Abstract
The primary objective of this paper is to develop an out-of-kilter algorithm to deal with the machine sequencing problem in which both job precedence and machine non-interference constraints are involved. This approach is inspired by the graph theoretical representation of the problem. In addition to the out-of-kilter concept, the algorithm employs a waiting feature and pertinent criteria for the selection of resolutions. The basic concepts of the approach are presented and the entire algorithm is then summarized and condensed to five basic steps. A sample problem is presented and manually solved to illustrate the technique to job-shop problems. Computational experiences as well as comparative evaluations of other existing techniques are included. Finally, a diagnostic view of the scheduling problem is reported with reference to specific characteristics which comprise a major share of the difficulty surrounding the problem.
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References
Ashour, S. and M. N. Quarishi, “Investigation of Various Bounding Procedures for Production Scheduling Problems,” Int. Jnl. Prod. Research, Vol. 7 (1969), pp. 249–252.
Ashour, S., “A Branch-and-Bound Algorithm for Flow-shop Scheduling Problems,” AIIE Transactions, Vol. 2 (1970), pp. 172–176.
Ashour, S., “An Experimental Investigation and Comparative Evaluation of Flow-Shop Scheduling Techniques,” Operations Research, Vol. 18 (1970), pp. 541–549.
Ashour, S. and R. G. Parker, “A Precedence Graph Algorithm for the Shop Scheduling Problem,” Operations Research Quarterly, Vol. 22 (1971), pp. 165–175.
Ashour, S. and S. R. Hiremath, “A Branch-and-Bound Approach to the Job-Shop Scheduling Problem,” Int. Jnl. Prod. Research, Vol. 9 (1972).
Ashour, S., K. Y. Chiu, and T. E. Moore, “An Optimal Schedule Time of a Job Shop-Like Disjunctive Graph,” submitted to Networks, January (1972).
Balas, E., “Discrete Programming by the Filter Method,” Operations Research, Vol. 15 (1967), p. 915.
Balas, E., “Machine Sequencing via Disjunctive Graphs: An Implicit Enumeration Algorithm,” Operations Research, Vol. 17 (1969), pp. 941–957.
Brooks, G. H. and C. White, “An Algorithm for Finding Optimal or Near Optimal Solutions to the Production Scheduling Problem,” Jnl. Ind. Engg., Vol. 16 (1965), pp. 34–40.
Charlton, J. M. and C. C. Death, “A Generalized Machine-scheduling Algorithm,” Operations Research Quarterly, Vol. 21 (1970), pp. 127–134.
Charlton, J. M. and C. C. Death, “A Method of Solving for General Machiner Scheduling Problems,” Operations Research, Vol. 18 (1970), pp. 689–707.
Fisher, H. and G. L. Thompson, “Probabilistic Learning Combinations of Local Job-shop Scheduling Rules,” Chapter 15 in Industrial Scheduling, Prentice-Hall Inc., Englewood Cliffs, N. J. (1963).
Florian, N., P. Frepant, and G. Mcmahon, “An Implicit Enumeration Algorithm for the Machine Sequencing Problem,” Management Science, Vol. 17 (1971), pp. B-782 — B-792.
Greenberg, H., “Solution of the General Scheduling Problem,” Operations Research, Vol. 16 (1968), p. 353.
Heller, J., “Some Numerical Experiments for an MXJ Flow-Shop and its Decision-Theoretical Aspects,” Operations Research, Vol. 8 (1960), pp. 178–184.
Moore, T. E., K. Y. Chiu, and S. Ashour, “An Implicit Enumeration Algorithm for the Non-Preemptive Shop Scheduling Problem,” submitted to Operational Research Quarterly, February (1972).
Schrage, L., “Solving Resource-constrained Network Problems by Implicit Enumeration-Nonpreemptive Case,” Operations Research, Vol. 18 (1970), pp. 263–278.
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Ashour, S., Parker, R.G. (1973). An Out-of-Kilter Approach for Machine Sequencing Problems. In: Elmaghraby, S.E. (eds) Symposium on the Theory of Scheduling and Its Applications. Lecture Notes in Economics and Mathematical Systems, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80784-8_15
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DOI: https://doi.org/10.1007/978-3-642-80784-8_15
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