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.
ASJC Scopus subject areas
- Strategy and Management
- Management Science and Operations Research