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The stochastic U‐line balancing problem

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  • Franco Guerriero
  • John Miltenburg

Abstract

A U‐line arranges tasks around a U‐shaped production line and organizes them into stations that can cross from one side of the line to the other. In addition to improving visibility and communication between operators on the line, which facilitates problem‐solving and quality improvement, U‐lines can reduce the total number of operators required on the line and make rebalancing the line easier compared to the traditional, straight production line. This paper studies the (type 1) U‐line balancing problem when task completion times are stochastic. Stochastic completion times occur when differences between operators cause completion times to vary somewhat and when machine processing times vary. A recursive algorithm is presented for finding the optimal solution when completion times have any distribution function. An equivalent shortest path network is also presented. An improvement for the special case of normally distributed task completion times is given. A computational study to determine the characteristics of instances that can be solved by the algorithms shows that they are able to solve instances of practical size (like the 114 Japanese and U.S. U‐lines studied in a literature review paper). © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003

Suggested Citation

  • Franco Guerriero & John Miltenburg, 2003. "The stochastic U‐line balancing problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(1), pages 31-57, February.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:1:p:31-57
    DOI: 10.1002/nav.10043
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    1. Allan L. Gutjahr & George L. Nemhauser, 1964. "An Algorithm for the Line Balancing Problem," Management Science, INFORMS, vol. 11(2), pages 308-315, November.
    2. Nakade, Koichi & Ohno, Katsuhisa, 1999. "An optimal worker allocation problem for a U-shaped production line," International Journal of Production Economics, Elsevier, vol. 60(1), pages 353-358, April.
    3. Edward P. C. Kao, 1976. "A Preference Order Dynamic Program for Stochastic Assembly Line Balancing," Management Science, INFORMS, vol. 22(10), pages 1097-1104, June.
    4. Edward P. C. Kao & Maurice Queyranne, 1982. "On Dynamic Programming Methods for Assembly Line Balancing," Operations Research, INFORMS, vol. 30(2), pages 375-390, April.
    5. Robert L. Carraway, 1989. "A Dynamic Programming Approach to Stochastic Assembly Line Balancing," Management Science, INFORMS, vol. 35(4), pages 459-471, April.
    6. Moshe Sniedovich, 1981. "Analysis of a Preference Order Assembly Line Problem," Management Science, INFORMS, vol. 27(9), pages 1067-1080, September.
    7. Michael Held & Richard M. Karp & Richard Shareshian, 1963. "Assembly-Line Balancing---Dynamic Programming with Precedence Constraints," Operations Research, INFORMS, vol. 11(3), pages 442-459, June.
    8. Roger V. Johnson, 1988. "Optimally Balancing Large Assembly Lines with "Fable"," Management Science, INFORMS, vol. 34(2), pages 240-253, February.
    9. Steven T. Hackman & Michael J. Magazine & T. S. Wee, 1989. "Fast, Effective Algorithms for Simple Assembly Line Balancing Problems," Operations Research, INFORMS, vol. 37(6), pages 916-924, December.
    10. F. Brian Talbot & James H. Patterson & William V. Gehrlein, 1986. "A Comparative Evaluation of Heuristic Line Balancing Techniques," Management Science, INFORMS, vol. 32(4), pages 430-454, April.
    11. Linus Schrage & Kenneth R. Baker, 1978. "Dynamic Programming Solution of Sequencing Problems with Precedence Constraints," Operations Research, INFORMS, vol. 26(3), pages 444-449, June.
    12. Thomas R. Hoffmann, 1992. "Eureka: A Hybrid System for Assembly Line Balancing," Management Science, INFORMS, vol. 38(1), pages 39-47, January.
    13. .Ilker Baybars, 1986. "A Survey of Exact Algorithms for the Simple Assembly Line Balancing Problem," Management Science, INFORMS, vol. 32(8), pages 909-932, August.
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    2. Emel Kızılkaya Aydoğan & Yılmaz Delice & Uğur Özcan & Cevriye Gencer & Özkan Bali, 2019. "Balancing stochastic U-lines using particle swarm optimization," Journal of Intelligent Manufacturing, Springer, vol. 30(1), pages 97-111, January.
    3. Pirogov, Aleksandr & Gurevsky, Evgeny & Rossi, André & Dolgui, Alexandre, 2021. "Robust balancing of transfer lines with blocks of uncertain parallel tasks under fixed cycle time and space restrictions," European Journal of Operational Research, Elsevier, vol. 290(3), pages 946-955.
    4. Daniel Leitold & Agnes Vathy-Fogarassy & Janos Abonyi, 2019. "Empirical working time distribution-based line balancing with integrated simulated annealing and dynamic programming," 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. 27(2), pages 455-473, June.

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