Optimal Control of a Two-Station Tandem Production/Inventory System

Michael H. Veatch · Lawrence M. Wein

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Advanced Queuing Theory Analysis Supply Chain and Inventory Management Management and Optimization Techniques

Abstract

A manufacturing facility consisting of two stations in tandem operates in a make-to-stock mode: After production, items are placed in a finished goods inventory that services an exogenous Poisson demand. Demand that cannot be met from inventory is backordered. Each station is modeled as a queue with controllable production rate and exponential service times. The problem is to control these rates to minimize inventory holding and backordering costs. Optimal controls are computed using dynamic programming and compared with the kanban, basestock and buffer control mechanisms that have been proposed for manufacturing facilities. Conditions are found under which certain simple controls are optimal using stochastic coupling arguments. Insights are gained into when to hold work-in-process and finished goods inventory, comparable to previous studies of production lines in make-to-order and unlimited demand environments.

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References

1977Toyota production system and Kanban system Materialization of just-in-time and respect-for-human system 2004Optimal Policies for a Multi-Echelon Inventory Problem 1990CONWIP: a pull alternative to kanban 1983Japanese manufacturing techniques 1992Manufacturing flow line systems: a review of models and analytical results 1975Applying a New Device in the Optimization of Exponential Queuing Systems 1988Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems 1988The Role of Work-in-Process Inventory in Serial Production Lines

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1997A comparison of production-line control mechanisms 2003Supply Chain Operations: Serial and Distribution Inventory Systems 2000A unified framework for pull control mechanisms in multi‐stage manufacturing systems 2004Optimal Policies for a Capacitated Two-Echelon Inventory System 1998Leadtime-Inventory Trade-Offs in Assemble-to-Order Systems 1997

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