Solving multi-stage stochastic in-house production and outsourcing planning by two-level decomposition

In-house production or outsourcing are important strategic decisions for planning production and capacity in business organizations. Outsourcing to overseas suppliers is often associated with risk with respect to the quality of the products. Hence, we developed a multi-stage stochastic programming model that takes into account the uncertainty involved in the production of the quality of outsourced products in the face of stochastic demand. The goal is to find an optimal way to choose between in-house capacity expansion and buying from local suppliers with assured quality versus buying from overseas suppliers. Moreover, we propose three alternative algorithms for solving the problem. These three approaches are: a two-level column generation by using the Analytic Center Cutting Plane Method (ACCPM), a two-level Benders’ decomposition by using the ACCPM, and a two-level decomposition where the fist level is solved by using the classical Dantzig-Wolfe decomposition approach and the second level is solved by using the ACCPM.