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Scheduling Jobs with Exponentially Distributed Processing Times on Two Machines with Resource Constraints

Author

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  • Michael Pinedo

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Gideon Weiss

    (Department of Statistics, Tel Aviv University, Tel Aviv, Israel)

Abstract

We consider the problem of minimizing the expected makespan of n jobs with independent exponentially distributed processing times on two parallel machines, under resource constraints. Job j has expected processing time 1/\mu j and requires throughout its processing an amount r j of a resource; the total amount of resource available is r. In the case where 1/\mu 1 n and r 1 n , we characterize all the optimal policies in the class of preemptive schedules, and show that the following nonpreemptive policy is optimal: Find the largest k for which r k + r k-1

Suggested Citation

  • Michael Pinedo & Gideon Weiss, 1984. "Scheduling Jobs with Exponentially Distributed Processing Times on Two Machines with Resource Constraints," Management Science, INFORMS, vol. 30(7), pages 883-899, July.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:7:p:883-899
    DOI: 10.1287/mnsc.30.7.883
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