Multi-Sourcing Supply Network Design: Two-Stage Chance-Constrained Model, Tractable Approximations, and Computational Results
In this paper, we study a multi-sourcing supply chain network design problem, in which each retailer faces uncertain demand and can source products from more than one distribution center (DC). The decisions to be simultaneously optimized include the locations and the inventory levels of DCs, the set of DCs serving each retailer, as well as the amount of shipment from DCs to retailers. We propose a nonlinear mixed integer programming model with a joint chance constraint describing a certain service level. Two approaches, namely, a set-wise approximation and a Linear Decision Rule based approximation, are constructed to robustly approximate the service level chance constraint with incomplete demand information. Both approaches yield sparse multi-sourcing distribution networks, which are effective in matching uncertain demand using on-hand inventory and hence successfully reach a high service level. We show through extensive numerical experiments that our approaches outperform other commonly adopted approximations of the chance constraint.