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The evolution of the attainable structures of a homogeneous Markov system by fixed size

Part of: Operations research and management science

Published online by Cambridge University Press:  14 July 2016

George M. Tsaklidis
George M. Tsaklidis*
Affiliation:
University of Thessaloniki
*
∗ Postal address: Statistics and Operatiọns Research Section, Mathematics Department, University of Thessaloniki, Thessaloniki 54006, Greece.
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Abstract

In order to describe the evolution of the attainable structures of a homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space as they are changing in time and we find the value of the volume asymptotically. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures; extensions are obtained concerning results from the Perron–Frobenius theory referring to Markov systems.

Keywords

MANPOWER SYSTEMSPERRON–FROBENIUS THEOREM

MSC classification

Primary: 90B70: Theory of organizations, manpower planning
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 348 - 361
Copyright
Copyright © Applied Probability Trust 1994 

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References

Bartholomew, D. J. (1975) A stochastic control problem in the social sciences. Bull. Internat. Statist. Inst. 46, 670–680.Google Scholar
Bartholomew, D. J. (1977) Maintaining a grade or age structure in stochastic environment. Adv. Appl. Prob. 9, 1–17.Google Scholar
Bartholomew, D. J. (1982) Stochastic Models for Social Processes, 3rd edn. Wiley, New York (2nd edn 1973).Google Scholar
Davies, G. S. (1973) Structural control in a graded manpower system. Management Sci. 20, 76–84.Google Scholar
Davies, G. S. (1978) Attainable and maintainable regions in Markov chain control. Recent Theoret. Developm. Control. 371–381.Google Scholar
Fichtenholz, G. M. (1964) Differential- und Integralrechnung. VEB Deutscher Verlag der Wissenschaften. Berlin.Google Scholar
Iosifescu, M. (1980) Finite Markov Processes and their Applications. Wiley, New York.Google Scholar
Isaacson, D. L. and Madsen, R. W. (1976) Markov Chains: Theory and Applications. Wiley, New York.Google Scholar
Mehlmann, A. (1980) An approach to optimal recruitment and transition strategies for manpower systems using dynamic programming. J. Operat. Res. Soc. 31, 1009–1015.Google Scholar
Schaal, H. (1976) Lineare Algebra und Analytische Geometrie. Vieweg, Braunschweig/Wiesbaden.Google Scholar
Stanford, R. E. (1980) The effects of promotion by seniority in growth-constrained organisations. Management Sci. 26, 680–693.CrossRefGoogle Scholar
Tsantas, N. and Vassiliou, P.-C. G. (1993) The nonhomogeneous Markov system in a stochastic environment. J. Appl. Prob. 30, 285–301.Google Scholar
Vajda, S. (1978) Mathematics of Manpower Planning. Wiley, New York.Google Scholar
Vassiliou, P.-C. G. (1982) Asymptotic behaviour of Markov systems. J. Appl. Prob. 19, 851–857.Google Scholar
Vassiliou, P.-C. G. and Georgiou, A. C. (1990) Asymptotically attainable structures in nonhomogeneous Markov systems. Operations Res 38, 537–545.Google Scholar
Vassiliou, P.-C. G., Georgiou, A. C. and Tsantas, N. (1990) Control of asymptotic variability in nonhomogeneous Markov systems. J. Appl. Prob. 28, 756–766.Google Scholar
Vassiliou, P.-C. G. and Papadopoulou, A. A. (1992) Nonhomogeneous semi-Markov systems and maintainability of the state sizes. J. Appl. Prob. 29, 519–534.Google Scholar
Vassiliou, P.-C. G. and Tsantas, N. (1984) Stochastic control in nonhomogeneous Markov systems. Internat. J. Computer Math. 16, 139–155.Google Scholar
Young, A. and Almond, G. (1961) Predicting distributions of staff. Computer J. 3, 246–250.Google Scholar