Managing Simple Re-entrant Ow Lines I. Theoretical Foundation

We address several aspects related to managing re-entrant lines in an uniied manner { capacity allocation, inventory management and production control { in a set of three papers. Our approach to study these systems is through simulation based optimization. Simulation ooers the exibility to model the complexities adequately while the gradient computation (via Innnitesimal Perturbation Analysis) helps identify good solutions quickly. In this rst paper, we concentrate on a very simple family of re-entrant systems as a rst step towards analyzing a broader family of production systems. Our framework is a discrete time capacitated multiple product production-inventory system operating under a base stock policy. We analyze several diierent production (Linear Scaling, Priority, Equalize Shortfall) and capacity allocation (No sharing, Partial sharing and Total sharing) rules. We develop expressions for and validate the appropriate IPA derivatives. These derivatives can then be used in an optimization tool which enables the determination of optimal parameters for the several policies proposed. In 6], we provide insights based on an extensive computational study using the results provided here. In 7], we show that our production rules and capacity allocation methods lead to stable systems under base stock policy.