Operations sequencing for a multi-stage production inventory system

This article studies operations sequencing for a multi-stage production inventory system with lead times under predictable (deterministic) yield losses and random demand. We consider various cases with either full or partial release of work-in-process inventories, for either pre-operation or post-operation cost structures, and under either the total discounted or average cost criteria. We derive necessary and sufficient criteria for the optimal sequence of operations in all cases. While the criteria differ in their specific forms, they all lead to the same principal: those operations with (1) lower yields, (2) lower processing costs, (3) longer lead times, and (4) lower inventory holding costs should be placed higher upstream in the system.