New solution approaches for the capacitated supplier selection problem with total quantity discount and activation costs under demand uncertainty

We study a multi-product multi-supplier procurement problem in the Automotive sector involving both supplier selection and ordering quantity decisions, and further complicated by the presence of total quantity discounts, business activation costs, and demand uncertainty. Recent works have shown the importance of explicitly incorporate demand uncertainty in this economic setting, along with the evidence about the computational burden of solving the relative Stochastic Programming models for a sufficiently large number of scenarios. In this work, we propose different solution strategies to efficiently cope with these models by taking advantage of the particular structure of the stochastic problem. More precisely, we propose and test several variants of a Progressive Hedging based heuristic approach as well as a Benders algorithm. The results obtained on benchmark instances show how the proposed methods outperform the existing ones and the state-of-the-art solvers in terms of efficiency and solution quality. In particular, thanks to the developed Progressive Hedging, we have been able to solve for the first time problem instances with up to 20 suppliers and 30 products.