IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v49y2001i2p246-270.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.49.2.246.13530
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.49.2.246.13530?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Paul H. Zipkin, 1980. "Simple Ranking Methods for Allocation of One Resource," Management Science, INFORMS, vol. 26(1), pages 34-43, January.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Lawrence M. Wein, 1992. "Dynamic Scheduling of a Multiclass Make-to-Stock Queue," Operations Research, INFORMS, vol. 40(4), pages 724-735, August.
    7. 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.
    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. Martin I. Reiman, 1984. "Open Queueing Networks in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 441-458, August.
    11. Salah E. Elmaghraby, 1978. "The Economic Lot Scheduling Problem (ELSP): Review and Extensions," Management Science, INFORMS, vol. 24(6), pages 587-598, February.
    12. 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.
    13. 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.
    14. Debashish Sarkar & Willard I. Zangwill, 1991. "Variance Effects in Cyclic Production Systems," Management Science, INFORMS, vol. 37(4), pages 444-453, April.
    15. 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.
    16. 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.
    17. 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.
    18. Viên Nguyen, 1998. "A Multiclass Hybrid Production Center in Heavy Traffic," Operations Research, INFORMS, vol. 46(3-supplem), pages 13-25, June.
    19. 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.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. René Caldentey & Lawrence M. Wein, 2006. "Revenue Management of a Make-to-Stock Queue," Operations Research, INFORMS, vol. 54(5), pages 859-875, October.
    4. 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.
    5. 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.
    6. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Chen Shaoxiang, 2004. "The Optimality of Hedging Point Policies for Stochastic Two-Product Flexible Manufacturing Systems," Operations Research, INFORMS, vol. 52(2), pages 312-322, April.
    3. Scott Carr & Izak Duenyas, 2000. "Optimal Admission Control and Sequencing in a Make-to-Stock/Make-to-Order Production System," Operations Research, INFORMS, vol. 48(5), pages 709-720, October.
    4. 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.
    5. José Niño-Mora, 2006. "Restless Bandit Marginal Productivity Indices, Diminishing Returns, and Optimal Control of Make-to-Order/Make-to-Stock M/G/1 Queues," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 50-84, February.
    6. Dimitris Bertsimas & Ioannis Ch. Paschalidis, 2001. "Probabilistic Service Level Guarantees in Make-to-Stock Manufacturing Systems," Operations Research, INFORMS, vol. 49(1), pages 119-133, February.
    7. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    8. Bora Kat & Zeynep Avṣar, 2011. "Using aggregate fill rate for dynamic scheduling of multi-class systems," Annals of Operations Research, Springer, vol. 182(1), pages 87-117, January.
    9. Rappold, James A. & Yoho, Keenan D., 2014. "Setting safety stocks for stable rotation cycle schedules," International Journal of Production Economics, Elsevier, vol. 156(C), pages 146-158.
    10. Francis De Vericourt & Fikri Karaesmen & Yves Dallery, 2000. "Dynamic Scheduling in a Make-to-Stock System: A Partial Characterization of Optimal Policies," Operations Research, INFORMS, vol. 48(5), pages 811-819, October.
    11. 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.
    12. Vaughan, Timothy S., 2007. "Cyclical schedules vs. dynamic sequencing: Replenishment dynamics and inventory efficiency," International Journal of Production Economics, Elsevier, vol. 107(2), pages 518-527, June.
    13. William Liang & Barış Balcıog̃lu & Robert Svaluto, 2013. "Scheduling policies for a repair shop problem," Annals of Operations Research, Springer, vol. 211(1), pages 273-288, December.
    14. Sox, Charles R. & Jackson, Peter L. & Bowman, Alan & Muckstadt, John A., 1999. "A review of the stochastic lot scheduling problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 181-200, September.
    15. Ganesh Janakiraman & Mahesh Nagarajan & Senthil Veeraraghavan, 2018. "Simple Policies for Managing Flexible Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 333-346, May.
    16. René Caldentey & Lawrence M. Wein, 2003. "Analysis of a Decentralized Production-Inventory System," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 1-17, November.
    17. H. G. H. Tiemessen & M. Fleischmann & G. J. Houtum, 2017. "Dynamic control in multi-item production/inventory systems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 165-191, January.
    18. Jian Yang, 2004. "Production Control in the Face of Storable Raw Material, Random Supply, and an Outside Market," Operations Research, INFORMS, vol. 52(2), pages 293-311, April.
    19. N Sanajian & H Abouee-Mehrizi & B Balcıog̃lu, 2010. "Scheduling policies in the M/G/1 make-to-stock queue," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 115-123, January.
    20. Alexey Matveev & Varvara Feoktistova & Ksenia Bolshakova, 2016. "On Global Near Optimality of Special Periodic Protocols for Fluid Polling Systems with Setups," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 1055-1070, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:49:y:2001:i:2:p:246-270. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.