an:06579224
Zbl 1335.90032
Bruno, John; Coffman, Edward G. jun.; Downey, Peter
Scheduling independent tasks to minimize the makespan on identical machines
EN
Probab. Eng. Inf. Sci. 9, No. 3, 447-456 (1995).
00185716
1995
j
90B35
Summary: In this paper we consider scheduling \(n\) tasks on \(m\) parallel machines where the task processing times are i.i.d. random variables with a common distribution function \(F\). Scheduling is done by an a priori assignment of tasks to machines. We show that if the distribution function \(F\) is a P??lya frequency function of order 2 (decreasing reverse hazard rate) then the assignment that attempts to place an equal number of tasks on each machine achieves the stochastically smallest makespan among all assignments. The condition embraces many important distributions, such as the gamma and truncated normal distributions. Assuming that the task processing times have a common density that is a P??lya frequency function of order 2 (increasing likelihood ratio), then we find that flatter schedules have stochastically smaller makespans in the sense of the ``joint'' likelihood ratio.