A Stochastic Programming Approach for the Capacitated Supplier Selection Problem with Total Quantity Discount and Activation Costs

We study the Capacitated Supplier Selection problem with Total Quantity Discount policy and Activation Costs, a procurement problem where a company needs a certain quantity of different products from a set of potential suppliers, and introduce its variant under uncertainty. In its deterministic form, the problem aims at selecting a subset of the suppliers and the relative purchasing plan satisfying the demands at minimum cost, taking into account that the suppliers offer discounts based on the total quantity of products purchased and that the activation of a business activity with a supplier has a fixed cost. However, due to the long-term nature of the problem, several parameters may be affected by uncertainty. Thus, we propose a two-stage stochastic programming formulation with recourse, highlighting the strategic and the operational decisions involved, as well as the effect of the different sources of uncertainty. In particular, we focus on the cases in which only the products price or only the products demand are stochastic. The general model and the recourse actions are adapted for these special cases, and the resulting modeling approaches are validated on a large set of instances. The experiments show the convenience of having in place models considering uncertainty explicitly with respect to using expected values for approximating it, and give rise to interesting managerial insights. Due to the computational burden of solving the resulting stochastic models (for a sufficiently large number of scenarios), we also propose a simple solution framework based on valid inequalities and other accelerating mechanisms.