SCHEDULING JOBS WITH EXPONENTIALLY DISTRIBUTED PROCESSING TIMES ON TWO MACHINES WITH RESOURCE CONSTRAINTS.

Consideration is given to 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 less than . . . less than 1/ mu //n and r//1 less than . . . less than r//n, authors 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 plus r//k// minus //1 less than r, and start processing jobs k minus 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.