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New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains

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  • Hoai Thi
  • Duc Tran

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 $$\epsilon $$ ϵ -optimal solution for large-scale problems in a reasonable time. Copyright Springer Science+Business Media New York 2014

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  • Hoai Thi & Duc Tran, 2014. "New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains," Journal of Global Optimization, Springer, vol. 60(1), pages 5-24, September.
  • Handle: RePEc:spr:jglopt:v:60:y:2014:i:1:p:5-24
    DOI: 10.1007/s10898-013-0081-y
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    References listed on IDEAS

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    1. Vidal, Carlos J. & Goetschalckx, Marc, 1997. "Strategic production-distribution models: A critical review with emphasis on global supply chain models," European Journal of Operational Research, Elsevier, vol. 98(1), pages 1-18, April.
    2. Pfeiffer, Thomas, 1999. "Transfer pricing and decentralized dynamic lot-sizing in multistage, multiproduct production processes," European Journal of Operational Research, Elsevier, vol. 116(2), pages 319-330, July.
    3. Gjerdrum, Jonatan & Shah, Nilay & Papageorgiou, Lazaros G., 2002. "Fair transfer price and inventory holding policies in two-enterprise supply chains," European Journal of Operational Research, Elsevier, vol. 143(3), pages 582-599, December.
    4. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Chien, T. William, 1993. "Determining profit-maximizing production/shipping policies in a one-to-one direct shipping, stochastic demand environment," European Journal of Operational Research, Elsevier, vol. 64(1), pages 83-102, January.
    7. Fred Glover, 1975. "Improved Linear Integer Programming Formulations of Nonlinear Integer Problems," Management Science, INFORMS, vol. 22(4), pages 455-460, December.
    8. Chauhan, Satyaveer S. & Proth, Jean-Marie, 2005. "Analysis of a supply chain partnership with revenue sharing," International Journal of Production Economics, Elsevier, vol. 97(1), pages 44-51, July.
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    1. Yiju Wang & Hengxia Gao & Wei Xing, 2018. "Optimal replenishment and stocking strategies for inventory mechanism with a dynamically stochastic short-term price discount," Journal of Global Optimization, Springer, vol. 70(1), pages 27-53, January.

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