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.