Robust preemptive scheduling on unrelated parallel machines under uncertain processing times

2017 ◽  
Author(s):  
Widad Naji ◽  
Van-Dat Cung ◽  
Marie-Laure Espinouse
Keyword(s):  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Unrelated Parallel Machines ◽  
Processing Times

scholarly journals Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

1986 ◽  
Vol 23 (03) ◽  
pp. 841-847 ◽  
Author(s):  
R. R. Weber ◽  
P. Varaiya ◽  
J. Walrand
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Total Reward ◽  
Processing Times ◽  
Identical Machines ◽  
Scheduling Strategies

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines

2018 ◽  
Vol 78 (4) ◽  
pp. 693-715 ◽  
Author(s):  
Min Kong ◽  
Xinbao Liu ◽  
Jun Pei ◽  
Panos M. Pardalos ◽  
Nenad Mladenovic
Keyword(s):  
Parallel Machines ◽  
Unrelated Parallel Machines ◽  
Parallel Batching ◽  
Processing Times ◽  
Nonlinear Processing

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

1995 ◽  
Vol 27 (03) ◽  
pp. 821-839 ◽  
Author(s):  
Gideon Weiss
Keyword(s):  
Single Machine ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Priority Rule ◽  
Priority Rules ◽  
Holding Costs ◽  
Processing Times ◽  
Stochastic Processing ◽  
Stochastic Processing Times

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

1995 ◽  
Vol 27 (3) ◽  
pp. 821-839 ◽  
Author(s):  
Gideon Weiss
Keyword(s):  
Single Machine ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Priority Rule ◽  
Priority Rules ◽  
Holding Costs ◽  
Processing Times ◽  
Stochastic Processing ◽  
Stochastic Processing Times

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

The optimality of LEPT in parallel machine scheduling

1994 ◽  
Vol 31 (03) ◽  
pp. 788-796 ◽  
Author(s):  
Cheng-Shang Chang ◽  
Rhonda Righter
Keyword(s):  
Cost Function ◽  
Likelihood Ratio ◽  
Random Function ◽  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Preemptive Scheduling ◽  
Time Processing ◽  
Processing Times ◽  
The Cost

We consider preemptive scheduling on parallel machines where the number of available machines may be an arbitrary, possibly random, function of time. Processing times of jobs are from a family of DLR (decreasing likelihood ratio) distributions, and jobs may arrive at random agreeable times. We give a constructive coupling proof to show that LEPT stochastically minimizes the makespan, and that it minimizes the expected cost when the cost function satisfies certain agreeability conditions.

scholarly journals Preemptive Scheduling on Uniform Parallel Machines with Controllable Job Processing Times

Algorithmica ◽  
2007 ◽  
Vol 51 (4) ◽  
pp. 451-473 ◽  
Author(s):  
Natalia V. Shakhlevich ◽  
Vitaly A. Strusevich
Keyword(s):  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Processing Times
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