Robust Multi-Sourcing Supply Chain Network Design Problem

In this paper, we study a multi-sourcing supply chain network design problem under demand uncertainty in which each retailer can source a single item from more than one distribution center. The problem takes into account the complex trade-off among the costs of facility location and inventory holding, as well as the fixed linkage and the per unit delivery costs between the distribution center and the retailer. We propose a nonlinear mixed integer programming model with a joint chance constraint (that imposes a certain service level on the network) to determine the locations, the inventory levels, and the retailer assignments of the distribution centers. Two approaches, namely, the set-wise approximation and the approximation based on the linear decision rule, are constructed to conservatively approximate the service level joint chance constraint with incomplete information of the demand distribution. Both approaches yield sparse distribution networks, which are effective in matching uncertain demand using the on-hand inventory and hence successfully achieve high service levels. We also show through numerical studies that the proposed approaches outperform other commonly adopted approximations of chance constraints