Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-09T01:18:02.168Z Has data issue: false hasContentIssue false

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

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 MtMt+1 does not exist in general, refutes the conjecture of Davies [3].

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1991 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 376382.Google Scholar
[3] Davies, G. S. (1981) Maintainable regions in a Markov manpower model. J. Appl. Prob. 18, 738742.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, 700705.Google Scholar
[6] Vajda, S. (1978) Mathematics of Manpower Planning. Wiley, London.Google Scholar