Scheduling Jobs with Exponentially Distributed Processing Times on Two Machines with Resource Constraints
Management Science · 1984 · Volume 30 · Issue 7
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/μ 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/μ 1 < ⋯ < 1/μ n and r 1 < ⋯ < r 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 < r , and start processing jobs k − 1, k . Thereafter, at any job completion, start processing on the machine that is freed, the longest job compatible with the job running on the other machine.
Keywords
production/scheduling: job shop, stochastic
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