Optimizing production capacity and safety stocks in general acyclic supply chains

Abstract This paper addresses the joint optimization of production capacity and safety stocks in supply chains under the guaranteed service approach (GSA). The integrated problem is formulated as a mixed integer nonlinear program (MINLP) and solution procedures are proposed in the cases of general acyclic and spanning tree networks. For general acyclic supply chains, the integrated problem is solved using a Lagrangian decomposition method which iteratively solves capacity planning and safety stock placement subproblems, and adds budget feasibility constraints to strengthen the Lagrangian decomposition lower bound. When the supply chain has a spanning tree structure, an efficient Lagrangian relaxation heuristic dualizes the budget constraint and solves the relaxed problem using a dynamic programming algorithm. Computational experiments on real-world instances show that the Lagrangian decomposition method is able to solve all instances within 0.1% optimality, while a state-of-the-art solver is unable to provide feasible solutions for large instances. In the case of spanning tree networks, the proposed Lagrangian relaxation heuristic finds optimal or near-optimal solutions and greatly improves running time in comparison to the Lagrangian decomposition method. In addition, numerical experiments show that savings can be achieved through joint optimization of capacity and safety stocks.