An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints

Kenneth R. Baker · Michael J. Magazine · Edward A. Silver

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Supply Chain and Inventory Management Scheduling and Optimization Algorithms Optimization and Mathematical Programming

Abstract

We consider the situation of a single item having a deterministic, time-varying demand pattern. Production lot sizes, so as to minimize the total of setup and carrying costs, are to be determined subject to production capacity restrictions that can vary with time. Two important theorems concerning properties of the optimal solution are exploited in developing a tree search algorithm. In addition, other properties are utilized to reduce the amount of search necessary. Results of extensive tests are presented and discussed.

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References

2004Dynamic Version of the Economic Lot Size Model 1969A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System—A Network Approach 1973Bounded Production and Inventory Models with Piecewise Concave Costs 1975Planning Horizons for the Dynamic Lot Size Model: Zabel vs. Protective Procedures and Computational Results

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2011Analysis of the maximum level policy in a production-distribution system 2001Capacity Acquisition, Subcontracting, and Lot Sizing 2006Joint Production and Pricing Decisions with Setup Costs and Capacity Constraints 2003Production and Distribution Lot Sizing in a Two Stage Supply Chain 2000Dynamic Economic Lot Size Model with Perishable Inventory 1998An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs 2005Integrated Lot Sizing in Serial Supply Chains with Production Capacities 1988An O(T2) Algorithm for the NI/G/NI/ND Capacitated Lot Size Problem

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