Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

13 years 4 months ago

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In 1958, Wagner and Whitin published a seminal paper on the deterministic uncapacitated lot-sizing problem, a fundamental model that is embedded in many practical production planning problems. In this paper we consider a basic version of this model in which demand (and other problem parameters) are stochastic: the stochastic uncapacitated lot-sizing problem. We define the production path property of an optimal solution for our model and use this property to develop a backward dynamic programming recursion. This approach allows us to show that the value function is piecewise linear and right continuous. We then use these results to show that the dynamic programming approach yields an O(n3 ) algorithm for the problem. In addition, we show that the value function for the problem without setup costs is continuous, piecewise linear, and convex, and therefore an even more efficient O(n2 ) dynamic programming algorithm can be developed for this special case. Key words: Lot-sizing; stochastic...

Yongpei Guan, Andrew J. Miller

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