Title: A Lagrangian Relaxation approach for production planning with demand uncertainty

Authors: Haoxun Chen

Addresses: Industrial Systems Optimisation Laboratory, Charles Delaunay Institute (FRE CNRS 2848), University of Technology of Troyes, Troyes 10010, France

Abstract: A production planning problem with stochastic demands is considered in this paper. The problem is to determine over a given time horizon the production quantity of each intermediate/final product at each facility of finite capacity so that a system-wide total cost is minimised while meeting given service level requirements for the final products. After reformulating the stochastic decision problem as a multiitem, multistage capacitated lot-sizing problem with a non-linear cost function using deterministic equivalence, it is solved by using a Lagrangian Relaxation (LR) approach enhanced with a local search method based on a modified simplex algorithm. Numerical experiments show that the approach can find high quality near-optimal solutions for randomly generated problems of realistic sizes in a computation time much shorter than that of an exact algorithm. [Received on 2 February 2007; Revised 28 May 2007; Accepted 7 June 2007]

Keywords: production planning; lot sizing; demand uncertainty; Lagrangian relaxation; local search.

DOI: 10.1504/EJIE.2007.015390

European Journal of Industrial Engineering, 2007 Vol.1 No.4, pp.370 - 390

Published online: 14 Oct 2007 *

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