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 from strategic and tactical perspectives in a planning horizon consisting of multiple periods. Long term decisions involve new installations, expansions and elimination of warehouses and factories handling multiple products. It is also considered which warehouses should be used as repair work-shops in order to store, repair and deliver used units to customers. Tactical planning includes deciding inventory levels (safety stock and expected inventory) for each type of spare part in distribution centers and customer plants, as well as the connection links between the supply chain nodes. Capacity constraints are also taken into account when planning inventory levels. 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. In addition, the risk-pooling effect is taken into account when defining inventory levels in distribution centers and customer zones. 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 can be adapted to several industry-critical units and the supply chain of electric motors is provided here as an example.