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

• DOI: 10.1016/j.ejor.2011.06.034
• Publication Date: 2011-07-06T13:59:05Z
• Authors: S. Armagan Tarim; Mustafa K. Dogˇru; Ulaş Özen; Roberto Rossi
• Keywords: Relaxation; Stochastic non-stationary demand; Mixed integer programming; Inventory; 0211 other engineering and technologies; Service level; 02 engineering and technology; Static-dynamic uncertainty

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.