A stochastic multi-item lot-sizing problem with bounded number of setups

Within a partnership with a consulting company, we address a production problem modeled as a stochastic multi-item lot-sizing problem with bounded numbers of setups per period and without setup cost. While this formulation seems to be rather non-standard in the lot-sizing landscape, it is motivated by concrete missions of the company. Since the deterministic version of the problem is NP-hard and its full stochastic version clearly intractable, we turn to approximate methods and propose a repeated two-stage stochastic programming approach to solve it. Using simulations on real-world instances, we show that our method gives better results than current heuristics used in industry. Moreover, our method provides lower bounds proving the quality of the approach. Since the computational times are small and the method easy to use, our contribution constitutes a promising response to the original industrial problem.