An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

S. Armagan Tarim, Mustafa K. Dogru, Ulas Oezen, Roberto Rossi

Research output: Contribution to journalArticlepeer-review

Abstract

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time. (C) 2011 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)563-571
Number of pages9
JournalEuropean Journal of Operational Research
Volume215
Issue number3
DOIs
Publication statusPublished - 16 Dec 2011

Keywords

  • Inventory
  • Relaxation
  • Stochastic non-stationary demand
  • Mixed integer programming
  • Service level
  • Static-dynamic uncertainty

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