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 where bundle bidding is possible. The problem is modelled as a bi-objective extension to the set covering problem. We consider both the minimisation of the total procurement costs and the maximisation of the service-quality level at which the transportation contracts are executed. Taking into account the size of real-world transport auctions, a solution method has to cope with problems of up to some hundred contracts and a few thousand bundle bids. To solve the problem, we propose a bi-objective branch-and-bound algorithm and eight variants of a multiobjective genetic algorithm. Artificial benchmark instances that comply with important economic features of the transport domain are introduced to evaluate the methods. The branch-and-bound approach is able to find the optimal trade-off solutions in reasonable time for very small instances only. The eight variants of the genetic algorithm are compared among each other by means of large instances. The best variant is also evaluated using the small instances with known optimal solutions. The results indicate that the performance largely depends on the initialisation heuristic and suggest also that a well-balanced combination of genetic operators is crucial to obtain good solutions.