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Notes: Toward Characterizing the Optimal Allocation of Storage Space in Production Line Systems with Variable Processing Times

Author

Listed:
  • Frederick S. Hillier

    (Department of Operations Research, Stanford University, Stanford, California 94305)

  • Kut C. So

    (Graduate School of Management, University of California, Irvine, Irvine, California 92717)

  • Ronald W. Boling

    (College of Business Administration, The University of Tennessee, Knoxville, Tennessee 37916)

Abstract

This investigation considers certain issues regarding the optimal design of unpaced production lines with variable processing times. Under certain assumptions, including an equal allocation of buffer storage space between the respective pairs of stations, it is known that the optimal allocation of work is characterized by the "bowl phenomenon" whereby the interior stations (especially the center ones) are given preferential treatment (less work) over the end stations. The key question now being posed is: given an equal allocation of work to the respective stations, does the optimal allocation of buffer storage space between the respective pairs of stations follow an analogous pattern (the "storage bowl phenomenon") whereby the interior buffers (especially the center ones) are given preferential treatment (more space) over the end buffers? Because the decision variables now are discrete instead of continuous, the answer found in this study is: sometimes, but not in general. Characterizing the optimal allocation of storage space is a surprisingly subtle and complex problem. Despite the ambiguities, one dominant theme that runs throughout all of the results obtained is that, to the extent that preferential treatment in storage space allocations should be given, priority should be given to the interior buffers (especially the center ones) over the end buffers. The other key conclusion is that, when the total amount of storage space also is a decision variable, the overall optimal solution commonly follows a storage bowl phenomenon whereby the allocation of buffer storage space fits an inverted bowl pattern.

Suggested Citation

  • Frederick S. Hillier & Kut C. So & Ronald W. Boling, 1993. "Notes: Toward Characterizing the Optimal Allocation of Storage Space in Production Line Systems with Variable Processing Times," Management Science, INFORMS, vol. 39(1), pages 126-133, January.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:1:p:126-133
    DOI: 10.1287/mnsc.39.1.126
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    Citations

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    Cited by:

    1. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2007. "A classification of assembly line balancing problems," European Journal of Operational Research, Elsevier, vol. 183(2), pages 674-693, December.
    2. Federico Nuñez-Piña & Joselito Medina-Marin & Juan Carlos Seck-Tuoh-Mora & Norberto Hernandez-Romero & Eva Selene Hernandez-Gress, 2018. "Modeling of Throughput in Production Lines Using Response Surface Methodology and Artificial Neural Networks," Complexity, Hindawi, vol. 2018, pages 1-10, January.
    3. Yi‐Chun Tsai & Nilay Tanık Argon, 2008. "Dynamic server assignment policies for assembly‐type queues with flexible servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(3), pages 234-251, April.
    4. Kirkavak, Nureddin & Dincer, Cemal, 1999. "The general behavior of pull production systems: The allocation problems," European Journal of Operational Research, Elsevier, vol. 119(2), pages 479-494, December.
    5. Boysen, Nils & Fliedner, Malte & Scholl, Armin, 2008. "Assembly line balancing: Which model to use when," International Journal of Production Economics, Elsevier, vol. 111(2), pages 509-528, February.
    6. Becker, Christian & Scholl, Armin, 2006. "A survey on problems and methods in generalized assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 694-715, February.
    7. Yarmand, Mohammad H. & Down, Douglas G., 2013. "Server allocation for zero buffer tandem queues," European Journal of Operational Research, Elsevier, vol. 230(3), pages 596-603.
    8. Hillier, Frederick S. & So, Kut C., 1996. "On the robustness of the bowl phenomenon," European Journal of Operational Research, Elsevier, vol. 89(3), pages 496-515, March.
    9. Bertazzi, Luca, 2011. "Determining the optimal dimension of a work-in-process storage area," International Journal of Production Economics, Elsevier, vol. 131(2), pages 483-489, June.
    10. Mehmet Savsar, 2016. "Reliability and availability analysis of a manufacturing line system," Journal of Applied and Physical Sciences, Prof. Vakhrushev Alexander, vol. 2(3), pages 96-106.
    11. Yamamoto, Hidehiko & Abu Qudeiri, Jaber & Marui, Etsuo, 2008. "Definition of FTL with bypass lines and its simulator for buffer size decision," International Journal of Production Economics, Elsevier, vol. 112(1), pages 18-25, March.
    12. Staley, Dan R. & Kim, David S., 2012. "Experimental results for the allocation of buffers in closed serial production lines," International Journal of Production Economics, Elsevier, vol. 137(2), pages 284-291.
    13. Boysen, Nils & Schulze, Philipp & Scholl, Armin, 2022. "Assembly line balancing: What happened in the last fifteen years?," European Journal of Operational Research, Elsevier, vol. 301(3), pages 797-814.
    14. Mehmet Ulaş Koyuncuoğlu & Leyla Demir, 2021. "A comparison of combat genetic and big bang–big crunch algorithms for solving the buffer allocation problem," Journal of Intelligent Manufacturing, Springer, vol. 32(6), pages 1529-1546, August.
    15. Nabil Nahas, 2017. "Buffer allocation and preventive maintenance optimization in unreliable production lines," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 85-93, January.
    16. Nahas, Nabil & Ait-Kadi, Daoud & Nourelfath, Mustapha, 2006. "A new approach for buffer allocation in unreliable production lines," International Journal of Production Economics, Elsevier, vol. 103(2), pages 873-881, October.
    17. Papadopoulos, H. T. & Vidalis, M. I., 2001. "Minimizing WIP inventory in reliable production lines," International Journal of Production Economics, Elsevier, vol. 70(2), pages 185-197, March.
    18. Nilay Tanık Argon & Sigrún Andradóttir, 2017. "Pooling in tandem queueing networks with non-collaborative servers," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 345-377, December.

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