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Efficient Reformulations for Uncapacitated and Capacitated Lot-Sizing with Substitutions and Initial Inventories

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Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 636)

Abstract

This section considers extensions of two well-known single-level lot-sizing models, namely the Wagner–Whitin Problem (WWP) and the Capacitated Lot-Sizing Problem (CLSP), that incorporate product substitution options.

The literature published on lot-sizing models with substitution until now does not cover two aspects that are important in real-world production planning problems: Initial inventories are not taken into account. While these can be neglected easily without loss of generality in standard lot-sizing models by netting demands, this cannot be done if substitutions are possible, as the net demands depend on substitution decisions which are part of the optimization problem. E.g., consider a lot-sizing problem with two products A and B whose initial inventory is 60 and 20 units, respectively. In addition, assume that A can substitute B, and the gross demand for A and B in period 1 is 40 and 30, respectively. In this case one cannot say that the net demand of B in period 1 is 30 − 20 = 10, because it could be optimal due to the cost parameters and demand in subsequent periods to partially substitute B by A in period 1, so that B is not set up in period 1. In addition, no models and algorithms for lot-sizing with substitution and capacitated resources have been developed. If production bottlenecks exist, it is necessary to consider production capacities in combination with substitutions: Capacitated resources can on the one hand be the reason for substitutions, on the other hand limit the amount of substitutions (e.g., if a machine that could produce substitutes is working almost to full capacity).

Keywords

Valid Inequality General Substitution Initial Inventory Substitution Instance Capacitate Facility Location Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Law, Business and Economics Chair of Operations ResearchTechnische Universität DarmstadtDarmstadtGermany

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