A Geometric Algorithm to Solve the Ni/G/Ni/Nd Capacitated Lot-Sizing Problem in O(T^2) Time

28 Pages Posted: 15 Oct 2003

See all articles by Wilco van den Heuvel

Wilco van den Heuvel

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE)

Albert P. M. Wagelmans

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT); Erasmus University Rotterdam (EUR) - Department of Econometrics

Date Written: 25 2003 9,

Abstract

In 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.

Keywords: production, capacitated lot-sizing problem, inventory

JEL Classification: M, M11, R4, L11

Suggested Citation

van den Heuvel, Wilco and Wagelmans, Albert P. M., A Geometric Algorithm to Solve the Ni/G/Ni/Nd Capacitated Lot-Sizing Problem in O(T^2) Time (25 2003 9,). ERIM Report Series Reference No. ERS-2003-066-LIS. Available at SSRN: https://ssrn.com/abstract=450998

Wilco Van den Heuvel (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

P.O. Box 1738
3000 DR Rotterdam, NL 3062 PA
Netherlands
+31 10 40 81307 (Phone)

Albert P. M. Wagelmans

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT) ( email )

3000 DR Rotterdam
Netherlands
+31 10 408 2576 (Phone)
+31 10 408 9162 (Fax)

Erasmus University Rotterdam (EUR) - Department of Econometrics

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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