On the Alternative Structures for a Three-Grade Markov Manpower System

This paper considers a manpower system modelled within the Markov chain context under the condition that recruitment is done to replace outgoing flows. The paper takes up the embeddability problem in a three-grade manpower system and examines it from the standpoint of generating function (i.e., the z-transform of stochastic matrices). The method constructs a stochastic matrix that is made up of a limiting-state probability matrix and a partial sum of transient matrices. Examples are provided to illustrate the utility of the method.

Full text (pdf)

1. D.J. Bartholomew, A.F. Forbes, S.I. McClean, Statistical Techniques for Manpower Planning, 2nd edn. John Wiley & Sons, Chichester, 1991.
2. M.O. Cacéres, I. Cacéres-Saez, Random Leslie matrices in population dynamics, Journal of Mathematical Biology 63 (2011) 519-556.
3. V.U. Ekhosuehi, A control rule for planning promotion in a university setting in Nigeria, Croatian Operational Research Review 7 (2) (2016) 171-188.
4. M.-A. Guerry, Monotonicity property of t-step maintainable structures in three-grade manpower systems: a counterexample, Journal of Applied Probability 28 (1) (1991) 221-224.
5. M.-A. Guerry, Properties of calculated predictions of grade sizes and the associated integer valued vectors. Journal of Applied Probability 34 (1) (1997) 94-100.
6. M.-A. Guerry, On the embedding problem for discrete-time Markov chains, Journal of Applied Probability 50 (4) (2013) 918-930.
7. M.-A. Guerry, T. De Feyter, Optimal recruitment strategies in a multi-level manpower planning model. Journal of the Operational Research Society 63 (2012), 931-940. DOI: 10.10.1057/jors.2011.99.
8. Komarudin, M.-A. Guerry, G. Vanden Berghe, T. De Feyter, Balancing attainability, desirability and promotion steadiness in manpower planning systems, Journal of the Operational Research Society 66 (12) (2015) 2004-2014. DOI: 10.1057/jors.2015.26.
9. K. Nilakantan, Evaluation of staffing policies in Markov manpower systems and their extension to organizations with outsource personnel, Journal of the Operational Research Society 66 (8) (2015) 1324-1340. DOI: 10.1057/jors.2014.82.
10. A.A. Osagiede, V.U. Ekhosuehi, Finding a continuous-time Markov chain via sparse stochastic matrices in manpower systems, Journal of the Nigeria Mathematical Society 34 (2015) 94-105.
11. B. Singer, S. Spilerman, The representation of social processes by Markov models, American Journal of Sociology 82 (1) (1976) 1-54.
12. G.M. Tsaklidis, The evolution of the attainable structures of a continuous time homogeneous Markov system with fixed size, Journal of Applied Probability 33 (1) (1996) 34-47.
13. A.U. Udom, Optimal controllability of manpower system with linear quadratic performance index, Brazilian Journal of Probability and Statistics 28 (2) (2014) 151-166.
14. S.H. Zanakis, M.W. Maret, A Markov chain application to manpower supply planning, Journal of the Operational Research Society 31 (12) (1980) 1095-1102.