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On the Optimality of Static Priority Policies in Stochastic Scheduling on Parallel Machines
Journal of Applied Probability
Vol. 24, No. 2 (Jun., 1987), pp. 430-448
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3214267
Page Count: 19
You can always find the topics here!Topics: Scheduling, Cost functions, Optimal policy, Numberings, Statics, Mathematical independent variables, Cost efficiency, Carrying costs, Operations research, Necessary conditions for optimality
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n jobs are to be preemptively scheduled for processing on n machines. The machines may have differing speeds and the jobs have processing requirements which are distributed as independent exponential random variables with different means. Holding cost g(U) is incurred per unit time that the set of uncompleted jobs is U and it is desired to minimize the total expected holding cost which is incurred until all jobs are complete. We show that if g satisfies certain simple conditions then the optimal policy is one which takes the jobs in the order 1,2⋯,n and assigns each uncompleted job in turn to the fastest available machine. In the special case in which the objective is to minimize the expected weighted flowtime, where there is a holding cost of wi while job i is incomplete, the sufficient condition is simply w1 ≥ ⋯ ≥ wn and λ1 w1 ≥ ⋯ ≥ λnwn.
Journal of Applied Probability © 1987 Applied Probability Trust