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Multilevel capacitated lotsizing: complexity and LP-based heuristics

Author: Van Wassenhove, Luk N. ; Maes, Johan ; McClain, JINSEAD Area: Technology and Operations ManagementIn: European Journal of Operational Research, no. 53, 1991 Language: EnglishDescription: p. 131-148.Type of document: INSEAD ArticleNote: Please ask us for this itemAbstract: This paper presents the first heuristics capable of solving multilevel lotsizing problems with capacity constraints on more than one level. Moreover, the form of the heuristics is quite general so that they can easily be extended to solve a variety of problems. If one wants to solve these problems on a routine basis in a real environment one needs to find fast and easy algorithms. However, it is shown that for certain problem classes this is a very difficult task, far more difficult than has been suggested in the literature. For problems with setup times finding a feasible solution is NP-complete. Even without setup times testing for feasibility can be very difficult. Just how time consuming such heuristics must be is demonstrated. This leaves little chance to build fast and easy heuristics except for the most simple cases. The exploration of the complexity issues points to mathematical programming as a potential source of heuristics for these problems.
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This paper presents the first heuristics capable of solving multilevel lotsizing problems with capacity constraints on more than one level. Moreover, the form of the heuristics is quite general so that they can easily be extended to solve a variety of problems. If one wants to solve these problems on a routine basis in a real environment one needs to find fast and easy algorithms. However, it is shown that for certain problem classes this is a very difficult task, far more difficult than has been suggested in the literature. For problems with setup times finding a feasible solution is NP-complete. Even without setup times testing for feasibility can be very difficult. Just how time consuming such heuristics must be is demonstrated. This leaves little chance to build fast and easy heuristics except for the most simple cases. The exploration of the complexity issues points to mathematical programming as a potential source of heuristics for these problems.

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