Coordinated Replenishment and Rework with Unreliable Supply Sources

Abstract

Having started in Chapter 3 from the customer end and gone through several different configurations of production facilities in Chapters 4 through 8, we have now reached the other end of the supply chain. Our focus here is on a set of suppliers, which have different grades of quality and collectively form the sources of supply to a production-inventory system. The system, in turn, fills in a single stream of customer demands. In addition to placing orders of different size with the difference sources, the system can choose to inspect a certain number of units received from each source and repair any identified defectives. We first study this optimal inspection decision, assuming the order quantities are given. This is formulated as an integer optimization problem, which minimizes an objective function that takes into account the inspection and repair costs, as well as the penalty for unmet demand and the salvage value of any surplus units. As the objective function is nonlinear and nonseparable, such an integer optimization problem is difficult to solve in general.