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

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-1production/scheduling: job shop, stochastic