An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints
We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman  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.
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- 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.
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- Tarim, S. Armagan & Smith, Barbara M., 2008. "Constraint programming for computing non-stationary (R,Â S) inventory policies," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1004-1021, September.
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