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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-andbound 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.

PurposeTo propose and to evaluate a new genetic algorithm (GA) for solving the dynamic pickup and delivery problem with time windows (DPDPTW).Design/methodology/approachFirst, a grouping genetic algorithm (GGA) for the (static) PDPTW is described. In order to solve the dynamic problem, the GGA then is embedded in a rolling horizon framework. Special updating mechanisms are provided which assure that reusable solution knowledge is preserved over the plan revisions. The approach is evaluated using a large number of test instances with varying degrees of dynamism.FindingsThe experimental results have demonstrated that the proposed approach is able to find high‐quality solutions when compared with two comparative heuristics.Research limitations/implicationsFuture research will be dedicated to the following issues: testing the proposed method using larger problem instances, using more sophisticated objective functions in order to further improve and evaluate the approach, integrating fast local search techniques into the genetic search, speeding up the algorithm by optimizing its implementation.Practical implicationsIn order to meet the increasing demands on the flexibility and the promptness of transportation services, algorithms are needed for dispatching transportation requests that arrive dynamically during the planning period. The findings of this contribution justify the employment of GAs in such dynamic transportation planning environments.Originality/valueAlthough the application of GAs in dynamic environments attracts growing attention, up to now no such algorithm has been published for the DPDPTW. To the best of the author's knowledge, this is the first time a GA has been applied to the DPDPTW.

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