Optimizing Strategic Safety Stock Placement in Two-Layer Supply Chains

In this paper, we minimize the holding cost of the safety stock in the supply chain subject to linear constraints on the service times between the nodes of the network. In the problem, the objective function is concave as we assume the demand to be bounded by a concave function. The optimal solutions of the problem belong to the set of extreme points of the polyhedron, specified by the constraints of the problem. We first characterize the extreme points for the two-layer networks and then provide bounds to use in a branch and bound algorithm.Singapore-MIT Alliance (SMA

Optimizing Safety Stock Placement in General Network Supply Chains

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

Optimizing safety stock placement in general network supply chains

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.Includes bibliographical references (p. 207-214).The amount of safety stock to hold at each stage in a supply chain is an important problem for a manufacturing company that faces uncertain demand and needs to provide a high level of service to its customers. The amount of stock held should be small to minimize holding and storage costs while retaining the ability to serve customers on time and satisfy most, if not all, of the demand. This thesis analyzes this problem by utilizing the framework of deterministic service time models and provides an algorithm for safety stock placement in general-network supply chains. We first show that the general problem is NP-hard. Next, we develop several conditions that characterize an optimal solution of the general-network problem. We find that we can identify all possible candidates for the optimal service times for a stage by constructing paths from the stage to each other stage in the supply chain. We use this construct, namely these paths, as the basis for a branch and bound algorithm for the general-network problem. To generate the lower bounds, we create and solve a spanning-tree relaxation of the general-network problem. We provide a polynomial algorithm to solve these spanning tree problems. We perform a set of computational experiments to assess the performance of the general-network algorithm and to determine how to set various parameters for the algorithm. In addition to the general network case, we consider two-layer network problems. We develop a specialized branch and bound algorithm for these problems and show computationally that it is more efficient than the general-network algorithm applied to the two-layer networks.by Ekaterina Lesnaia.Ph.D

The Complexity of Safety Stock Placement in General-Network Supply Chains

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