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Linear Control of a Markov Production System

Author

Listed:
  • Eric V. Denardo

    (Yale University, New Haven, Connecticut)

  • Christopher S. Tang

    (University of California, Los Angeles, California)

Abstract

This paper presents a model of a facility that processes many jobs. Each job requires a sequence of activities. The sequence of activities required by a job is random because each activity ends with a test, and the outcome of that test determines the activity that must be performed next. Evolution from activity to activity is Markovian, i.e., is determined by transition probabilities. A few (e.g., six) different types of job can share this facility, each type having its own transition probabilities between the activities. Each activity takes place in a designated sector. Several activities can share a sector. Each sector has a capacity, and buffers of inventory serve to decouple the sectors. In this paper, we introduce a family of linear control rules that smooth the flow through each sector and regulate the amount of inventory in each buffer. The operating characteristics of each linear control rule are computed. These include the mean and variance of the flow into each sector, the inventory in each buffer, the throughput of the systems, and the cycle time. These operating characteristics are optimized by a convex nonlinear program.

Suggested Citation

  • Eric V. Denardo & Christopher S. Tang, 1992. "Linear Control of a Markov Production System," Operations Research, INFORMS, vol. 40(2), pages 259-278, April.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:2:p:259-278
    DOI: 10.1287/opre.40.2.259
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    Citations

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    Cited by:

    1. Awi Federgruen & Nan Yang, 2014. "Infinite Horizon Strategies for Replenishment Systems with a General Pool of Suppliers," Operations Research, INFORMS, vol. 62(1), pages 141-159, February.
    2. Kim, Ilhyung & Tang, Christopher S., 1997. "Lead time and response time in a pull production control system," European Journal of Operational Research, Elsevier, vol. 101(3), pages 474-485, September.
    3. John S. Hollywood, 2005. "An approximate planning model for distributed computing networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 590-605, September.
    4. Hadjinicola, George C. & Soteriou, Andreas C., 2003. "Reducing the cost of defects in multistage production systems: A budget allocation perspective," European Journal of Operational Research, Elsevier, vol. 145(3), pages 621-634, March.
    5. G C Hadjinicola, 2010. "Manufacturing costs in serial production systems with rework," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(2), pages 342-351, February.
    6. L. Gong & H. Matsuo, 1997. "Control Policy for a Manufacturing System with Random Yield and Rework," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 149-175, October.
    7. Bordoloi, Sanjeev K. & Matsuo, Hirofumi, 2001. "Human resource planning in knowledge-intensive operations: A model for learning with stochastic turnover," European Journal of Operational Research, Elsevier, vol. 130(1), pages 169-189, April.
    8. Sanjeev Bordoloi, 2006. "A control rule for recruitment planning in engineering consultancy," Journal of Productivity Analysis, Springer, vol. 26(2), pages 147-163, October.
    9. Weng, Z. Kevin, 1998. "Managing production with flexible capacity deployment for serial multi-stage manufacturing systems," European Journal of Operational Research, Elsevier, vol. 109(3), pages 587-598, September.
    10. Scott Webster & Z. Kevin Weng, 2001. "Improving Repetitive Manufacturing Systems: Model and Insights," Operations Research, INFORMS, vol. 49(1), pages 99-106, February.

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