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Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers

Author

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  • Stanley B. Gershwin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Irvin C. Schick

    (Scientific Systems, Inc., Cambridge, Massachusetts)

Abstract

In an important class of systems, which arises in manufacturing, chemical process, and computer contexts, objects move sequentially from one work station to another, and rest between stations in buffers. In the manufacturing context, such systems are called transfer lines. The dynamic behavior of a buffered transfer line with unreliable work stations is modeled as a Markov chain. The system states consist of the operational conditions of the work stations and the levels of material in the buffers. The steady-state probabilities of these states are sought in order to establish relationships between system parameters and performance measures such as production rate (efficiency), forced-down times, and expected in-process inventory. The steady state probabilities are found by choosing a sum-of-products form solution for a class of states, and deriving the remaining expressions by using the transition equations. In this way, the order of the system of equations to be solved is drastically reduced. This algorithm suggests a general approach for solving large scale structured Markov chain problems.

Suggested Citation

  • Stanley B. Gershwin & Irvin C. Schick, 1983. "Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers," Operations Research, INFORMS, vol. 31(2), pages 354-380, April.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:2:p:354-380
    DOI: 10.1287/opre.31.2.354
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    Cited by:

    1. Stefan Helber & Katja Schimmelpfeng & Raik Stolletz & Svenja Lagershausen, 2011. "Using linear programming to analyze and optimize stochastic flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 193-211, January.
    2. Shi, Chuan & Gershwin, Stanley B., 2009. "An efficient buffer design algorithm for production line profit maximization," International Journal of Production Economics, Elsevier, vol. 122(2), pages 725-740, December.
    3. Chang, Ping-Chen & Lin, Yi-Kuei & Chiang, Yu-Min, 2019. "System reliability estimation and sensitivity analysis for multi-state manufacturing network with joint buffers––A simulation approach," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 103-109.
    4. Chame, Anna & Tsallis, Constantino, 1990. "Criticality of the discrete N-vector ferromagnet in a cubic lattice with a free surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(1), pages 41-63.
    5. Hatice Ucar Guner & Alper Murat & Ratna Babu Chinnam, 2024. "Performance analysis of a production system with two deteriorating machines and a finite buffer," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 621-651, September.
    6. Suliman, S. M. A., 2000. "A mathematical model for a buffered two-stage manufacturing cell with an unreliable transfer device," International Journal of Production Economics, Elsevier, vol. 63(1), pages 69-81, January.
    7. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Other publications TiSEM 015cb8ee-38d7-41b1-b9fc-7, Tilburg University, School of Economics and Management.
    8. Widom, B. & Clarke, A.S., 1990. "Line tension at the wetting transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 168(1), pages 149-159.
    9. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Discussion Paper 1997-97, Tilburg University, Center for Economic Research.
    10. Marcello Colledani & Tullio Tolio, 2011. "Performance evaluation of transfer lines with general repair times and multiple failure modes," Annals of Operations Research, Springer, vol. 182(1), pages 31-65, January.
    11. Zhang, Yongjin & Zhao, Ming & Zhang, Yanjun & Pan, Ruilin & Cai, Jing, 2020. "Dynamic and steady-state performance analysis for multi-state repairable reconfigurable manufacturing systems with buffers," European Journal of Operational Research, Elsevier, vol. 283(2), pages 491-510.
    12. Hołyst, R. & Poniewierski, A., 1988. "Quasi-wetting on a sphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 149(3), pages 622-630.
    13. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Discussion Paper 1996-98, Tilburg University, Center for Economic Research.
    14. Upset Robert & P.Van Til Robert & Sengupta Sankar, 1998. "Development of a model for a two-station serial transfer line subject to machine and buffer failure," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 4(3), pages 231-246, January.
    15. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    16. Blöte, H.W.J. & Nightingale, M.P., 1984. "The temperature exponent of the n-component cubic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 129(1), pages 1-16.
    17. Helber, Stefan, 1998. "Decomposition of unreliable assembly/disassembly networks with limited buffer capacity and random processing times," European Journal of Operational Research, Elsevier, vol. 109(1), pages 24-42, August.
    18. S. Göttlich & S. Kühn & J. A. Schwarz & R. Stolletz, 2016. "Approximations of time-dependent unreliable flow lines with finite buffers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 295-323, June.
    19. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Other publications TiSEM 77da022b-635b-46fd-bf4a-f, Tilburg University, School of Economics and Management.
    20. Elisa Gebennini & Andrea Grassi & Cesare Fantuzzi & Stanley Gershwin & Irvin Schick, 2013. "Discrete time model for two-machine one-buffer transfer lines with restart policy," Annals of Operations Research, Springer, vol. 209(1), pages 41-65, October.
    21. 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.
    22. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.
    23. Stoebe, T. & Jiang, I.M. & Huang, S.N. & Jin, A.J. & Huang, C.C., 1994. "Novel results of extremely thin substrate-free liquid-crystal films obtained from calorimetric and computer simulation studies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 205(1), pages 108-121.

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