A winner determination problem of tendering transportation services

For the tendering of long-term transportation contracts in the bulk industry, shippers use bidbooks that specify for each lane the load location, the destination, the product and the volume that has to be transported over the next so many years. Bidbooks are sent out to a preselected group of carriers, who subsequently quote a price for each of the lanes. After the return of the bidbooks, the shipper determines the winning carriers. The winner determination problem is the problem of finding an allocation of the lanes to the carriers so as to minimize total transportation costs. The winner determination problem is NP-hard in the strong sense. We model the winner determination problem as an integer linear programming (ILP) problem and try and solve the model by use of CPLEX, a state-of-the-art ILP solver. It turns out, that the model can solve problems optimally with no more than 270 lanes. We also develop a fast randomized heuristic, and we show that it performs remarkably well, with a gap of no more than 0.8% from optimality.