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A Lagrangian Relaxation approach for production planning with demand uncertainty


  • Haoxun Chen


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]

Suggested Citation

  • Haoxun Chen, 2007. "A Lagrangian Relaxation approach for production planning with demand uncertainty," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 1(4), pages 370-390.
  • Handle: RePEc:ids:eujine:v:1:y:2007:i:4:p:370-390

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