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A primal‐dual algorithm for the dynamic lotsizing problem with joint set‐up costs

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  • Ömer Kirca

Abstract

In this article the multi‐item dynamic lotsizing problem with joint set‐up costs (LPJS) is considered. A tight formulation of the problem and the dual of the linear relaxation of this formulation is presented. A procedure to solve this dual problem is developed where the solution provides a strong lower bound for the LPJS. This lower bound is used in a branch and bound procedure to find an optimal solution to the problem. The extensive computational experiments with this procedure revealed that it outperforms the other available branch and bound algorithm in the literature. With the proposed algorithm the average time requirement was about 113 seconds on a 486DX33 processor for solving a difficult class of LPJS problems that have 50 items and 24 periods. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • Ömer Kirca, 1995. "A primal‐dual algorithm for the dynamic lotsizing problem with joint set‐up costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 791-806, August.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:5:p:791-806
    DOI: 10.1002/1520-6750(199508)42:53.0.CO;2-8
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    1. Dev Joneja, 1990. "The Joint Replenishment Problem: New Heuristics and Worst Case Performance Bounds," Operations Research, INFORMS, vol. 38(4), pages 711-723, August.
    2. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
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    1. Chia‐Shin Chung & Sin‐Hoon Hum & Omer Kirca, 2000. "An optimal procedure for the coordinated replenishment dynamic lot‐sizing problem with quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 686-695, December.

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