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

TARIM Ş. A. , Dogru M. K. , Oezen U., Rossi R.

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, vol.215, no.3, pp.563-571, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 215 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.ejor.2011.06.034
  • Page Numbers: pp.563-571


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.