Solving a bi-objective winner determination problem in a transportation procurement auction

This paper introduces a bi-objective winner determination problem which arises in the procurement of transportation contracts via combinatorial auctions. The problem is modelled as an extension to the set covering problem and considers the minimisation of the total procurement costs and the maximisation of the service-quality level of the execution of all transportation contracts tendered. To solve the problem, an exact branch–and–bound algorithm and eight variants of a multiobjective genetic algorithm are proposed. The algorithms are tested using a set of new benchmark instances which comply with important economic features of the transportation domain. For some smaller instances, the branch–and–bound algorithm finds all optimal solutions. Large instances are used to compare the relative performance of the eight genetic algorithms. The results indicate that the quality of a solution depends largely on the initialisation heuristic and suggest also that a well-balanced combination of different operators is crucial to obtain good solutions. The best of all eight genetic algorithms is also evaluated using the small instances with the results being compared to those of the exact branch–and–bound algorithm. keywords: bi-objective winner determination problem; multiobjective genetic algorithm; combinatorial auction University of Hagen, Faculity of Business Administration and Economics Department of Information Systems, Prof. Dr. H. Gehring Profilstr. 8, 58084 Hagen, Germany E-Mail [email protected] [email protected] Tel. +49 2331 987 4399 Fax +49 2331 987 4447 Please cite as: Buer, T. and Pankratz, G.: Solving a Bi-Objective Winner Determination Problem in a Transportation Procurement Auction, Working Paper No. 448, Faculty of Business Administration and Economics, University of Hagen (Germany), 2010. Solving a Bi-Objective Winner Determination Problem in a Transportation Procurement Auction Tobias Buer and Giselher Pankratz 1 Procurement of Transportation Contracts Shippers, like retailers as well as industrial enterprises often procure the transportation services they require via reverse auctions, where the objects under auction are transportation contracts. Usually, such contracts are designed as framework agreements lasting for a period of one to three years, and defining a pick-up location, a delivery location, and the type and volume of goods that are to be transported between both locations. Additionally, further details such as a contract-execution frequency, e.g. delivery twice a week, and the required quality of service, e.g. an on-time delivery quota, are specified in a transportation contract. A carrier can bid for one or more contracts. In each bid, the carrier states how much he wants to be paid for accepting the specified contracts. Transportation procurement auctions are of high economic relevance. Caplice and Sheffi [4] report on the size of real world transportation auctions in which they were involved over a period of five years. According to their report, in a single transportation auction up to 470 (median 100) carriers participated, up to 5,000 (median 800) lanes were tendered, and the annual cost of transportation amounted up to US-$ 700 million (median US-$ 75 million). Elmaghraby and Keskinocak [9] present a case study of a procurement auction event in which a do-it-yourself chain operating mainly in North America procured transportation services for about a quarter of the in-bound moves to their chain stores, which corresponds to a number of over 600 lanes. In the study at hand, the terms lane and transportation contract are used interchangeably. In the scenario presented here there are a number of interesting problems on the carrier’s as well as on the shipper’s side. This paper focuses on the allocation problem that has to be solved by the shipper after all bids are submitted. In particular, two characteristics of the given scenario are of interest. First, from a carrier’s point of view, there are complementarities between some of the contracts. That is, the costs for executing some contracts simultaneously are lower than the sum of the costs of executing each of these contracts in isolation. The cost effect of such complementarities is also referred to as economies of scope. Second, allocation of contracts to carriers has to be done taking into account multiple, often conflicting