A geometric algorithm to solve the NI/G/NI/ND capacitated lot-sizing problem in O(T2) 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. The purpose of this paper is twofold. First, we derive a backward algorithm based on the forward algorithm by Chen et al. (1994), which solves the general CLSP. We give a problem instances that requires exponential running time using the backward algo- rithm. Second, we provide a new O(T2) algorithm for the CLSP with non-increasing setup cost, general holding cost, non-increasing production cost and non-decreasing capacities over time. This is done by adapting the backward algorithm. Numerical tests show the better performance of our algorithm compared to the algorithm proposed by Chung and Lin (1988).
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2003-24.
Date of creation: 01 Jan 2003
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capacitated lot-sizing problem; inventory; production;
Other versions of this item:
- Heuvel, W. van den & Wagelmans, A.P.M., 2003. "A Geometric Algorithm to solve the NI/G/NI/ND Capacitated Lot-Sizing Problem in O(T^2) Time," Research Paper ERS-2003-066-LIS, 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 Uni.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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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