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Monotonicity property of t-step maintainable structures in three-grade manpower systems: a counterexample

Published online by Cambridge University Press:  14 July 2016

M. A. Guerry
M. A. Guerry*
Affiliation:
Vrije Universiteit Brussel
*
∗Postal address: Centrum voor Statistiek en Operationeel Onderzoek, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium.
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Abstract

In this paper the t-step maintainable regions Mt are examined in a three-graded system under the following conditions: the total size of the system remains constant during each intermediate step, demotions do not occur and recruitment control is considered.

A counterexample, showing that the monotonicity property Mt ⊆ Mt+1 does not exist in general, refutes the conjecture of Davies [3].

Keywords

MANPOWER PLANNINGMARKOV CHAINRECRUITMENT CONTROLRE-ATTAINABLE STRUCTURES
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 221 - 224
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Bartholomew, D. J. (1978) Stochastic Models for Social Processes, 2nd edn. Wiley, London.Google Scholar
[2] Davies, G. S. (1975) Maintainability of structures in Markov chain models under recruitment control. J. Appl. Prob. 12, 376–382.Google Scholar
[3] Davies, G. S. (1981) Maintainable regions in a Markov manpower model. J. Appl. Prob. 18, 738–742.Google Scholar
[4] Guerry, M. A. (1989) Properties of t-step maintainable structures in three-graded manpower systems. Center for Manpower Planning, Free University of Brussels.Google Scholar
[5] Haigh, J. (1983) Maintainability of manpower structures – counterexamples, results and conjectures. J. Appl. Prob. 20, 700–705.Google Scholar
[6] Vajda, S. (1978) Mathematics of Manpower Planning. Wiley, London.Google Scholar