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 [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. -------------------------------------------------------------------------------

Heuristic methods for the capacitated stochastic lot-sizing problem under the static-dynamic uncertainty strategy

We consider a lot-sizing problem in a single-item single-stage production system facing non-stationary stochastic demand in a finite planning horizon. Motivated by common practice, the set-up times need to be determined and frozen once and for all at the beginning of the horizon while decisions on the exact lot sizes can be deferred until the setup epochs. This operating scheme is referred to as the static dynamic uncertainty strategy in the literature. It has been shown that a modified base stock policy is optimal for a capacitated system with minimum lot size restrictions under the static-dynamic uncertainty strategy. However, the optimal policy parameters require an exhaustive search, for which the computational time grows exponentially in the number of periods in the planning horizon. In order to alleviate the computational burden for real-life size problems, we developed and tested seven different heuristics for computational efficiency and solution quality. Our extensive numerical experiments showed that average optimality gaps less than 0.1% and maximum optimality gaps below 4% can be attained in reasonable running times by using a combination of these heuristics. (C) 2019 Published by Elsevier Ltd

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 [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.Inventory Relaxation Stochastic non-stationary demand Mixed integer programming Service level Static-dynamic uncertainty