Integrating supplier selection decisions into an inventory location problem for designing the supply chain network

This paper proposes a novel Inventory-Location problem that integrates supplier selection decisions to design a three-echelon supply chain network, under a continuous (s,Q) inventory control policy at the warehouses. In this problem, a set of warehouses must be selected within a set of potential locations to serve several customers or demand zones, additionally involving the selection of the suppliers for fulfilling incoming orders from the located warehouses. The optimal solution must be determined while minimizing total system costs including supplier selection, transportation (i.e., suppliers-warehouses and warehouses-customers), inventory (i.e., cycle and safety stock), and warehouse location costs. A key element of the problem is the consideration of variable lead-times for the warehouses, which are dependent on the selection of the supplier that serve them, thus increasing model complexity. Accordingly, an efficient algorithm based on the Generalized Benders Decomposition is developed and implemented to solve the proposed Mixed Integer, Nonlinear, Nonconvex, Programming Model. The proposed solution approach relies on a convenient model formulation and decomposition that yields a Mixed Integer Linear master problem and a continuous, convex subproblem. A wide set of medium-sized synthetic instances are optimally solved in affordable times, denoting the efficiency and effectiveness of the proposed model along with the proposed solution approach. Significant scientific and managerial insights are provided and discussed.