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Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem

Author

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  • David M. Markowitz

    (Program Analysis and Evaluation, Office of the Secretary of Defense, Washington, District of Columbia 20301-1800)

  • Lawrence M. Wein

    (Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

Abstract

This paper examines how setups, due dates, and the mix of standardized and customized products affect the scheduling of a single machine operating in a dynamic and stochastic environment. We restrict ourselves to the class of dynamic cyclic policies, where the machine busy/idle policy and lot-sizing decisions are controlled in a dynamic fashion, but different products must be produced in a fixed sequence. As in earlier work, we conjecture that an averaging principle holds for this queueing system in the heavy traffic limit, and optimize over the class of dynamic cyclic policies. The results allow for a detailed discussion of the interactions between the due-date, setup, and product mix facets of the problem.

Suggested Citation

  • David M. Markowitz & Lawrence M. Wein, 2001. "Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem," Operations Research, INFORMS, vol. 49(2), pages 246-270, April.
    • Handle: RePEc:inm:oropre:v:49:y:2001:i:2:p:246-270
    DOI: 10.1287/opre.49.2.246.13530
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    References listed on IDEAS

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    1. Viên Nguyen, 1995. "Fluid and Diffusion Approximations of a Two-Station Mixed Queueing Network," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 321-354, May.
    2. E. G. Coffman & A. A. Puhalskii & M. I. Reiman, 1998. "Polling Systems in Heavy Traffic: A Bessel Process Limit," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 257-304, May.
    3. Martin I. Reiman & Lawrence M. Wein, 1998. "Dynamic Scheduling of a Two-Class Queue with Setups," Operations Research, INFORMS, vol. 46(4), pages 532-547, August.
    4. Salah E. Elmaghraby, 1978. "The Economic Lot Scheduling Problem (ELSP): Review and Extensions," Management Science, INFORMS, vol. 24(6), pages 587-598, February.
    5. Agnes Peña Perez & Paul Zipkin, 1997. "Dynamic Scheduling Rules for a Multiproduct Make-to-Stock Queue," Operations Research, INFORMS, vol. 45(6), pages 919-930, December.
    6. Martin I. Reiman & Lawrence M. Wein, 1999. "Heavy Traffic Analysis of Polling Systems in Tandem," Operations Research, INFORMS, vol. 47(4), pages 524-534, August.
    7. Guillermo Gallego, 1990. "Scheduling the Production of Several Items with Random Demands in a Single Facility," Management Science, INFORMS, vol. 36(12), pages 1579-1592, December.
    8. David M. Markowitz & Martin I. Reiman & Lawrence M. Wein, 2000. "The Stochastic Economic Lot Scheduling Problem: Heavy Traffic Analysis of Dynamic Cyclic Policies," Operations Research, INFORMS, vol. 48(1), pages 136-154, February.
    9. Yu-Sheng Zheng & Paul Zipkin, 1990. "A Queueing Model to Analyze the Value of Centralized Inventory Information," Operations Research, INFORMS, vol. 38(2), pages 296-307, April.
    10. Robert C. Leachman & André Gascon, 1988. "A Heuristic Scheduling Policy for Multi-Item, Single-Machine Production Systems with Time-Varying, Stochastic Demands," Management Science, INFORMS, vol. 34(3), pages 377-390, March.
    11. Albert Y. Ha, 1997. "Optimal Dynamic Scheduling Policy for a Make-To-Stock Production System," Operations Research, INFORMS, vol. 45(1), pages 42-53, February.
    12. Debashish Sarkar & Willard I. Zangwill, 1991. "Variance Effects in Cyclic Production Systems," Management Science, INFORMS, vol. 37(4), pages 444-453, April.
    13. Martin I. Reiman & Rodrigo Rubio & Lawrence M. Wein, 1999. "Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem," Transportation Science, INFORMS, vol. 33(4), pages 361-380, November.
    14. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    15. Lawrence M. Wein, 1992. "Dynamic Scheduling of a Multiclass Make-to-Stock Queue," Operations Research, INFORMS, vol. 40(4), pages 724-735, August.
    16. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    17. Viên Nguyen, 1998. "A Multiclass Hybrid Production Center in Heavy Traffic," Operations Research, INFORMS, vol. 46(3-supplem), pages 13-25, June.
    18. Awi Federgruen & Ziv Katalan, 1996. "The Stochastic Economic Lot Scheduling Problem: Cyclical Base-Stock Policies with Idle Times," Management Science, INFORMS, vol. 42(6), pages 783-796, June.
    19. Dimitris Bertsimas & José Niño-Mora, 1996. "Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; A Polyhedral Approach to Indexable Systems," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 257-306, May.
    20. Izak Duenyas & Mark P. Van Oyen, 1996. "Heuristic Scheduling of Parallel Heterogeneous Queues with Set-Ups," Management Science, INFORMS, vol. 42(6), pages 814-829, June.
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    Cited by:

    1. Germs, Remco & Van Foreest, Nicky D., 2011. "Admission policies for the customized stochastic lot scheduling problem with strict due-dates," European Journal of Operational Research, Elsevier, vol. 213(2), pages 375-383, September.
    2. Winands, E.M.M. & Adan, I.J.B.F. & van Houtum, G.J., 2011. "The stochastic economic lot scheduling problem: A survey," European Journal of Operational Research, Elsevier, vol. 210(1), pages 1-9, April.
    3. Otis B. Jennings, 2008. "Heavy-Traffic Limits of Queueing Networks with Polling Stations: Brownian Motion in a Wedge," Mathematics of Operations Research, INFORMS, vol. 33(1), pages 12-35, February.
    4. Han Wu & Gerald Evans & Ki-Hwan Bae, 2016. "Production control in a complex production system using approximate dynamic programming," International Journal of Production Research, Taylor & Francis Journals, vol. 54(8), pages 2419-2432, April.
    5. René Caldentey & Lawrence M. Wein, 2006. "Revenue Management of a Make-to-Stock Queue," Operations Research, INFORMS, vol. 54(5), pages 859-875, October.
    6. Lopez de Haro, Santiago & Gershwin, Stanley B. & Rosenfield, Donald B., 2009. "Schedule evaluation in unstable manufacturing environments," International Journal of Production Economics, Elsevier, vol. 121(1), pages 183-194, September.
    7. Wei-Min Lan & Tava Lennon Olsen, 2006. "Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules," Operations Research, INFORMS, vol. 54(3), pages 505-522, June.
    8. Jan A. Van Mieghem, 2003. "Due-Date Scheduling: Asymptotic Optimality of Generalized Longest Queue and Generalized Largest Delay Rules," Operations Research, INFORMS, vol. 51(1), pages 113-122, February.
    9. Donald D. Eisenstein, 2005. "Recovering Cyclic Schedules Using Dynamic Produce-Up-To Policies," Operations Research, INFORMS, vol. 53(4), pages 675-688, August.

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