Chapter 6

Continuous Dynamic Models, Clearing Functions, and Discrete-Event Simulation in Aggregate Production Planning

Dieter Armbruster
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, armbruster@asu.edu

Reha Uzsoy
Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, North Carolina 2769, ruzsoy@ncsu.edu

Abstract

We consider the problem of representing the capabilities of production systems to convert inputs into outputs over time in the face of deterministic demand. The fact that planning models generally operate in discrete-time while the factory being modeled operates in continuous time suggests the use of multimodel methods combining an optimization model that plans the releases into the plant over time with a simulation model that assesses the impacts of these releases on performance. We discuss several such schemes that have been implemented using discrete-event simulation, present recent computational results, and discuss their strengths and weaknesses. We then consider two alternative approaches that have emerged in the recent literature: the use of discrete-time linear programming models based on nonlinear clearing functions, and methods using systems of coupled partial differential equations based on transport phenomena. We identify the relationships between queueing models, clearing functions, and transport model-based methods, and we discuss future research directions.

Key words: production planning; clearing functions; linear programming; transport equations; partial differential equations

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Citation information:

Armbruster D., R. Uzsoy. Continuous Dynamic Models, Clearing Functions, and Discrete-Event Simulation in Aggregate Production Planning. P. Mirchandani, ed. INFORMS TutORials in Operations Research, Vol. 9. INFORMS, Hanover, MD, pp. 103--126