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

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


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        "affiliation": "Hacettepe Univ, Dept Management, Ankara, Turkey", 
        "name": "Tarim, S. Armagan"
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        "affiliation": "Alcatel Lucent Bell Labs, Murray Hill, NJ 07974 USA", 
        "name": "Dogru, Mustafa K."
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      {
        "affiliation": "Alcatel Lucent Bell Labs, Dublin 15, Ireland", 
        "name": "Oezen, Ulas"
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      {
        "affiliation": "Wageningen UR, Logist Decis & Informat Sci Grp, Wageningen, Netherlands", 
        "name": "Rossi, Roberto"
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    "description": "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.", 
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