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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
Conway, R. W. and W. L. Maxwell, “Network Dispatching by the Shortest Operation Discipline” Operations Research, Vol. 10, No. 1, 1962, pp. 51–73.
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.
Elmaghraby, S. E., “The Machine Sequencing Problem - Review and Extensions” Naval Research Logistics Quarterly, Vol. 15, No. 2, 1968, pp. 205–232.
Giffler, B., “Schedule Algebra: A Progress Report” Naval Research Logistic Quarterly, Vol. 15, No. 2, 1968, pp. 255–280.
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.
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.
Johnson, S. M., “Discussion” Sequencing n Jobs on 2 Machines with Arbitrary Time Lags Management Science, Vol. 5, No. 3, 1959, pp. 299–303.
Mitten, L. G., “Sequencing n Jobs on Two Machines with Arbitrary Time Lags” Management Science, Vol. 5, No. 3, 1959, pp. 292–298.
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.
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.
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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1972 Springer-Verlag Berlin • Heidelberg
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive