Multilevel Lot-Sizing with Inventory Bounds

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.

Automated summary

We propose a novel dynamic programming algorithm for a single-item multilevel lot-sizing problem with a serial structure, where one level has an inventory capacity. The algorithm combines Zangwill's approach for the uncapacitated problem and the basis-path approach for the production capacitated problem. Computational tests show that our algorithm is significantly faster than the commercial solver CPLEX for reasonably sized instances.