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On a job resequencing issue in parallel processor stochastic scheduling

Published online by Cambridge University Press:  01 July 2016

Susan H. Xu*
Affiliation:
Pennsylvania State University
*
Postal address: Department of Management Science, College of Business Administration, The Pennsylvania State University, University Park, PA 16802, USA.

Abstract

In flexible assembly systems, it is often necessary to coordinate jobs and materials so that specific jobs are matched with specific materials. This requires that jobs depart from upstream parallel workstations in some predetermined order. One way to satisfy this requirement is to temporarily hold the serviced jobs getting out of order at a resequencing buffer and to release them to downstream workstations as soon as all their predecessors are serviced. In this paper we consider the problem of scheduling a fixed number of non-preemptive jobs on two IHR non-identical processors with the resequencing requirement. We prove that the individually optimal policy, in which each job minimizes its own expected departure time subject to the constraint that available processors are offered to jobs in their departure order, is of a threshold type. The policy is independent of job weights and the jobs residing at the resequencing buffer and possesses the monotonicity property which states that a job will never utilize a processor in the future once it has declined the processor. Most importantly, we prove that the individually optimal policy has the stability property; namely: if at any time a job deviated from the individually optimal policy, then the departure time of every job, including its own, would be prolonged. As a direct consequence of this property, the individually optimal policy is socially optimal in the sense that it minimizes the expected total weighted departure time of the system as a whole. We identify situations under which the individually optimal policy also minimizes the expected makespan of the system.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1992 

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References

Agrawala, A. K., Coffman, E. G. Jr., Garey, M. R. and Tripathi, S. K. (1984) A stochastic optimization algorithm minimizing expected flowtime on uniform processors. IEEE Trans. Comput. 33, 351357.CrossRefGoogle Scholar
Buzacott, J. A. (1988) Abandoning the moving assembly line: models of human operator and job sequencing. WATMIMS Research Group Working Paper #88–02. Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L3GL.Google Scholar
Buzacott, J. A. and Shanthikumar, J. G. (1991) Stochastic Models of Manufacturing Systems . Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Coffman, E. G., Flatto, L., Garey, M. R. and Weber, R. R. (1987) Minimizing expected makespan on uniform processor systems. Adv. Appl. Prob. 19, 177201.CrossRefGoogle Scholar
Harrus, G. and Plateau, B. (1982) Queueing analysis of a reordering issue. IEEE Trans. Software Eng. 8, 113123.CrossRefGoogle Scholar
Iliadis, I. and Lien, Y. C. (1987) Resequencing delay analysis for a queueing system with two heterogeneous servers under a threshold type scheduling. IEEE Infocom , 643651.Google Scholar
Kamoun, F., Kleinrock, L. and Muntz, R. (1981) Queueing analysis of the ordering issue in a distributed database concurrency control mechanism. In IEEE 2nd Internat. Conf. on Distributed Computing Systems , pp. 1323.Google Scholar
Kumar, P. R. and Walrand, J. (1985) Individual routing in parallel systems. J. Appl. Prob. 22, 989995.CrossRefGoogle Scholar
Larson, R. C. (1987) Social justice and other attributes of queueing. Working Paper, MIT, Cambridge, MA.Google Scholar
Lin, W. and Kumar, P. R. (1984) Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Autom. Control 29, 211216.Google Scholar
Righter, R. (1988) Job scheduling to minimize expected weighted flowtime on uniform processors. Syst. Control Lett. 10, 211216.CrossRefGoogle Scholar
Righter, R. and Xu, S. H. (1991), Scheduling jobs on nonidentical IFR processors to minimize general cost functions. Adv. Appl. Prob. 23, 909924.Google Scholar
Ross, S. (1982) Introduction to Stochastic Dynamic Programming. Academic Press, New York.Google Scholar
Udomkesmalee, N. and Daganzo, C. F. (1989) Impact of parallel processing on job sequences in flexible assembly systems. Int. J. Prod. Res. 27, 7389.CrossRefGoogle Scholar
Varma, S. (1988) Optimal allocation of customers in a two server queue with resequencing. ORSA/TIMS Joint National Meeting, Washington, DC.Google Scholar
Walrand, J. (1984) A note on optimal control of a queueing system with two heterogeneous servers. Syst. Control Lett. 4, 131134.CrossRefGoogle Scholar
White, W. (1984) The amount of overtaking in a network of queues. Network 14, 411426.CrossRefGoogle Scholar
Xu, S. H. (1991) Socially and individually optimal routing of stochastic jobs on parallel processors systems. Operat. Res. 38, 367375.Google Scholar
Xu, S. H. (1991) Minimizing expected makespans of multi-priority classes of jobs on uniform processors. Operat. Res. Lett. 10, 273280.CrossRefGoogle Scholar