Price-directed control of remnant inventory systems

Motivated by make-to-order cable manufacturing, we describe a remnant inventory system in which orders arrive for units of raw material that are produced-to-stock. As orders are satisfied, the partially consumed units of material, or remnants, are either scrapped or returned to inventory for future allocation to orders. We present a linear program that minimizes the long-run average scrap rate. Its dual prices exhibit many rational properties, including monotonicity and superadditivity. We use these prices in an integer-programming-based control scheme, which we simulate and compare with an existing control scheme previously used in practice.