We consider the optimization problem of safety stock placement in a supply chain, as formulated in [1]. We prove that this problem is NP-Hard for supply chains modeled as general acyclic networks. Thus, we do not expect to find a polynomial-time algorithm for safety stock placement for a general-network supply chain. / Singapore-MIT Alliance (SMA)

In the paper, we minimize the holding cost of the safety stock held in a supply chain modeled as a general network. By our assumption, the demand is bounded by a concave function. This fact allows us to formulate the problem as a deterministic optimization. We minimize a concave function over a discrete polyhedron. The main goal of the paper is to describe an algorithm to solve the problem without assuming any particular structure of the underlying supply chain. The algorithm is a branch and bound algorithm. / Singapore-MIT Alliance (SMA)