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Some Numerical Experiments for an M × J Flow Shop and its Decision-Theoretical Aspects

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  • J. Heller

    (AEC Computing and Applied Mathematics Center, New York University, New York, New York)

Abstract

Numerical experiments for M × J deterministic flow shops performed on an IBM 704 digital computer lead to the conclusion that the schedule times are approximately normally distributed for large numbers of jobs. The meaning of this result in the decision-theoretical problem of sampling for a minimum is discussed. Examples of these results for 10 × 100 and 10 × 20 schedules are given.

Suggested Citation

  • J. Heller, 1960. "Some Numerical Experiments for an M × J Flow Shop and its Decision-Theoretical Aspects," Operations Research, INFORMS, vol. 8(2), pages 178-184, April.
    • Handle: RePEc:inm:oropre:v:8:y:1960:i:2:p:178-184
    DOI: 10.1287/opre.8.2.178
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    Cited by:

    1. Donald Davendra & Ivan Zelinka & Magdalena Bialic-Davendra & Roman Senkerik & Roman Jasek, 2012. "Clustered enhanced differential evolution for the blocking flow shop scheduling problem," 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. 20(4), pages 679-717, December.
    2. Mohamed Abdel-Basset & Reda Mohamed & Mohamed Abouhawwash & Ripon K. Chakrabortty & Michael J. Ryan, 2021. "A Simple and Effective Approach for Tackling the Permutation Flow Shop Scheduling Problem," Mathematics, MDPI, vol. 9(3), pages 1-23, January.
    3. Christoph Schuster, 2006. "No-wait Job Shop Scheduling: Tabu Search and Complexity of Subproblems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 473-491, July.
    4. Agarwal, Anurag & Colak, Selcuk & Eryarsoy, Enes, 2006. "Improvement heuristic for the flow-shop scheduling problem: An adaptive-learning approach," European Journal of Operational Research, Elsevier, vol. 169(3), pages 801-815, March.
    5. A.J. Scott, 1969. "Combinatorial Programming and the Planning of Urban and Regional Systems," Environment and Planning A, , vol. 1(2), pages 125-142, December.
    6. S.S. Panwalkar & Christos Koulamas, 2015. "Scheduling research and the first decade of NRLQ: A historical perspective," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(4), pages 335-344, June.
    7. Jianhui Mou & Xinyu Li & Liang Gao & Wenchao Yi, 2018. "An effective L-MONG algorithm for solving multi-objective flow-shop inverse scheduling problems," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 789-807, April.
    8. Vallada, Eva & Ruiz, Rubén & Framinan, Jose M., 2015. "New hard benchmark for flowshop scheduling problems minimising makespan," European Journal of Operational Research, Elsevier, vol. 240(3), pages 666-677.
    9. Ansis Ozolins, 2019. "Improved bounded dynamic programming algorithm for solving the blocking flow shop problem," 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(1), pages 15-38, March.
    10. Fernandez-Viagas, Victor & Ruiz, Rubén & Framinan, Jose M., 2017. "A new vision of approximate methods for the permutation flowshop to minimise makespan: State-of-the-art and computational evaluation," European Journal of Operational Research, Elsevier, vol. 257(3), pages 707-721.
    11. Moritz, Ruby L.V. & Reich, Enrico & Schwarz, Maik & Bernt, Matthias & Middendorf, Martin, 2015. "Refined ranking relations for selection of solutions in multi objective metaheuristics," European Journal of Operational Research, Elsevier, vol. 243(2), pages 454-464.

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