zbMATH — the first resource for mathematics

Prospective control in an enhanced manpower planning model. (English) Zbl 1176.90345
Summary: The present paper deals with the exercise of recruitment control to a time dependent, hierarchical system which incorporates training classes as well as two streams of recruitment; one coming from the outside environment and another from an auxiliary external system. The motivation for this model lies in the need to take into account not only the tendency of the employees to attend seminar courses so as to improve their career prospects, but also the organizations’ intention to avoid situations associated with the unavailability of skilled individuals for hiring. For the suggested model, we define its attainable structures and the sets containing these structures, i.e. attainable sets. We examine the geometrical properties of these sets and it is proved that they form convex polytopes. Moreover, by adopting the equivalent approach of describing convex polyhedral sets via inequalities, we specify the attainable sets of the model for every time point \(t\). An illustrative example follows.

90B70 Theory of organizations, manpower planning in operations research
cdd; R; rcdd
Full Text: DOI
[1] McClean, S.I., Manpower planning models and their estimation, European journal of operational research, 51, 179-187, (1991)
[2] Seal, H.L., The mathematics of a population composed of K strata each recruited from the stratum below and supported at the lowest level by a uniform annual number of entrants, Biometrika, 33, 226-230, (1945) · Zbl 0060.31802
[3] Bartholomew, D.J., Stochastic models for social processes, (1982), Wiley Chichester · Zbl 0578.92026
[4] Bartholomew, D.J.; Forbes, A.F.; McClean, S.I., Statistical techniques for manpower planning, (1991), John Wiley & Sons
[5] Ugwuowo, F.I.; McClean, S.I., Modelling heterogeneity in a manpower system. A review, Applied stochastic models in business and industry, 16, 19-110, (2000) · Zbl 0976.62113
[6] Wang, J., A review of operations research applications in workforce planning and potential modelling of military training, (2005), DSTO Systems Sciences Laboratory Edinburgh Australia
[7] De Feyter, T., Modeling heterogeneity in manpower planning: dividing the personnel system in more homogeneous subgroups, Applied stochastic models in business and industry, 22, 321-334, (2006) · Zbl 1126.90035
[8] Vassiliou, P.-C.G., Asymptotic behaviour of Markov systems, Journal of applied probability, 19, 851-857, (1982) · Zbl 0498.60075
[9] Vassiliou, P.-C.G., The evolution of the theory of non-homogeneous Markov systems, Applied stochastic models and data analysis, 13, 159-176, (1997) · Zbl 0918.60062
[10] De Feyter, T., Modeling mixed push and pull promotion flows in manpower planning, Annals of operations research, 155, 25-39, (2007) · Zbl 1145.90035
[11] Nilakantan, K.; Raghavendra, B.G., Control aspects in proportionality Markov manpower systems, Applied mathematical modelling, 29, 85-116, (2005) · Zbl 1090.90196
[12] Georgiou, A.C.; Tsantas, N., Modelling recruitment training in mathematical human resource planning, Applied stochastic models in business and industry, 18, 53-74, (2002) · Zbl 1007.91033
[13] Guerry, M.A., The probability of attaining a structure in a partially stochastic model, Advances in applied probability, 25, 818-824, (1993) · Zbl 0787.90034
[14] Abdallaoui, G., Probability of maintaining or attaining a structure in one step, Journal of applied probability, 24, 1006-1011, (1987) · Zbl 0634.60063
[15] Tsantas, N., Stochastic analysis of a non-homogeneous Markov system, European journal of operational research, 85, 670-685, (1995) · Zbl 0910.90200
[16] Davies, G.S., Control of grade sizes in a partially stochastic Markov manpower model, Journal of applied probability, 19, 439-443, (1982) · Zbl 0483.60062
[17] Georgiou, A.C., Asprirations and priorities in a three phase approach of a nonhomogeneous Markov system, European journal of operational research, 116, 565-583, (1999) · Zbl 1009.90125
[18] Yadavalli, V.S.S.; Natarajan, R.; Udayabhaskaran, S., Time dependent behaviour of stochastic models of manpower system – impact of pressure on promotion, Stochastic analysis and applications, 20, 863-882, (2002) · Zbl 1020.90020
[19] Farina, L.; Rinaldi, S., Positive linear systems: theory and applications, (2000), Wiley New York · Zbl 0988.93002
[20] Rockafellar, R.T., Convex analysis, (1970), Princeton University Press · Zbl 0229.90020
[21] Horn, R.A.; Johnson, C.R., Matrix analysis, (1990), Cambridge University Press · Zbl 0704.15002
[22] Panik, M.J., Fundamentals of convex analysis, (1993), Kluwer Academic Publishers · Zbl 0799.90131
[23] Magaril-Ilyaev, G.G.; Tikhomirov, V.M., Convex analysis: theory and applications, (2003), American Mathematical Society · Zbl 1041.49001
[24] Motzkin, T.S.; Raiffa, H.; Thompson, G.L.; Thralli, M.R., The double description method, (), 51-73
[25] K. Fukuda, A. Prodon, Double description method revisited, in combinatorics and computer science, in: M. Deza, R. Euler, Y. Manoussakis (Eds.), Eighth Franco-Japanese and Fourth Franco-Chinese Conference, Brest, France, July 30-5, 1995, Selected Papers, Lecture Notes in Computer Science, vol. 1120, Springer-Verlag, Berlin, 1996, pp. 91-111.
[26] K. Fukuda, <http://www.cs.mcgill.ca/ fukuda/soft/cdd_home>.
[27] Rumchev, V.G., Constructing the reachability sets for positive linear discrete time systems, Systems science, 15, 3, 11-20, (1989) · Zbl 0725.93009
[28] Caccetta, L.; Rumchev, V.G., A survey of reachability and controllability for positive linear systems, Annals of operations research, 98, 101-122, (2000) · Zbl 0972.93003
[29] R Development Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0, 2008, <http://www.R-project.org>.
[30] C.J. Geyer, G.D. Meeden and incorporates code from cddlib (ver 0.94f) written by Komei Fukuda rcdd: rcdd (C Double Description for R). R package version 1.1., 2008, <http://www.stat.umn.edu/geyer/rcdd/>.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.