Paula METZKER SOARES thesis defense

Résumé: Manufacturers must efficiently manage their production capacities and their performances to satisfy customer demands with quality goods. They also have been constantly challenged to optimize resource usage and production performance in a dynamic and volatile market context in a cost effective manner. To achieve this business objective, we consider lot-sizing problems under yield uncertainty via a robust, adaptive robust and distributionally robust optimization methodologies to determine the production setups and quantities that meet demands with quality goods, while minimizing the overall production and inventory management costs. To propose sufficiently robust production plans, for the static robust case, we formulate a single-item MILP (Mixed-Integer Linear Programming) model, we propose an optimal policy for the inventory management problem, and we also develop a dynamic program to solve problems with stationary production yield. For the adaptive case, we model an MILP approximation of the quadratic adaptive robust single-item problem, we design a column and constraint generation algorithm to compute an optimal adaptive plan, and we also provide an optimal myopic policy valid for the adaptive inventory management problem. Considering the distributionally robust model, we propose a MILP model to address the multi-item based on a scenario-wised formulation that partitions the available data into scenarios that define different patterns influencing the quality of the goods. The robust and adaptive robust models disregard the distributive aspect of the uncertain data which yields more conservative plans. On the other side, distributionally robust models incorporate available distributive information gathered from the highly volatile production context and optimize against the worst-case distribution realization. The experimental results show that robust-wise production plans have better cost cutting strategy compared with other resolution approaches. The computational experiments show the robustness and effectiveness of the robust model through an average and worst case analyses. The experiments also demonstrate the performances and the value of the adaptive robust solutions and the low sensitiveness to errors in predictions of the distributionally robust models.