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Basic Structure

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Sequencing Theory

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 69))

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Abstract

Different scheduling problems naturally lead to different models. In this chapter we shall discuss several classes of these models. In order to provide an insight into the structure of the problem, we shall introduce an explicit mathematical formulation which can be represented by Gantt chart, and a linear graph. Finally, several assumptions restricting the analytical models, which have been developed to date, will be discussed.

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References

  1. Ashour, S. and R. G. Parker, “A Precedence Graph Algorithm for the Shop Scheduling Problem” Operational Research Quarterly, Vol. 22, No. 2, 1971, pp. 165–175.

    Article  Google Scholar 

  2. Conway, R. W. and W. L. Maxwell, “Network Dispatching by the Shortest Operation Discipline” Operations Research, Vol. 10, No. 1, 1962, pp. 51–73.

    Article  Google Scholar 

  3. Cunningham-Green, R. A., “Describing Industrial Processes with Interference and Approximating their Steady-State Behaviour” Operational Research Quarterly, Vol. 13, No. 1, 1962, pp. 95–100.

    Article  Google Scholar 

  4. Elmaghraby, S. E., “The Machine Sequencing Problem - Review and Extensions” Naval Research Logistics Quarterly, Vol. 15, No. 2, 1968, pp. 205–232.

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  5. Giffler, B., “Schedule Algebra: A Progress Report” Naval Research Logistic Quarterly, Vol. 15, No. 2, 1968, pp. 255–280.

    Google Scholar 

  6. Heller, J., “Combinatorial Properties of Machine Shop Scheduling” Report NYO-2879, AEC Computed and Applied Mathematics Center, Institute of Mathematical Science, New York University, New York, N.Y., July 1959.

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  7. Heller, J. and G. Logemann, “An Algorithm for the Construction and Evaluation of Feasible Schedules” Management Science, Vol. 8, No. 2, 1962, pp. 168–183.

    Article  Google Scholar 

  8. Johnson, S. M., “Discussion” Sequencing n Jobs on 2 Machines with Arbitrary Time Lags Management Science, Vol. 5, No. 3, 1959, pp. 299–303.

    Article  Google Scholar 

  9. Mitten, L. G., “Sequencing n Jobs on Two Machines with Arbitrary Time Lags” Management Science, Vol. 5, No. 3, 1959, pp. 292–298.

    Article  Google Scholar 

  10. Muth, J. F., “The Effect of Uncertainty in Job Times on Optimal Schedules” Chapter 18 in Industrial Scheduling, (eds. J. F. Muth and G. L. Thompson), Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1963.

    Google Scholar 

  11. Nabeshima, I., “Sequencing of Two Machines with Start Lag and Stop Lag” Journal of Operations Research Society of Japan, Vol. 5, No. 3, 1963, pp. 97–101.

    Google Scholar 

  12. Nugent, C. E., “On Sampling Approaches to the Solution of the n-by-m Static Sequencing Problem” Ph.D. Thesis, Cornell University, Ithaca, N.Y., 1964.

    Google Scholar 

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© 1972 Springer-Verlag Berlin • Heidelberg

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Ashour, S. (1972). Basic Structure. In: Sequencing Theory. Lecture Notes in Economics and Mathematical Systems, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80693-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-80693-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05877-9

  • Online ISBN: 978-3-642-80693-3

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