A remnant inventory system is one in which items that are removed from inventory may be partially consumed and then either returned to inventory or scrapped. We investigate remnant inventory systems in which orders arrive for units of raw material that are produced-to-stock. Such systems arise in fiber-optic cable manufacturing, where the orders are for cables and the raw materials are optical fibers. We propose an integer programming-based, price-directed scheme for minimizing the long-run average scrap rate while giving short-term priority to orders according to their due dates. Dual prices from a long-range linear program yield objective function coefficients for the integer program. These prices are shown to exhibit many properties. We present simulation results demonstrating superior performance of our scheme over an existing remnant inventory control algorithm.
We also consider a generalized remnant inventory system which allows multiple orders as a group, called a concatenation, to be allocated to a unit. Since multiple orders are satisfied instead of a single order, only one setup needs to be done rather than many. In addition to saving production time, process scrap is also saved. We investigate how to incorporate due date lead times, which limit the frequency orders may be concatenated, into the dual price calculation. We also generalize the properties satisfied by the dual prices without concatenation, and present several additional ones satisfied when concatenation is allowed.
This work is based on our development and implementation of an integer programming model for making fiber allocation decisions in a fiber-optic cable manufacturing plant. We describe this application context in detail, present the full-fidelity integer programming model that has been implemented, investigate some associated computational issues, and report on actual factory usage and performance.
Finally, we discuss extensions and future research directions such as including additional factory dynamics and devising computational solution methodologies. Applications of our general metholodology in other settings are also given.
