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Journal of Mathematics and Applications

Journal of Mathematics and Applications
3/39, DOI: 10.7862/rf.2016.3

On the Evolution of Academic Staff Structure in a University Setting

Virtue U. Ekhosuehi

DOI: 10.7862/rf.2016.3


This paper models the academic staff structure in a university as a system of stocks and flows in a three-dimensional space, ℝ3. The stocks are the number of academic staff in a particular state at a given time and the flows are the staff moving between any two states over an interval of time. The paper places emphasis on the grade-specific completion rates of Graduate Assistants, who choose to study in the university in which they are employed for higher degrees. The study describes the evolution of structures in the university as a linear recurrence system. Some aspects of linear algebra are employed as a theoretical underpinning to gain insights into the transformation matrix of the recurrence system. A number of resulting propositions are presented along with their proofs. We provide two theorems to serve as a means of predicting a university manpower structure. Following that a numerical illustration of the theorems and propositions is provided with data which are representative of the kind of data in a Nigerian university system.

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  1. D.J. Bartholomew, A.F. Forbes, S.I. McClean, Statistical Techniques for Manpower Planning (2nd Ed.), Chichester: John Wiley & Sons, 1991.
  2. F. Chatelin, Eigenvalues of Matrices: Revised Edition, Classics in Applied Mathematics, SIAM, 2012.
  3. V.U. Ekhosuehi, A.A. Osagiede, W.A. Iguodala, A procedure for distributing recruits in manpower systems, Accepted for publication in Yugoslav Journal of Operations Research 24 (2) (2015). DOI: 10.2298/YJOR131219031E.
  4. V.U. Ekhosuehi, A.A. Osagiede, Evolution of Structures in a University System, Scholar's Press, Saarbrucken, 2015.
  5. I. Gerontidis, On certain aspects of non-homogeneous Markov systems in continuous time, Journal of Applied Probability 27 (3) (1990) 530-544.
  6. M.A. Guerry, Properties of calculated predictions of graded sizes and the associated integer valued vectors, Journal of Applied Probability 34 (1) (1997) 94-100.
  7. J. Johnes, Operational research in education, European Journal of Operational Research (2014). doi: 10.1016/j.ejor.2014.10.043.
  8. I. Kipouridis, G. Tsaklidis, The size order of the state vector of discrete-time homogeneous Markov systems, Journal of Applied Probability 38 (2) (2001) 357-368.
  9. S. Lipschutz, M. Lipson, Schaum's Outlines: Linear Algebra (Fourth Edition), McGraw-Hill, 2009.
  10. S. McClean, E. Montgomery, F. Ugwuowo, Non-homogeneous continuous-time Markov and semi-Markov manpower models, Applied Stochastic Models and Data Analysis 13 (1998) 191-198.
  11. 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 (2015) 1324-1340.
  12. M.G. Nicholls, The use of Markov models as an aid to the evaluation, planning and benchmarking of doctoral programs, Journal of the Operational Research Society 60 (2009) 1183-1190.
  13. O. Osasona, Tools for academic planning, In: Uvah, I. I. (Editor), Practical Guide on Academic Planning in Nigerian Universities: A Compendium of Academic Planning Tools (2012) 62-105.
  14. F.I. Ugwuowo, S.I. McClean, Modelling heterogeneity in a manpower system: a review, Applied Stochastic Models in Business and Industry 16 (2000) 99-110.
  15. P.-C.G. Vassiliou, On the periodicity of non-homogeneous Markov chains and systems, Linear Algebra and its Applications 471 (2015) 654-684.
  16. P.-C.G. Vassiliou, A.A. Papadopoulo, Non-homogeneous semi-Markov systems and maintainability of the state sizes, Journal of Applied Probability 29 (1992) 519-534.
  17. P.-C.G. Vassiliou, N. Tsantas, Maintainability of structures in nonhomogeneous Markov systems under cyclic behaviour and input control, SIAM Journal on Applied Mathematics 44 (5) (1984) 1014-1022.

About this Article

On the Evolution of Academic Staff Structure in a University Setting

Virtue U. Ekhosuehi

Department of Mathematics, University of Benin, Benin City, Edo State, Nigeria

Journal of Mathematics and Applications

Diagonalisable matrices, Eigenvalues, Linear mapping, Man-power planning, Recurrence system





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