Skip to main content Accessibility help
×
Home

Single-machine stochastic scheduling with dependent processing times

Published online by Cambridge University Press:  01 July 2016

K. D. Glazebrook
Affiliation:
University of Newcastle upon Tyne
Lyn R. Whitaker
Affiliation:
Naval Postgraduate School

Abstract

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1992 

Access options

Get access to the full version of this content by using one of the access options below.

Footnotes

Research supported by the National Research Council.

Research supported by the NPS Research Foundation.

References

Alam, K. and Wallenius, K. T. (1976) Positive dependence and monotonicity in conditional distributions. Commun. Statist. A5, 525534.CrossRefGoogle Scholar
Barlow, R. and Proschan, F. (1981) Statistical Theory of Life Testing: Probability Models. To Begin With, Silver Spring, Maryland.Google Scholar
Bergman, S. W. and Gittins, J. C. (1985) Statistical Methods for Planning Pharmaceutical Research . Marcel Dekker, New York.Google Scholar
Block, H. W., Savits, T. H. and Shaked, M. (1982) Some concepts of negative dependence. Ann. Prob. 10, 765772.CrossRefGoogle Scholar
Brindley, E. C. Jr. and Thompson, W. A. Jr. (1972) Dependence and aging aspects of multivariate survival. J. Amer. Stat. Assoc. 67, 822830.CrossRefGoogle Scholar
Bruno, J. and Hofri, M. (1975) On scheduling chains of jobs on one processor with limited preemption. SIAM J. Comput. 4, 478490.CrossRefGoogle Scholar
Emmons, H. and Pinedo, M. (1990) Scheduling stochastic jobs with due dates on parallel machines. Eur. J. Operat. Res. 47, 4955.CrossRefGoogle Scholar
Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Wiley, New York.Google Scholar
Glazebrook, K. D. and Fay, N. A. (1987) On the scheduling of alternative stochastic jobs on a single machine. Adv. Appl. Prob. 19, 955973.CrossRefGoogle Scholar
Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. 29, 289300.CrossRefGoogle Scholar
Hardy, G. H., Littlewood, J. E. and Pólya, G. (1934) Inequalities. Cambridge University Press.Google ScholarPubMed
Harris, R. (1970) A multivariate definition for increasing hazard rate distribution functions. Ann. Math. Statist. 41, 713717.CrossRefGoogle Scholar
Johnson, N. and Kotz, S. (1975) A vector multivariate hazard rate. J. Multivariate Anal. 5, 5366.CrossRefGoogle Scholar
Lee, M. L. T. (1985) Dependence by total positivity. Ann. Prob. 13, 572582.CrossRefGoogle Scholar
Nash, P. (1973) Optimal Allocation of Resources between Research Projects. Ph.D. thesis, Cambridge University.Google Scholar
Nash, P. and Gittins, J. C. (1977) A Hamiltonian approach to optimal stochastic resource allocation. Adv. Appl. Prob. 9, 5568.CrossRefGoogle Scholar
Ritchie, E. M. (1972) Planning and control of R and D activities. Operat. Res. Quart. 23, 477490.CrossRefGoogle Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Shaked, M. (1975) On Concepts of Dependence for Multivariate Distributions. Ph.D. thesis, University of Rochester, Rochester, NY.Google Scholar
Shaked, M. (1977) A family of concepts of dependence for bivariate distributions. J. Amer. Statist. Assoc. 72, 642650.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (1987) Multivariate hazard rates and stochastic ordering. Adv. Appl. Prob. 19, 123137.CrossRefGoogle Scholar
Yanagimoto, T. (1972) Families of positive dependent random variables. Ann. Inst. Statist. Math. A24, 559573.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 13 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 18th January 2021. This data will be updated every 24 hours.

Hostname: page-component-77fc7d77f9-g622z Total loading time: 0.266 Render date: 2021-01-18T22:58:47.039Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Mon Jan 18 2021 22:02:48 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": true, "languageSwitch": true, "figures": false, "newCiteModal": false, "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Single-machine stochastic scheduling with dependent processing times
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Single-machine stochastic scheduling with dependent processing times
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Single-machine stochastic scheduling with dependent processing times
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *