Multilevel Lot-Sizing with Inventory Bounds

Hark Chin Hwang, Wilco van den Heuvel*, Albert P.M. Wagelmans

*Corresponding author for this work

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We consider a single-item multilevel lot-sizing problem with a serial structure where one of the levels has an inventory capacity (the bottleneck level). We propose a novel dynamic programming algorithm combining Zangwill’s approach for the uncapacitated problem and the basis-path approach for the production capacitated problem. Under reasonable assumptions on the cost parameters the time complexity of the algorithm is O(LT6) with L the number of levels in the supply chain and T the length of the planning horizon. Computational tests show that our algorithm is significantly faster than the commercial solver CPLEX applied to a standard formulation and can solve reasonably sized instances up to 48 periods and 12 levels in a few minutes.

Original languageEnglish
Pages (from-to)1470-1490
Number of pages21
JournalINFORMS Journal on Computing
Issue number6
Publication statusPublished - Nov 2023

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