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.

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.

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.

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.

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.

Bounds for discounted stochastic scheduling problems

1991 ◽  
Vol 28 (04) ◽  
pp. 791-801
Author(s):  
K. D. Glazebrook
Keyword(s):  
Resource Allocation ◽  
Policy Evaluation ◽  
Stochastic Scheduling ◽  
Upper Bounds ◽  
The Other ◽  
Stochastic Environment ◽  
Scheduling Problems ◽  
Total Reward

Suppose that π is a policy for resource allocation in a stochastic environment and π ∗ is an optimal policy. Two existing procedures for policy evaluation are described and compared. Both of these evaluate π by means of upper bounds on R(π ∗) – R(π), the total reward lost when making resource allocations according to π rather than π∗. The bounds developed by these two methods are called Type 1 and Type 2. We demonstrate by example that neither of these procedures dominates the other in the sense of always yielding tighter bounds. A modification to Type 2 bounds is proposed resulting in an improved procedure which always dominates the Type 1 approach.

Single-Machine Due-Window Assignment and Scheduling with Learning Effect and Resource-Dependent Processing Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450036 ◽  
Author(s):  
Ji-Bo Wang ◽  
Ming-Zheng Wang
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Processing Time ◽  
Window Size ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Earliness And Tardiness ◽  
Processing Times ◽  
Due Window ◽  
Due Window Assignment

We consider a single-machine common due-window assignment scheduling problem, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, window size, earliness, and tardiness. For two different processing time functions, we provide a polynomial time algorithm to find the optimal job sequence and resource allocation, respectively.

Some problems of stochastic resource allocation

1972 ◽  
Vol 9 (02) ◽  
pp. 360-369 ◽  
Author(s):  
J. C. Gittins
Keyword(s):  
Resource Allocation ◽  
Hazard Rates ◽  
Processing Unit ◽  
Completion Rates ◽  
Chemical Research ◽  
Scheduling Policy ◽  
Processing Times ◽  
Simultaneous Processing ◽  
Stochastic Resource Allocation ◽  
Optimal Policies

Suppose that a number of jobs are to be carried out by a single processing unit orserver. The server can process any number of jobs at the same time but the time taken to finish all the jobs is the same no matter what scheduling policy is used, provided the server is never left idle. It is, however, possible to minimise the total delays to individual jobs by adopting a suitable policy. Optimal policies are derived here for the situation when the processing times are random variables. If the completion rates (analogous to hazard rates) for every job are increasing it is optimal to process the jobs in sequence. If they are decreasing the optimal policy involves simultaneous processing. These results are applied to a more general resource allocation problem arising in industrial chemical research.

Single-Machine Scheduling with Learning Effect, Deteriorating Jobs and Convex Resource Dependent Processing Times

2015 ◽  
Vol 32 (05) ◽  
pp. 1550033 ◽  
Author(s):  
Xin-Jun Li ◽  
Jian-Jun Wang ◽  
Xue-Ru Wang
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Learning Effect ◽  
Waiting Times ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Optimal Sequence ◽  
Processing Times ◽  
Convex Resource Allocation

This paper considers single-machine scheduling with learning effect, deteriorating jobs and convex resource dependent processing times, i.e., the processing time of a job is a function of its starting time, its position in a sequence and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately to minimize a cost function containing makespan, total completion (waiting) time, total absolute differences in completion (waiting) times and total resource cost. It is proved that the problem can be solved in polynomial time.

Some problems of stochastic resource allocation

1972 ◽  
Vol 9 (2) ◽  
pp. 360-369 ◽  
Author(s):  
J. C. Gittins
Keyword(s):  
Resource Allocation ◽  
Hazard Rates ◽  
Processing Unit ◽  
Completion Rates ◽  
Chemical Research ◽  
Scheduling Policy ◽  
Processing Times ◽  
Simultaneous Processing ◽  
Stochastic Resource Allocation ◽  
Optimal Policies

Suppose that a number of jobs are to be carried out by a single processing unit orserver. The server can process any number of jobs at the same time but the time taken to finish all the jobs is the same no matter what scheduling policy is used, provided the server is never left idle. It is, however, possible to minimise the total delays to individual jobs by adopting a suitable policy. Optimal policies are derived here for the situation when the processing times are random variables. If the completion rates (analogous to hazard rates) for every job are increasing it is optimal to process the jobs in sequence. If they are decreasing the optimal policy involves simultaneous processing. These results are applied to a more general resource allocation problem arising in industrial chemical research.

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