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Exact and heuristic solutions of the global supply chain problem with transfer pricing

Sylvain Perron (sylvain.perrron***at***gerad.ca)
Pierre Hansen (Pierre.Hansen***at***gerad.ca)
Sébastien Le Digabel (Sebastien.Le.Digabel***at***gerad.ca)
Nenad Mladenović (Nenad.Mladenovic***at***brunel.ac.uk)

Abstract: 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 (2001) proposed a bilinear model of this problem and solved it by an Alternate heuristic. We propose a reformulation of this model reducing the number of bilinear terms and accelerating considerably the exact solution. We also present three other solution methods: an implementation of Variable Neighborhood Search (VNS) designed for any bilinear model, an implementation of VNS specif- ically designed for the problem considered here and an exact method based on a branch and cut algorithm. The solution methods are tested on artificial instances. These results show that our implementation of VNS outperforms the two other heuristics. The exact method found the optimal solution of all small instances and of 26% of medium instances.

Keywords: Metaheuristics, Alternate heuristic, Supply chain management, Transfer pricing, Bilinear programming, Branch and cut.

Category 1: Applications -- OR and Management Sciences

Category 2: Applications -- OR and Management Sciences (Supply Chain Management )

Category 3: Nonlinear Optimization (Other )

Citation: European Journal of Operational Research, 202(3), p. 864-879, 2010 (http://dx.doi.org/10.1016/j.ejor.2009.06.018).

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Entry Submitted: 04/16/2008
Entry Accepted: 04/16/2008
Entry Last Modified: 11/12/2009

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