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

Michael Pinedo and Gideon Weiss
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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

Management Science, 1984, vol. 30, issue 7, 883-899

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

Keywords: production/scheduling: job shop; stochastic (search for similar items in EconPapers)
Date: 1984
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