Job scheduling to minimize expected weighted flowtime on uniform processors
Systems & Control Letters
Approximation results in parallel machines stochastic scheduling
Annals of Operations Research
Introduction to Stochastic Dynamic Programming: Probability and Mathematical
Introduction to Stochastic Dynamic Programming: Probability and Mathematical
The Dependence of Optimal Returns from Multi-class Queueing Systems on Their Customer Base
Queueing Systems: Theory and Applications
Discounted Multiarmed Bandit Problems on a Collection of Machines with Varying Speeds
Mathematics of Operations Research
Single-Machine Scheduling with Exponential Processing Times and General Stochastic Cost Functions
Journal of Global Optimization
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Computers and Operations Research
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We study stochastic scheduling on m parallel identical machines with random processing times. The cost involved in the problem is discounted to the present value and the objective is to minimize the expected discounted holding cost, which covers in a unified framework many performance measures discussed in the literature as special cases, including discounted rewards, flowtime, and makespan. We prove that the SEPT rule is optimal, on a fairly general ground, in the class of preemptive dynamic policies, the class of nonpreemptive dynamic policies, and the class of nonpreemptive static list policies. The LEPT rule, on the other hand, is optimal to minimize the expected discounted makespan only under certain restrictive conditions. Without such conditions, the LEPT rule is found no longer optimal for discounted makespan by a counterexample, in contrast to the case without discounting.