Dynamic lot size problems with one-way product substitution

Vernon Ning Hsu · Chung‐Lun Li · WEN-QIANG XIAO

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

Abstract

We consider two multi-product dynamic lot size models with one-way substitution, where the products can be indexed such that a lower-index product may be used to substitute for the demand of a higher-index product. In the first model, the product used to meet the demand of another product must be physically transformed into the latter and incur a conversion cost. In the second model, a product can be directly used to satisfy the demand for another product without requiring any physical conversion. Both problems are generally computationally intractable. We develop dynamic programming algorithms that solve the problems in polynomial time when the number of products is fixed. A heuristic is also developed, and computational experiments are conducted to test the effectiveness of the heuristic and the efficiency of the optimal algorithm.

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1958Dynamic Version of the Economic Lot Size Model 2004Dynamic Version of the Economic Lot Size Model 1983Production and inventory management 2000Foundations of Inventory Management 2000Management of Multi-Item Retail Inventory Systems with Demand Substitution 1993Improved Algorithms for Economic Lot Size Problems 1999Single-Period Multiproduct Inventory Models with Substitution 1969Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems

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