Abstract
This paper presents a new Lagrangian heuristic to solve the general capacitated single item lot sizing problem (CSILSP) where the total costs of production, setup, and inventory are to be minimized. We introduce a pre-smoothing procedure to transform the problem into a CSILSP with non-customer specific time windows and relax constraints that are specific to the CSILSP. The resulting uncapacitated single item problems with non-customer specific production time windows can be solved in polynomial time. We also analyze the performance of the Lagrangian heuristic for solving the CSILSP with non-customer specific time windows. Finally, the heuristic is adapted to the customer specific case. The introduction of pre-smoothing and the relaxation of CSILSP-specific constraints help to decrease the gap between lower bounds and upper bounds from 26.22 to 1.39 %, on average. The heuristic can be used to solve aggregate production planning problems, or can be integrated into a general procedure to solve more complex lot sizing problems.
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The authors would like to express their gratitude to the anonymous reviewers for their very helpful comments which considerably contributed to the improvement of the quality of this paper.
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Brahimi, N., Dauzère-Pérès, S. A Lagrangian heuristic for capacitated single item lot sizing problems. 4OR-Q J Oper Res 13, 173–198 (2015). https://doi.org/10.1007/s10288-014-0266-3
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DOI: https://doi.org/10.1007/s10288-014-0266-3