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

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  • Tarim, S. Armagan
  • Dogru, Mustafa K.
  • Özen, Ulas
  • Rossi, Roberto

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.

Suggested Citation

  • Tarim, S. Armagan & Dogru, Mustafa K. & Özen, Ulas & Rossi, Roberto, 2011. "An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints," European Journal of Operational Research, Elsevier, vol. 215(3), pages 563-571, December.
  • Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:563-571
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    References listed on IDEAS

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    1. Tarim, S. Armagan & Smith, Barbara M., 2008. "Constraint programming for computing non-stationary (R, S) inventory policies," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1004-1021, September.
    2. Tarim, S. Armagan & Kingsman, Brian G., 2004. "The stochastic dynamic production/inventory lot-sizing problem with service-level constraints," International Journal of Production Economics, Elsevier, vol. 88(1), pages 105-119, March.
    3. James H. Bookbinder & Jin-Yan Tan, 1988. "Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints," Management Science, INFORMS, vol. 34(9), pages 1096-1108, September.
    4. Vargas, Vicente, 2009. "An optimal solution for the stochastic version of the Wagner-Whitin dynamic lot-size model," European Journal of Operational Research, Elsevier, vol. 198(2), pages 447-451, October.
    5. Arthur M. Geoffrion, 1970. "Elements of Large-Scale Mathematical Programming Part I: Concepts," Management Science, INFORMS, vol. 16(11), pages 652-675, July.
    6. Tempelmeier, Horst, 2007. "On the stochastic uncapacitated dynamic single-item lotsizing problem with service level constraints," European Journal of Operational Research, Elsevier, vol. 181(1), pages 184-194, August.
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    Cited by:

    1. repec:eee:ejores:v:269:y:2018:i:1:p:244-257 is not listed on IDEAS
    2. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2013. "A simple approach for assessing the cost of system nervousness," International Journal of Production Economics, Elsevier, vol. 141(2), pages 619-625.
    3. Pauls-Worm, Karin G.J. & Hendrix, Eligius M.T. & Haijema, René & van der Vorst, Jack G.A.J., 2014. "An MILP approximation for ordering perishable products with non-stationary demand and service level constraints," International Journal of Production Economics, Elsevier, vol. 157(C), pages 133-146.
    4. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.

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