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On a Class of Stochastic Arrangement Inequalities Arising in Optimal Allocation of Resources

Published online by Cambridge University Press:  27 July 2009

Haijun Li
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Abstract

Motivated by stochastic allocation problems, we study sufficient conditions that imply a general class of stochastic arrangement inequalities. This class includes many known and useful arrangement inequalities in the literature. Some illustrative examples in reliability theory are also given.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1994

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References

1.Boland, P.J., El-Neweihi, E., & Proschan, F. (1988). Active redundancy allocation in coherent systems. Probability in the Engineering and Information Sciences 2: 343353.CrossRefGoogle Scholar
2.Boland, P.J., El-Neweihi, E., & Proschan, F. (1991). Redundancy importance and allocation of spares in coherent systems. Journal of Statistical Planning and Inference 29: 5566.CrossRefGoogle Scholar
3.Boland, P.J., El-Neweihi, E., & Proschan, F. (1992). Stochastic order for redundancy allocation in series and parallel systems. Advances in Applied Probability 24: 161171.CrossRefGoogle Scholar
4.Buzacott, J.A. & Shanthikumar, J.G. (1992). Stochastic models of manufacturing systems. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
5.Chang, C.-S. (1992). A new ordering for stochastic majorization: Theory and applications. Advances in Applied Probability 24: 604634.CrossRefGoogle Scholar
6.Chang, C.-S. & Yao, D. (1990). Rearrangement, majorization and stochastic scheduling. Technical Report, T.J. Watson Research Center, Yorktown Heights, NY 10598.Google Scholar
7.El-Neweihi, E., Proschan, F., & Sethuraman, J. (1986). Optimal allocation of components in parallel-series and series-parallel systems. Journal of Applied Probability 23: 770777.CrossRefGoogle Scholar
8.Liyanage, L. & Shanthikumar, J.G. (1992). Allocation through stochastic Schur convexity and stochastic transposition increasingness. In Shaked, M. & Tong, Y.L. (eds.), Stochastic inequalities, Vol. 22. IMS Lecture Notes. Hayward, CA: Institute of Mathematical Statistics, pp. 253273.CrossRefGoogle Scholar
9.Marshall, M. & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. New York: Academic Press.Google Scholar
10.Shaked, M. & Shanthikumar, J.G. (1990). Reliability and maintainability. In Heyman, O.P. & Sobel, M.J. (eds.), Handbook in OR and MS, Vol. 2. Amsterdam: North-Holland, Chapter 13.Google Scholar
11.Shaked, M. & Shanthikumar, J.G. (1992). Optimal allocation of resources to nodes of parallel and series systems. Advances in Applied Probability 24: 894914.CrossRefGoogle Scholar
12.Shanthikumar, J.G. (1987). Stochastic majorization of random variables with proportional equilibrium rates. Advances in Applied Probability 19: 854872.CrossRefGoogle Scholar
13.Shanthikumar, J.G. & Yao, D. (1988). On server allocation in multiple center manufacturing systems. Operations Research 36: 333342.CrossRefGoogle Scholar
14.Shanthikumar, J.G. & Yao, D. (1991). Bivariate characterization of some stochastic order relations. Advances in Applied Probability 23: 642659.CrossRefGoogle Scholar
15.Yao, D. & Shanthikumar, J.G. (1987). The optimal input rates to a system of manufacturing cells. INFOR, Canadian Journal of Operational Research and Information Processing 25: 5765.CrossRefGoogle Scholar