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Control Policy for a Manufacturing System with Random Yield and Rework

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Abstract

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.

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Authors and Affiliations

  1. Department of Information Systems and Decision Sciences, E. J. Ourso College of Business Administration, Louisiana State University, Baton Rouge, Louisiana

    L. Gong (Professor)

  2. Department of Management, Graduate School of Business, University of Texas at Austin, Austin, Texas

    H. Matsuo (Professor)

Authors
  1. L. Gong
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  2. H. Matsuo
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Gong, L., Matsuo, H. Control Policy for a Manufacturing System with Random Yield and Rework. Journal of Optimization Theory and Applications 95, 149–175 (1997). https://doi.org/10.1023/A:1022639529617

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  • DOI: https://doi.org/10.1023/A:1022639529617

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