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Optimal control of manufacturing systems with buffer holding costs

  • Part I Optimal Production Planning
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Recent Advances in Control and Optimization of Manufacturing Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 214))

Abstract

In this paper, we examine the optimal control of a fluid flow model for manufacturing systems. The objective is to minimize inventory and shortfall costs. Under the assumption that the machines are reliable, we discuss and extend the method of solution used by Perkins and Kumar [31]. This approach exploits the structural properties of controls which perform well, and shows that an optimal control is determined by solving a series of quadratic programming problems having linear inequality constraints. Equivalently, the optimal control can be expressed by the description of a series of linear switching surfaces, which can be computed off-line (for a given manufacturing system).

In the second part of the paper, we assume the machines are failure-prone. Motivated by the results when the machines are reliable, we consider the application of linear switching curve controls. Under such controls, for systems consisting of two buffers and two machine states, we show that the steady-state probability densities of the buffer levels satisfy a set of coupled hyperbolic partial differential equations. Perkins and Srikant [33] use transform techniques to explicitly determine these probability densities. For a certain class of policies, called prioritized hedging point policies, these results straightforwardly extend to an arbitrary number of part-types. We then discuss the application of these results to the determination of optimal and near-optimal controls.

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Author information

Authors and Affiliations

  1. Department of Manufacturing Engineering, Boston University, 44 Cummington St., 02215, Boston, MA

    James R. Perkins

  2. Coordinated Science Laboratory, University of Illinois, 1308 W. Main St., 61801, Urbana, IL

    R. Srikant

Authors
  1. James R. Perkins
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  2. R. Srikant
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George Yin (Dr)Qing Zhang (Dr)

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© 1996 Springer-Verlag London Limited

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Perkins, J.R., Srikant, R. (1996). Optimal control of manufacturing systems with buffer holding costs. In: Yin, G., Zhang, Q. (eds) Recent Advances in Control and Optimization of Manufacturing Systems. Lecture Notes in Control and Information Sciences, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015114

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  • DOI: https://doi.org/10.1007/BFb0015114

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76055-9

  • Online ISBN: 978-3-540-40949-6

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