scholarly journals A bicriterion approach to preemptive scheduling of parallel machines with controllable job processing times

1995 ◽  
Vol 63 (3) ◽  
pp. 237-256 ◽  
Author(s):  
Eugeniusz Nowicki ◽  
Stanisław Zdrzałka
Keyword(s):  
Parallel Machines ◽  
Preemptive Scheduling ◽  
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.

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

The Stochastic Optimality of SEPT in Parallel Machine Scheduling

1994 ◽  
Vol 8 (2) ◽  
pp. 179-188 ◽  
Author(s):  
Cheng-Shang Chang ◽  
Arie Hordijk ◽  
Rhonda Righter ◽  
Gideon Weiss
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Concave Function ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Preemptive Scheduling ◽  
Processing Times ◽  
Schur Concave ◽  
Completion Times ◽  
Stochastic Optimality

We consider preemptive scheduling on parallel machines where processing times of jobs are i.i.d. but jobs may already have received distinct amounts of service. We show that when processing times are increasing in likelihood ratio, SEPT (shortest expected [remaining] processing time first) stochastically minimizes any increasing and Schur-concave function of the job completion times. The same result holds when processing times are exponential with possibly different means.

The optimality of LEPT in parallel machine scheduling

1994 ◽  
Vol 31 (3) ◽  
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 Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

1986 ◽  
Vol 23 (3) ◽  
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.

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