Abstract
We consider a multi-period problem of fair transfer prices and inventory holding policies in two enterprise supply chains. This problem was formulated as a mixed integer non-linear program by Gjerdrum et al. (Eur J Oper Res 143:582–599, 2002). Existing global optimization methods to solve this problem are computationally expensive. We propose a continuous approach based on difference of convex functions (DC) programming and DC Algorithms (DCA) for solving this combinatorial optimization problem. The problem is first reformulated as a DC program via an exact penalty technique. Afterward, DCA, an efficient local approach in non-convex programming framework, is investigated to solve the resulting problem. For globally solving this problem, we investigate a combined DCA-Branch and Bound algorithm. DCA is applied to get lower bounds while upper bounds are computed from a relaxation problem. The numerical results on several test problems show that the proposed algorithms are efficient: DCA provides a good integer solution in a short CPU time although it works on a continuous domain, and the combined DCA-Branch and Bound finds an \(\epsilon \)-optimal solution for large-scale problems in a reasonable time.
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Vidal, C.J., Goetschalckx, M.: Strategic production-distribution models: a critical review with emphasis on global supply chain models. Eur. J. Oper. Res. 98, 1–18 (1997)
Glover, F.: Improved linear integer programming formulation of non-linear integer problem. Manag. Sci. 22(4), 455–460 (1975)
Le Thi, H.A.: Contribution à l’optimisation Non-Convex and l’optimisation Globale: Théorie, Algorithmes et Applications, Habilitation à Diriger des Recherches. Université de Rouen, Rouen (1997)
Le Thi, H.A., Pham Dinh, T.: A continuous approach for globally solving linearly constrained quadratic zero-one programming problem. Optimization 50(1–2), 93–120 (2001)
Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world non-convex optimization problems. Ann. Oper. Res. 133, 23–46 (2005)
Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Exact penalty techniques in DC programming. J. Global Optimiz. 24 (September 2011), 1–27 (2011). doi: 10.1007/s10898-011-9765-3
Waysman, I.: A model of negotiated transfer pricing. J. Account. Econ. 25, 349–384 (1998)
Gjerdrum, J., Shah, N., Papageogiou, L.G.: Fair transfer price and inventory holding policies in two-enterprise supply chain. Eur. J. Oper. Res. 143, 582–599 (2002)
Nash, J.: The bargaining problem. Econometrica 18, 155–160 (1950)
Shunko, M., Gavirneni, S.: Role of transfer price in global supply chain with random demands. J. Indus. Manag. Optimiz. 3(1), 99–117 (2007)
Sylvain, P., Pierre, H., Sebastien, L.D., Nenad, M.: Exact and heuristic solutions of the global supply chain problem with transfer pricing. Eur. J. Oper. Res. 202(3), 864–879 (2010)
Hansen, P.H., Hegedahl, B., Hjorkjaer, S., Obel, B.: A heuristic solution to the warehouse location-routing problem. Eur. J. Oper. Res. 76, 111–127 (1993)
Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: theory, algorithms and applications. Acta Mathematica Vietnamica, dedicated to Professor Hoang Tuy on the occasion of his 70th birthday, 22(1), 289–355 (1997)
Pham Dinh, T., Le Thi, H.A.: DC optimization algorihms for solving the trust region subproblem. SIAM J. Optimiz. 8, 476–505 (1998)
Pfeiffer, T.: Transfer pricing and decentralized lot sizing in multistage, multiproduct production processes. Eur. J. Oper. Res. 116, 319–330 (1999)
Chien, T.W.: Determining profit-maximizing production/shipping, policies in a one-to-one direct shipping stochastic demand environment. Eur. J. Oper. Res. 64, 83–102 (1993)
Chauhan, S.S., Proth, J.M.: Analysis of a supply chain partnership with revenue sharing. Int. J. Prod. Econ. 97, 44–51 (2005)
Rockafellar, R.T.: Convex Analysis, 1st edn. Princeton University Press, Princeton (1970)
Howe, W.G., Cox, J.F.: Enterprise implications of transfer pricing. Prod. Inventory Manag. J. 35(2), 35–38 (1994)
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Le Thi, H.A., Tran, D.Q. New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains. J Glob Optim 60, 5–24 (2014). https://doi.org/10.1007/s10898-013-0081-y
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DOI: https://doi.org/10.1007/s10898-013-0081-y