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Further counterexamples to the monotonicity property of t-step maintainable structures

Part of: Operations research and management science Markov processes

Published online by Cambridge University Press:  14 July 2016

John Haigh
John Haigh*
Affiliation:
University of Sussex
*
∗Postal address: Mathematics Division, University of Sussex, Falmer, Brighton BN1 9QH, UK.
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Abstract

Until Guerry's (1990) counterexample to a conjecture of Davies about three-state hierarchical organisations kept at constant size via annual promotion, wastage and recruitment, it was easy to believe that such structures maintainable in t steps would also be maintainable in t + 1 steps. Here we present further counterexamples, which show that t-step maintainability does not imply (t + 1)-step maintainability, for astonishingly large values of t.

Keywords

MANPOWER PLANNINGSUBSTOCHASTIC MATRICES

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 90B70: Theory of organizations, manpower planning
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 441 - 447
Copyright
Copyright © Applied Probability Trust 1992 

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