Multi-period Multi-item Lot sizing under Random Yield and Stochastic Capacity

International audienceThis study addresses a multi-product multi-period lot-sizing problem with stochastic yield and capacity. Typically, random yield is the result of defective items, whereas the capacity is uncertain due to machine breakdowns. Considering both stochastic yield and capacity leads to a complex problem, since these two uncertainty types are in conflict. Indeed, the planners tend to produce large batches to overcome random yields, but the resulting plan might not be feasible due to random capacity. We provide an analytical expression for the service level function. A dynamic programming algorithm is also proposed to find the optimal released quantities. We validate the proposed methodology with a numerical example