We report on a project with Polaroid Corporation in which we developed a supply chain model to provide decision support for planning production and transportation. Production occurs in Asia to serve world-wide demand. Production planners must determine both the production quantities as well as whether to ship by sea or by air. We develop a model to optimize a static version of this problem and then show how to use this static model in a dynamic setting. We test the model with data from Polaroid and show its effectiveness. / Singapore-MIT Alliance (SMA)

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)