Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part I: MINLP and MILP models

An optimization model is proposed to redesign the supply chain of spare part delivery under demand uncertainty in a specified planning horizon. Long term decisions involve new installations, expansions and elimination of warehouses handling multiple products. It is considered which warehouses should be used as repair work-shops to store, repair and deliver used units to customers. Tactical planning includes deciding inventory, and the connection links between the supply chain nodes. At the tactical level it is determined how demand of failing units is satisfied, and whether to use new or used parts. The uncertain demand is addressed by defining the optimal amount of safety stock that guarantees certain service level at a customer plant. Due to the nonlinear nature of the original formulation, a piece-wise linearization approach is applied to obtain a tight lower bound of the optimal solution. The formulation is applied to the supply chain of electric motors.