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Extension of the bivariate characterization for stochastic orders

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Rhonda Righter  and
J. George Shanthikumar
Rhonda Righter*
Affiliation:
Santa Clara University
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Decision and Information Sciences, Santa Clara University, Santa Clara, CA 95053, USA.
∗∗ Postal address: Walter A. Haas School of Business, University of California, Berkeley, CA 94720, USA.
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Abstract

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The bivariate characterization of stochastic ordering relations given by Shanthikumar and Yao (1991) is based on collections of bivariate functions g(x, y), where g(x, y) and g(y, x) satisfy certain properties. We give an alternate characterization based on collections of pairs of bivariate functions, g1(x, y) and g2(x, y), satisfying certain properties. This characterization allows us to extend results for single machine scheduling of jobs that are identical except for their processing times, to jobs that may have different costs associated with them.

Keywords

LIKELIHOOD RATIO ORDERINGHAZARD RATE ORDERINGSTOCHASTIC SCHEDULING

MSC classification

Primary: 60E05: Distributions
Secondary: 90B35: Scheduling theory, deterministic
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 2 , June 1992 , pp. 506 - 508
Copyright
Copyright © Applied Probability Trust 1992 

Footnotes

Supported in part by NSF grant ECS-8811234.

References

Chang, C. S. and Yao, D. D. (1990) Rearrangement, majorization and stochastic scheduling. Preprint.Google Scholar
Frenk, J. B. G. (1991a) A general framework for stochastic one-machine scheduling problems with zero release times and no partial ordering. Prob. Eng. Inf. Sci. 5, 297–315.Google Scholar
Frenk, J. B. G. (1991b) A note on one-machine scheduling problems with imperfect information. Prob. Eng. Inf. Sci. 5, 317–331.Google Scholar
Shanthikumar, J. G. and Yao, D. D. (1991) Bivariate characterization of some stochastic order relations. Adv. Appl. Prob. 23, 642–659.CrossRefGoogle Scholar