In this presentation, I will discuss the use of stochastic optimization methods for Material Requirements Planning (MRP) systems under demand uncertainty. The problem solved by MRP systems is a multi-echelon multi-item capacitated lot-sizing problem. This problem is commonly solved under the assumption of deterministic demand since safety stocks hedge against uncertainty. However, the computations of the lot-sizes and safety stocks are usually separated and based on different assumptions, which leads to sub-optimal decisions. The critical impact of inventory costs in manufacturing motivates the study of stochastic optimization approaches to remove the boundaries between lot-sizes and safety-stocks computations in MRP systems.
In this work, a two-stage and a multi-stage formulation of the multi-echelon multi-item capacitated lot-sizing problem are considered. To address the scalability issues arising with stochastic optimization, a fix-and-optimize heuristic and advanced sampling methods are proposed. In addition, to allow real-time execution, an S-policy is derived from the solution of the multi-stage model. The execution of the considered methods is simulated in a rolling-horizon framework, and the results show that stochastic optimization methods lead to significantly lower costs than classical approaches. Our experiments also show that the multi-stage model slightly outperforms the two-stage model, whereas the latter one could be solved much more efficiently.
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