Overview ■ 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. ■ Although price is the main driver, a shipper may take into account many additional con- siderations, including upper bounds on the number of winning carriers in total, per load location, per country of destination, and the maximal transport volume any carrier is allowed to win. The winner determination problem is the problem of finding an allo- cation of the lanes to the carriers so as to minimize total transportation costs such that each lane is assigned to exactly one carrier and the additional constraints are satisfied. ■ The winner determination problem is extremely hard in practice, and most carriers re- sort to simple rules of thumb to select the winning carriers. This is no surprise: we prove that the 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. ■ Tested on a comprehensive set of instances generated along the characteristics of a real world case of a European chemical shipper with about 4,000 lanes, CPLEX is capable of solving instances with no more than 270 lanes to optimality, underlining the practi- cal difficulty of the winner determination problem. However, 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. ■ This performance supports our conclusion that our heuristic can be used to obtain good approximations quickly for realistic, much larger instances. 125 ZfB 76. Jg. (2006), H. 2, 125–137 A Winner Determination Problem of Tendering Transportation Services Praxis Forschung State of the Art By Linda van Norden, Jo van Nunen, and Steef van de Velde Accepted: 02 November 2005  Gabler-Verlag 2006 Linda van Norden, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands, E-mail: L.vanNorden@ewi.tudelft.nl. Jo van Nunen, RSM Erasmus University, P.O. Box 1738, 3000 DR Rotter- dam, The Netherlands, E-mail: {jnunen,svelde}@rsm.nl. Steef van de Velde, RSM Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, E-mail: {jnunen,svelde}@rsm.nl.