Résumé
We study the single item lot-sizing problem with supplier selectionand uncertain lead time. We consider the situation where a companyhad preselected a set of suppliers for an item, and these suppliers havedifferent prices, different lead times, but also different reliability. Weaim to provide a robust optimization approach to decide when to order,how much to order, and from which suppliers, in the context of un-certain delivery lead time. We formulate the robust optimization prob-lem with polyhedral budgeted uncertainty sets. This formulation doesnot require assumptions on order crossovers, order splitting, or on thestructure of the demand or lead times. We propose an exact row andcolumn generation algorithm to solve the considered problem, alongwith some enhancements including a fast cut generation procedure. Toimprove the scalability of the approach we propose several heuristics,including a hybrid of the robust counterpart reformulation and row andcolumn generation, and a fix-and-optimize approach in the row andcolumn generation framework. Experimental results show that the fix-and-optimize approach provides good results. Finally, we provide in-sight into the reaction of the decision-maker to unreliable suppliers.One of the conclusions is that in the considered framework, an ex-tremely risk-averse decision-maker selects a single supplier, namelythe most reliable one even if it does not offer the lowest price.