-5545/$ - see front matter 2009 Elsevier Ltd. All rights reserved.

    * Corresponding author. Tel.: +886 6 275 7575x53240; fax: +886 275 3882.E-mail address: (C.-C. Lin).

    Transportation Research Part E 45 (2009) 525537

    Contents lists available at ScienceDirect

    Transportation Research Part Edoi:10.1016/j.tre.2008.12.004nancial services. With this expansion in services, to sort, load and transfer all products according to their contractualand temporal needs becomes both a key competitive advantage and an inescapable requirement for shippers. In response,the 3rd-party LSPs provide various service levels, all with guaranteed delivery times.

    The time-denite less-than-truckload (LTL) freight delivery common carriers, one of the 3rd-party LSP, publish tariffs anddeliver small shipments door-to-door with various service levels all with guaranteed delivery times for shippers. To besuccessful, cost minimization is a basic and effective strategy. For this reason, most research has focused on the design ofa cost-effective operations plan. However, cost consciousness is but one of several successful factors. In fact, carriers muststrategically combine prices with a cost-effective delivery network and optimized operations plan in order to maximizeHub-and-spoke networkLagrangian RelaxationImplicit enumeration

    1. Introduction

    The mission of 3rd-party logistic scustomized services to shippers (Mu3rd-party LSPs. To meet the one-stopdirections, (1) from a single functionhave chosen to expand their singlereplenish management, and also toe providers (LSPs) is to establish a long-term relationship with and provide broaderand Poist, 2000). Transportation and warehousing are two common services of thee-range integrated logistics services, their services recently have expanded in twoal solutions, (2) from domestic to global services. To be a full service provider, theynd to multiple modal transportation services, from warehousing to automaticd physical distribution to integrate their operations with e-commerce as well asPrice planning for time-denite less-than-truckload freight services

    Cheng-Chang Lin *, Dung-Ying Lin, Melanie M. YoungDepartment of Transportation and Communication Management Science, National Cheng Kung University, 1 University Road, 701 Tainan, Taiwan, ROC

    a r t i c l e i n f o

    Article history:Received 3 October 2006Received in revised form 29 September2008Accepted 15 December 2008


    a b s t r a c t

    Price planning simultaneous determines the service demand (with associated prices) andan operational plan to maximize a carriers prot. We modeled this integral-constrainedconcave program in the link formulation and proposed an implicit enumeration embeddedwith Lagrangian Relaxation upper bounds to determine the optimal prices. Computationson Taiwans time-denite less-than-truckload freight market showed that the carrier needsto simultaneously re-evaluate its network capacity while determining prices. The commonpractice of distance-based pricing that sets price by a base rate over direct shipment dis-tance underestimates operating cost, specically operating losses for short distanceshipments.

    journal homepage: www.elsevier .com/locate / t re

  • Weatherford and Bodily, 1992). These studies determine discriminating prices and simultaneously allocate capacity to max-imize their prots. The pricing scheme is implemented through booking as well as limited overbooking. Such an approachcannot be applied to common carriers, who must provide service indiscriminately for anyone who pays the published rates.This constraint motivates us to study the pricing planning for time-denite LTL freight delivery common carriers. In this re-search, we make the following assumptions: (1) The demand is a continuous and invertible function of price (which is ver-ied in the computational results in Section 6); (2) the revenue function is a concave continuous function; (3) the capacity inthe hub-and-spoke network is xed. The pricing planning is dened so as to simultaneously determine the demand (withassociated prices) for service and develop an operational plan in which the prot is maximized while meeting the servicecommitment, capacity and other operational restrictions.

    The structure of this paper is as follows. In Section 2, we give a brief overview of carriers line-haul operations in a purehub-and-spoke network and review the research on operational planning. In Section 3, we represent the carrier pricing plan-ning problem in a capacitated directed operations network for mathematical formulation and algorithmic design. The math-ematical model in the link formulation is formulated in Section 4, resulting in an integer concave program. In Section 5, wepropose an exact algorithm, an implicit enumeration on paths with embedded concave programming subproblem to deter-mine the optimal pricing for carrier. The subproblem is solved by FrankWolfe algorithm. The Lagrangian Relaxation (LR)upper bounds, by relaxing the capacity constraints, are implemented to improve the computational efciency. Conceptually,the algorithmic scheme needs to maintain feasibility while searching for optimality. In Section 6, we select a small pure hub-and-spoke network of one of the three top time-denite LTL freight delivery carriers in Taiwan to provide a basis for numer-ical testing. The computational results are presented, analyzed and discussed. We conclude our research in the eld of

    526 C.-C. Lin et al. / Transportation Research Part E 45 (2009) 525537pricing in the last section.

    2. Line-haul operations in a pure hub-and-spoke network

    The line-haul operations in a pure hub-and-spoke network consist of facilities, centers and hubs, and long-haul feeders thatare carrying equipment feeding freight between facilities. All the feeders must either depart or end at hubs (Fig. 1). As a re-sult, no center-to-center direct feeds are allowed with the result that all the freight requires at least one handle operation athub facilities. Each center serves an exclusive geographic area for delivering shipments to consignees and, subsequently,picking up new shipments from shippers, using a eet of package cars. Pickups are typically completed at twilight, at whencenter runs a local sort operation. New shipments are unloaded from the package cars, sorted and reloaded onto long-haulfeeders. Feeders are subsequently dispatched to the hubs, which are points of consolidation for partial loads. All the hubs willoperate at least a night sort, unload inbound freight, rehandle and reload unto outbound feeders. Providing sufcient staffrotation times in between, hubs may operate additional sorts to increase the total handling volume to lower unit overheadcost, if necessary. At dawn, centers receive daily delivery freight, when they run a preload sort to unload freight from thefeeders, rehandle and reload unto package cars for local deliveries. Thus, local sorts and preload sorts are freight originsand destination, together is called OD pair for each shipment in the pure hub-and-spoke network.

    The pure hub-and-spoke network may substantially reduce center-to-center partial loads, resulting in a lower total oper-ating cost. Carriers develop the most cost-effective line-haul operations plan to guide daily operations. The plan consists offreight routing planning (Lin, 2001), trailer assignment and balancing planning (Lamar and Shef, 1987), and feeder schedulingplanning (Lin and Lin, 2001) that, respectively, determine freight paths, a balanced feeder network and feeder schedules tophysically move the loads/empties. To account for mutually interactive effects, the load planning simultaneously determinesthe freight routes and a balanced trailer network (Leung et al., 1990). Lin and Wu (2001) extended the single-frequency to

    center 2

    center 1hub-A


    Line-haul operations

    Local services Loca

    l ser



    shippers/congineesfeeders package cars

    center 3

    Fig. 1. Time-denite delivery operations network illustration.

  • multiple-frequency load planning problem, while Lin (2004) extended the deterministic to stochastic in demand. Lastly, theload planning with aircraft scheduling problem not only determines the air cargo routes but also designs a balanced aircraftnetwork with schedules. Barnhart and Schneur (1996) developed a branch-and-bound algorithm for the set of feasibleschedules with high reduced cost values to study a single air hub case for air express time-denite services. Overall, the pric-ing plan to optimize the carriers prot is yet to be fully studied.

    3. The pricing planning network

    The line-haul operations hub-and-spoke network can be represented as a capacitated directed pricing planning network(N,A) of a set N of i nodes and a set A of ij links. Each center has two nodes associated with local and preload sorts, whileeach hub has as many nodes as its respective sorts. A network conguration for two hubs (with night sorts) and three centersis shown in Fig. 2. The given attributes for a node i e N are ci [cd ], ti [td ] and U^i, respectively, denoted as the unit handling cost(of a ce


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