On the scheduling of alternative stochastic jobs on a single machine

1987 ◽  
Vol 19 (04) ◽  
pp. 955-973 ◽  
Author(s):  
K. D. Glazebrook ◽  
N. A. Fay
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Stochastic Scheduling ◽  
Major Area ◽  
Research Planning ◽  
Stochastic Resource Allocation ◽  
Standard Models ◽  
Set Up ◽  
Area Of Application

Standard models in stochastic resource allocation concern the economic processing of all jobs in some set J. We consider a set up in which tasks in various subsets of J are deemed to be alternative to one another, in that only one member of such a subset of alternative tasks will be completed during the evolution of the process. Existing stochastic scheduling methodology for single-machine problems is developed and extended to this novel class of models. A major area of application is in research planning.

On the scheduling of alternative stochastic jobs on a single machine

1987 ◽  
Vol 19 (4) ◽  
pp. 955-973 ◽  
Author(s):  
K. D. Glazebrook ◽  
N. A. Fay
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Stochastic Scheduling ◽  
Major Area ◽  
Research Planning ◽  
Stochastic Resource Allocation ◽  
Standard Models ◽  
Set Up ◽  
Area Of Application

Standard models in stochastic resource allocation concern the economic processing of all jobs in some set J. We consider a set up in which tasks in various subsets of J are deemed to be alternative to one another, in that only one member of such a subset of alternative tasks will be completed during the evolution of the process. Existing stochastic scheduling methodology for single-machine problems is developed and extended to this novel class of models. A major area of application is in research planning.

Single-machine stochastic scheduling with dependent processing times

1992 ◽  
Vol 24 (03) ◽  
pp. 635-652 ◽  
Author(s):  
K. D. Glazebrook ◽  
Lyn R. Whitaker
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Simple Structure ◽  
Stochastic Scheduling ◽  
Negative Dependence ◽  
Total Reward ◽  
Processing Times ◽  
Optimal Policies ◽  
Positive And Negative Dependence ◽  
Machine Allocation

A single machine is available to process a collection of stochastic jobs preemptively. Rewards are received at job completions. We seek policies for machine allocation which maximize the total reward. Application areas point to the need to study such models for resource allocation when job processing requirements are dependent. To this end, models are developed in which the nature of such dependence is derived from various notions of positive and negative dependence in common usage in reliability. Optimal policies for resource allocation of simple structure are obtained for a variety of such models.

Single-machine stochastic scheduling with dependent processing times

1992 ◽  
Vol 24 (3) ◽  
pp. 635-652 ◽  
Author(s):  
K. D. Glazebrook ◽  
Lyn R. Whitaker
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Simple Structure ◽  
Stochastic Scheduling ◽  
Negative Dependence ◽  
Total Reward ◽  
Processing Times ◽  
Optimal Policies ◽  
Positive And Negative Dependence ◽  
Machine Allocation

A single machine is available to process a collection of stochastic jobs preemptively. Rewards are received at job completions. We seek policies for machine allocation which maximize the total reward. Application areas point to the need to study such models for resource allocation when job processing requirements are dependent. To this end, models are developed in which the nature of such dependence is derived from various notions of positive and negative dependence in common usage in reliability. Optimal policies for resource allocation of simple structure are obtained for a variety of such models.

On stochastic scheduling with precedence relations and switching costs

1980 ◽  
Vol 17 (4) ◽  
pp. 1016-1024 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Probability Distribution ◽  
Single Machine ◽  
Optimal Strategy ◽  
Switching Costs ◽  
Stochastic Scheduling ◽  
Random Variable ◽  
Precedence Relation ◽  
Precedence Relations

A collection of jobs is to be processed by a single machine. The amount of processing required by each job is a random variable with a known probability distribution. The jobs must be processed in a manner which is consistent with a precedence relation but the machine is free to switch from one job to another at any time; such switches are costly, however. This paper discusses conditions under which there is an optimal strategy for allocating the machine to the jobs which is given by a fixed permutation of the jobs indicating in which order they should be processed. When this is so, existing algorithms may be helpful in giving the best job ordering.

Single-Machine Due-Window Assignment Scheduling with Resource Allocation and Generalized Earliness/Tardiness Penalties

2021 ◽  
pp. 2150041
Author(s):  
Yu Tian
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Window Size ◽  
Single Machine Scheduling ◽  
Start Time ◽  
Optimal Sequence ◽  
Optimal Resource ◽  
Due Window ◽  
Weighted Earliness ◽  
Due Window Assignment

In this study, the due-window assignment single-machine scheduling problem with resource allocation is considered, where the processing time of a job is controllable as a linear or convex function of amount of resource allocated to the job. Under common due-window and slack due-window assignments, our goal is to determine the optimal sequence of all jobs, the due-window start time, due-window size, and optimal resource allocation such that a sum of the scheduling cost (including weighted earliness/tardiness penalty, weighted number of early and tardy job, weighted due-window start time, and due-window size) and resource consumption cost is minimized. We analyze the optimality properties, and provide polynomial time solutions to solve the problem under four versions of due-window assignment and resource allocation function.

A Bicriteria Approach for Single Machine Scheduling with Resource Allocation, Learning Effect and a Deteriorating Maintenance Activity

2017 ◽  
Vol 34 (04) ◽  
pp. 1750011 ◽  
Author(s):  
Zhusong Liu ◽  
Zhenyou Wang ◽  
Yuan-Yuan Lu
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Learning Effect ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Maintenance Activity ◽  
Optimal Resource ◽  
Deteriorating Maintenance ◽  
Polynomially Solvable ◽  
Completion Times

This paper considers the single machine scheduling with learning effect, resource allocation and deteriorating maintenance activity simultaneously. For the convex resource allocation consumption function, we provide a bicriteria analysis where the first (schedule) criterion is to minimize the total weighted sum of makespan, total completion time and total absolute differences in completion times, and the second (resource) criterion is to minimize the total weighted resource consumption. Our aim is to find the optimal resource allocations and job sequence that minimize the three different models of considering the two criterion. We show that these three models are polynomially solvable respectively.

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