Strategic supply network planning with vendor selection under consideration of risk and demand uncertainty

• A MINLP model formulation for a three-layer supply network planning problem under demand uncertainty.
• Approximation of non-linear functions by a piecewise linearization.
• Robust supply network configuration in the presence of uncertain demand.

We present a stochastic version of a three-layer supply network planning problem that includes the selection of vendors that must be equipped with company-specific tools. The configuration of a supply network must be determined by using demand forecasts for a long planning horizon to meet a given service level. The risk induced by the uncertain demand is explicitly considered by incorporating the conditional value at risk. The objective is to maximize the weighted sum of the expected net present value of discounted cash flows and the conditional value at risk. This would lead to a non-linear model formulation that is approximated by a mixed-integer linear model. This approximation is realized by a piecewise linearization of the expected backlogs and physical inventory as non-linear functions of cumulative production quantities. A two-stage stochastic programming approach is proposed. Our numerical analysis of generic test instances indicates that solving the linearized model formulation yields a robust and stable supply network configuration when demand is uncertain.