A Geometric Algorithm to solve the NI/G/NI/ND Capacitated Lot-Sizing Problem in O(T^2) Time
AbstractIn this paper we consider the capacitated lot-sizing problem (CLSP) with linear costs. It is known that this problem is NP-hard, but there exist special cases that can be solved in polynomial time. We derive a backward algorithm, based on the forward algorithm by Chen et al. (1994), to solve the general CLSP. By adapting this backward algorithm, we arrive at a new O(T^2) algorithm for the CLSP with non-increasing setup cost, general holding cost, non-increasing production cost and non-decreasing capacities over time. Numerical tests show the superior performance of our algorithm compared to the algorithm proposed by Chung and Lin (1988). We also analyze why this is the case.
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Bibliographic InfoPaper provided by Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam. in its series Research Paper with number ERS-2003-066-LIS.
Date of creation: 25 Sep 2003
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capacitated lot-sizing problem; inventory; production;
Other versions of this item:
- Heuvel, W.J. van den & Wagelmans, A.P.M., 2003. "A geometric algorithm to solve the NI/G/NI/ND capacitated lot-sizing problem in O(T2) time," Econometric Institute Report EI 2003-24, Erasmus University Rotterdam, Econometric Institute.
- NEP-ALL-2003-12-07 (All new papers)
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- Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
- Dong X. Shaw & Albert P. M. Wagelmans, 1998. "An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Management Science, INFORMS, vol. 44(6), pages 831-838, June.
- Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
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