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Batching to Minimize Flow Times on One Machine

Author

Listed:
  • Gregory Dobson

    (Graduate School of Management, University of Rochester, Rochester, New York 14627)

  • Uday S. Karmarkar

    (Graduate School of Management, University of Rochester, Rochester, New York 14627)

  • Jeffrey L. Rummel

    (Fuqua School of Business, Duke University, Durham, North Carolina 27706)

Abstract

Machine sequencing formulations typically assume that the characteristics of the job set to be processed are given. However, in many applications, jobs can be batched in different ways. Two types of minimum flow-time sequencing problems with lot sizing are formulated. The "item-flow" formulation is solved giving an index rule for ordering items. The "batch-flow" formulation is solved for the single product case showing that processing is done in unequal batches ordered in decreasing size. Heuristics and bounds are provided for the multiproduct case.

Suggested Citation

  • Gregory Dobson & Uday S. Karmarkar & Jeffrey L. Rummel, 1987. "Batching to Minimize Flow Times on One Machine," Management Science, INFORMS, vol. 33(6), pages 784-799, June.
    • Handle: RePEc:inm:ormnsc:v:33:y:1987:i:6:p:784-799
    DOI: 10.1287/mnsc.33.6.784
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    Citations

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    Cited by:

    1. Bruggemann, Wolfgang & Jahnke, Hermann, 2000. "The discrete lot-sizing and scheduling problem: Complexity and modification for batch availability," European Journal of Operational Research, Elsevier, vol. 124(3), pages 511-528, August.
    2. Lin, B. M. T. & Jeng, A. A. K., 2004. "Parallel-machine batch scheduling to minimize the maximum lateness and the number of tardy jobs," International Journal of Production Economics, Elsevier, vol. 91(2), pages 121-134, September.
    3. Chung-Lun Li & Chung-Yee Lee, 1997. "Scheduling with agreeable release times and due dates on a batch processing machine," European Journal of Operational Research, Elsevier, vol. 96(3), pages 564-569, February.
    4. Esaignani Selvarajah & George Steiner, 2009. "Approximation Algorithms for the Supplier's Supply Chain Scheduling Problem to Minimize Delivery and Inventory Holding Costs," Operations Research, INFORMS, vol. 57(2), pages 426-438, April.
    5. Daniel Adelman & George L. Nemhauser & Mario Padron & Robert Stubbs & Ram Pandit, 1999. "Allocating Fibers in Cable Manufacturing," Manufacturing & Service Operations Management, INFORMS, vol. 1(1), pages 21-35.
    6. Grundel, Soesja & Çiftçi, Barış & Borm, Peter & Hamers, Herbert, 2013. "Family sequencing and cooperation," European Journal of Operational Research, Elsevier, vol. 226(3), pages 414-424.
    7. Liaee, Mohammad Mehdi & Emmons, Hamilton, 1997. "Scheduling families of jobs with setup times," International Journal of Production Economics, Elsevier, vol. 51(3), pages 165-176, September.
    8. Lambrecht, Marc R. & Vandaele, Nico J., 1996. "A general approximation for the single product lot sizing model with queueing delays," European Journal of Operational Research, Elsevier, vol. 95(1), pages 73-88, November.
    9. Bongjin Gim & Min-Hong Han, 1997. "Economic scheduling of products with N components on a single machine," European Journal of Operational Research, Elsevier, vol. 96(3), pages 570-577, February.
    10. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
    11. Ching, Chung Yaw & Liao, Ching-Jong & Wu, Chutao John, 1997. "Batching to minimize total production time for two part types," International Journal of Production Economics, Elsevier, vol. 48(1), pages 63-72, January.
    12. Paul Schikora & Andrew Manikas & Michael Godfrey, 2015. "Determining Optimal Flow-Time Schedules For The Multiple-Product Batch-Flow Problem," International Journal of Management and Marketing Research, The Institute for Business and Finance Research, vol. 8(2), pages 19-35.
    13. Gregory H. Graves & Chung‐Yee Lee, 1999. "Scheduling maintenance and semiresumable jobs on a single machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 845-863, October.
    14. Selvarajah, Esaignani & Steiner, George, 2006. "Batch scheduling in a two-level supply chain--a focus on the supplier," European Journal of Operational Research, Elsevier, vol. 173(1), pages 226-240, August.
    15. Gur Mosheiov & Daniel Oron & Yaacov Ritov, 2004. "Flow‐shop batch scheduling with identical processing‐time jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 783-799, September.
    16. Mosheiov, Gur & Oron, Daniel, 2008. "A single machine batch scheduling problem with bounded batch size," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1069-1079, June.
    17. Xinxin Hu & James D Blocher & Hans Sebastian Heese & Feng Zhou, 2016. "Scheduling products with subassemblies and changeover time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1025-1033, August.
    18. Zhou, Feng & Blocher, James D. & Hu, Xinxin & Sebastian Heese, H., 2014. "Optimal single machine scheduling of products with components and changeover cost," European Journal of Operational Research, Elsevier, vol. 233(1), pages 75-83.

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