Stochastic scheduling for a two-machine open shop

1997 ◽  
Vol 34 (03) ◽  
pp. 733-744
Author(s):  
Rhonda Righter
Keyword(s):  
Processing Time ◽  
Stochastic Scheduling ◽  
Open Shop ◽  
Preemptive Scheduling ◽  
Processing Times ◽  
Dependent Rate ◽  
One Machine

We study the problem of preemptive scheduling of jobs in a two-machine open shop. Jobs require processing on both machines, but the order does not matter. We define the D-LERPT (double longest expected remaining processing time) policy as the policy that first processes jobs that have not yet been processed by either machine (double jobs), in decreasing order of expected remaining processing times, and then processes jobs that require processing on only one machine in any order. We show that D-LERPT stochastically minimizes the makespan when preemption is not permitted and jobs (but not machines) are stochastically identical, and that D-LERPT minimizes the makespan in the increasing convex sense when preemption is permitted and the machines are stochastically identical and processing times are exponential or geometric with a job dependent rate.

Stochastic scheduling for a two-machine open shop

1997 ◽  
Vol 34 (3) ◽  
pp. 733-744
Author(s):  
Rhonda Righter
Keyword(s):  
Processing Time ◽  
Stochastic Scheduling ◽  
Open Shop ◽  
Preemptive Scheduling ◽  
Processing Times ◽  
Dependent Rate ◽  
One Machine

We study the problem of preemptive scheduling of jobs in a two-machine open shop. Jobs require processing on both machines, but the order does not matter. We define the D-LERPT (double longest expected remaining processing time) policy as the policy that first processes jobs that have not yet been processed by either machine (double jobs), in decreasing order of expected remaining processing times, and then processes jobs that require processing on only one machine in any order. We show that D-LERPT stochastically minimizes the makespan when preemption is not permitted and jobs (but not machines) are stochastically identical, and that D-LERPT minimizes the makespan in the increasing convex sense when preemption is permitted and the machines are stochastically identical and processing times are exponential or geometric with a job dependent rate.

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.

Stochastic dispatching of multi-priority jobs to heterogeneous processors

1990 ◽  
Vol 27 (4) ◽  
pp. 852-861 ◽  
Author(s):  
Susan H. Xu ◽  
Pitu B. Mirchandani ◽  
Srikanta P. R. Kumar ◽  
Richard R. Weber
Keyword(s):  
Processing Time ◽  
The Other ◽  
Preemptive Scheduling ◽  
Threshold Values ◽  
Heterogeneous Processors ◽  
Priority Class ◽  
Scheduling Strategy ◽  
Processing Times ◽  
The Social ◽  
The Individual

A number of multi-priority jobs are to be processed on two heterogeneous processors. Of the jobs waiting in the buffer, jobs with the highest priority have the first option of being dispatched for processing when a processor becomes available. On each processor, the processing times of the jobs within each priority class are stochastic, but have known distributions with decreasing mean residual (remaining) processing times. Processors are heterogeneous in the sense that, for each priority class, one has a lesser average processing time than the other. It is shown that the non-preemptive scheduling strategy for each priority class to minimize its expected flowtime is of threshold type. For each class, the threshold values, which specify when the slower processor is utilized, may be readily computed. It is also shown that the social and the individual optimality coincide.

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.

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.

Stochastic dispatching of multi-priority jobs to heterogeneous processors

1990 ◽  
Vol 27 (04) ◽  
pp. 852-861 ◽  
Author(s):  
Susan H. Xu ◽  
Pitu B. Mirchandani ◽  
Srikanta P. R. Kumar ◽  
Richard R. Weber
Keyword(s):  
Processing Time ◽  
The Other ◽  
Preemptive Scheduling ◽  
Threshold Values ◽  
Heterogeneous Processors ◽  
Priority Class ◽  
Scheduling Strategy ◽  
Processing Times ◽  
The Social ◽  
The Individual

A number of multi-priority jobs are to be processed on two heterogeneous processors. Of the jobs waiting in the buffer, jobs with the highest priority have the first option of being dispatched for processing when a processor becomes available. On each processor, the processing times of the jobs within each priority class are stochastic, but have known distributions with decreasing mean residual (remaining) processing times. Processors are heterogeneous in the sense that, for each priority class, one has a lesser average processing time than the other. It is shown that the non-preemptive scheduling strategy for each priority class to minimize its expected flowtime is of threshold type. For each class, the threshold values, which specify when the slower processor is utilized, may be readily computed. It is also shown that the social and the individual optimality coincide.

A Note on Stochastic Scheduling on a Single Machine Subject to Breakdown–The Preemptive Repeat Model

1991 ◽  
Vol 5 (3) ◽  
pp. 349-354 ◽  
Author(s):  
Esther Frostig
Keyword(s):  
Single Machine ◽  
Random Variables ◽  
Stochastic Scheduling ◽  
Independent Random Variables ◽  
Processing Times ◽  
Optimal Policies ◽  
Number Of Late Jobs ◽  
One Machine ◽  
Late Jobs ◽  
Weighted Flowtime

This paper considers scheduling n jobs on one machine to minimize the expected weighted flowtime and the number of late jobs. The processing times of the jobs are independent random variables. The machine is subject to failure and repair where the uptimes are exponentially distributed. We find the optimal policies for the preemptive repeat model.

A new tool for rapid development of electron microscopy negatives and micrographs: Initial impressions of the MOHR/PRO-8 processor

1992 ◽  
Vol 50 (2) ◽  
pp. 972-973
Author(s):  
James C. Long
Keyword(s):  
Electron Microscopy ◽  
Processing Time ◽  
Rapid Development ◽  
Processing Times ◽  
Initial Impressions ◽  
Transport Method

Over the years, many techniques and products have been developed to reduce the amount of time spent in a darkroom processing electron microscopy negatives and micrographs. One of the latest tools, effective in this effort, is the Mohr/Pro-8 film and rc paper processor.At the time of writing, a unit has been recently installed in the photographic facilities of the Electron Microscopy Center at Texas A&M University. It is being evaluated for use with TEM sheet film, SEM sheet film, 35mm roll film (B&W), and rc paper.Originally designed for use in the phototypesetting industry, this processor has only recently been introduced to the field of electron microscopy.The unit is a tabletop model, approximately 1.5 × 1.5 × 2.0 ft, and uses a roller transport method of processing. It has an adjustable processing time of 2 to 6.5 minutes, dry-to-dry. The installed unit has an extended processing switch, enabling processing times of 8 to 14 minutes to be selected.

Unrelated Parallel-Machine Scheduling with Controllable Processing Times and Impact of Deteriorating Maintenance Activities under Consideration

2016 ◽  
Vol 33 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Chun-Lai Liu ◽  
Jian-Jun Wang
Keyword(s):  
Processing Time ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Controllable Processing Times ◽  
Maintenance Activity ◽  
Processing Times ◽  
Unrelated Parallel Machine Scheduling ◽  
Deteriorating Maintenance ◽  
Maintenance Activities

In this paper, we study the problem of unrelated parallel machine scheduling with controllable processing times and deteriorating maintenance activity. The jobs are nonresumable. The processing time of each job is a linear function of the amount of a continuously divisible resource allocated to the job. During the planning horizon, there is at most one maintenance activity scheduled on each machine. Additionally, if the starting time of maintenance activity is delayed, the length of the maintenance activity required to perform will increase. Considering the total completion times of all jobs, the impact of maintenance activity in the form of the variation in machine load and the amounts of compression, we need to determine the job sequence on each machine, the location of maintenance activities and processing time compression of each job simultaneously. Accordingly, a polynomial time solution to the problem is provided.

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