We consider one of the most important issues for multinationals, the determination of transfer prices. To do so, we examine the example of a multinational corporation that attempts to maximize its global after tax profits by determining the flow of goods, the transfer prices, and the transportation cost allocation between each of its subsidiaries. Vidal and Goetschalckx (EJOR, 2001) proposed a bilinear model for this problem and used an Alternate heuristic for the resolution. We propose a new model reducing substantially the number of bilinear terms and accelerating drastically the exact solution. We also present three other solution methods: an implementation of Variable Neighborhood Search (VNS) designed for any bilinear model, a new implementation of VNS specifically designed for the problem considered here as well as an exact method based on the branch and cut algorithm of Audet et al. (Math. Program, Ser.A, 2000). The four solution methods (Alternate, two VNS versions, and branch and cut) are tested on artificial instances. These results show that our new implementation of VNS outperforms the two other heuristics. The branch and cut algorithm allows us to find the optimal solution of all small instances and of 26% of medium instances.
Published February 2008 , 31 pages