A polynomial time algorithm for the stochastic uncapacitated lot-sizing problem with backlogging

Authors:
Yongpei Guan;Andrew Miller
Affiliations:
School of Industrial Engineering, University of Oklahoma;Department of Industrial and Systems Engineering, University of Wisconsin
Venue:
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Year:
2008

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Abstract

Since Wagner and Whitin published a seminal paper on the deterministic uncapacitated lot-sizing problem, many other researchers have investigated the structure of other fundamental models on lot-sizing that are embedded in practical production planning problems. In this paper we consider basic versions of such models in which demand (and other problem parameters) are stochastic rather than deterministic. It is named stochastic uncapacitated lot-sizing problem with backlogging. We define a production path property of optimal solutions for this model and use this property to develop backward dynamic programming recursions. This approach allows us to show that the value function is piecewise linear and continuous, which we can further use to define a polynomial time algorithm for the problem in a general stochastic scenario tree setting.