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Approximate dynamic programming methods for an inventory allocation problem under uncertainty. (English) Zbl 1141.90330
Summary: We propose two approximate dynamic programming methods to optimize the distribution operations of a company manufacturing a certain product at multiple production plants and shipping it to different customer locations for sale. We begin by formulating the problem as a dynamic program. Our first approximate dynamic programming method uses a linear approximation of the value function and computes the parameters of this approximation by using the linear programming representation of the dynamic program. Our second method relaxes the constraints that link the decisions for different production plants. Consequently, the dynamic program decomposes by the production plants. Computational experiments show that the proposed methods are computationally attractive, and in particular, the second method performs significantly better than standard benchmarks.

90B05 Inventory, storage, reservoirs
90C39 Dynamic programming
Full Text: DOI
[1] Adelman, Oper Res 52 pp 499– (2004)
[2] Dynamic bid-prices in revenue management, Technical report, The University of Chicago, Graduate School of Business, 2005.
[3] , Relaxations of weakly coupled stochastic dynamic programs, Working paper Graduate School of Business, The University of Chicago, Chicago, IL, 2004.
[4] , , Nonlinear Programming: Theory and Algorithms, second edn, John Wiley & Sons, Inc., New York, 1993.
[5] , Neuro-Dynamic Programming, Athena Scientific, Belmont, MA, 1996. · Zbl 0924.68163
[6] , Adaptive interactive marketing to a customer segment, Working paper, Graduate School of Business, The University of Chicago, Chicago, IL, 2005.
[7] Cheung, Transport Sci 30 pp 43– (1996)
[8] de Farias, Oper Res 51 pp 850– (2003)
[9] Godfrey, Transport Sci 36 pp 21– (2002)
[10] , Eds., Handbooks in Operations Research and Management Science, Volume on Logistics of Production and Inventory, North Holland, Amsterdam, 1981.
[11] A Lagrangian Decomposition Approach to Weakly Coupled Dynamic Optimization Problems and its Applications, PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, 2003.
[12] Karmarkar, Oper Res 29 pp 215– (1981)
[13] Karmarkar, Manage Sci 33 pp 86– (1987)
[14] Kleywegt, Transport Sci 36 pp 94– (2002)
[15] Magnanti, Oper Res 29 pp 464– (1981)
[16] , Integer and Combinatorial Optimization, John Wiley & Sons, Inc., Chichester, 1988. · Zbl 0652.90067 · doi:10.1002/9781118627372
[17] Papadaki, Nav Res Logist 50 pp 742– (2003)
[18] Powell, Transport Sci 32 pp 90– (1998)
[19] Markov Decision Processes, John Wiley and Sons, Inc., New York, 1994. · doi:10.1002/9780470316887
[20] ”Decomposition methods,” Eds., Handbook in Operations Research and Management Science, Volume on Stochastic Programming, North Holland, Amsterdam, 2003.
[21] Schweitzer, J Math Anal Appl 110 pp 568– (1985)
[22] , Eds., Quantitative Models for Supply Chaing Management, Kluwer Academic Publishers, Norwell, MA, 1998.
[23] Topaloglu, INFORMS J Comput 18 pp 31– (2006)
[24] Yost, Nav Res Logist Q 47 pp 607– (2000)
[25] Foundations of Inventory Management, McGraw-Hill, Boston, MA, 2000. · Zbl 1370.90005
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