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This paper introduces a bi-objective winner-determination problem and presents a multiobjective genetic algorithm to solve it. The problem examined arises in the procurement of transportation contracts via combinatorial auctions. It is modeled as an extension to the set-covering problem and considers the minimization of the total procurement costs and the maximization of the service-quality level of the execution of all transportation contracts tendered. To solve the problem, a multiobjective genetic algorithm is used. Different operators for population initialization, mutation and repair are applied. Eight variants of the algorithm are tested using a set of 30 new benchmark instances. The results indicate that the quality of a solution depends largely on the initialization heuristic and suggest also that a wellbalanced combination of different operators is crucial to obtain good solutions.