On the Stable Gani-Type Attainability Problem Controlled by Promotion at Maximum Entropy

doi:10.1007/s40305-020-00301-0

Abstract

Abstract: This study considers the attainability problem in one-step for the stable Gani-type model controlled by promotion within the context of maximum entropy. The technique adopted involves formulating the attainability problem as a constrained optimisation problem wherein the objective is to maximise the Shannon entropy rate subject to certain constraints imposed by the attainable configuration and the sub-stochastic transition matrix. The principle of maximum entropy is used to obtain results that are consistent with the exponential representation of transition probabilities for manpower systems.

Key words: Attainability, Entropy, Gani-type model, Manpower planning, Markov models

CLC Number:

62B10
90B70

Virtue Uwabomwen Ekhosuehi. On the Stable Gani-Type Attainability Problem Controlled by Promotion at Maximum Entropy[J]. Journal of the Operations Research Society of China, 2021, 9(3): 673-690.

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References

[1] Gani, J.:Formulae for projecting enrolment and degrees awarded in universities. J. R. Stat. Soc. A 126, 400-409(1963)
[2] Bartholomew, D.J., Forbes, A.F., McClean, S.I.:Statistical Techniques for Manpower Planning, 2nd edn. Wiley, Chichester (1991)
[3] Vassiliou, P.-C.G.:A note on stability in Gani-type models in manpower systems. J. Oper. Res. Soc. 31(10), 953-954(1980)
[4] Abdallaoui, G.:Probability of maintaining or attaining a structure in one step. J. Appl. Probab. 24(4), 1006-1011(1987)
[5] Komarudin, K., Guerry, M.-A., Vanden Berghe, G., De Feyter, T.:Balancing attainability, desirability and promotion steadiness in manpower planning systems. J. Oper. Res. Soc. (2015). https://doi.org/10.1057/jors.2015.26
[6] Komarudin, De Feyter, T., Guerry, M.-A., Vanden Berghe, G.:Balancing desirability and promotion steadiness in partially stochastic manpower systems. Commun. Stat. Theory Methods 45(6), 1805-1818(2016). https://doi.org/10.1080/03610926.2014.1001495
[7] De Feyter, T., Guerry, M.-A., Komarudin:Optimizing cost-effectiveness in a stochastic Markov manpower planning system under control by recruitment. Ann. Oper. Res. 253, 117-131(2017). https://doi.org/10.1007/s10479-016-2311-4
[8] Ekhosuehi, V.U., Osagiede, A.A., Iguodala, W.A.:A procedure for distributing recruits in manpower systems. Yugosl. J. Oper. Res. 25(3), 441-452(2015). https://doi.org/10.2298/YJOR131219031E
[9] Shannon, C.E.:A mathematical theory of communication. Bell Syst. Tech. J. 27(379-423), 623-656(1948)
[10] Wilson, A.G.:The use of the concept of entropy in system modeling. Oper. Res. Q. 21, 247-265(1970)
[11] Bartholomew, D.J.:The control of a grade structure in a stochastic environment using promotion control. Adv. Appl. Probab. 11(3), 603-615(1979)
[12] Mehlmann, A.:Markovian manpower models in continuous time. J. Appl. Probab. 14(2), 249-259(1977)
[13] Ernst, A.T., Jiang, H., Krishnamoorthy, M., Sier, D.:Staff scheduling and rostering:a review of applications, methods and models. Eur. J. Oper. Res. 153, 3-27(2004)
[14] Agnihothri, S.R., Mishra, A.K., Simmons, D.E.:Workforce cross-training decisions in field service systems with two job types. J. Oper. Res. Soc. 54(4), 410-418(2003)
[15] Nilakantan, K.:Evaluation of staffing policies in Markov manpower systems and their extension to organizations with outsource personnel. J. Oper. Res. Soc. 66(8), 1324-1340(2015). https://doi.org/10.1057/jors.2014.82
[16] Zhu, X., Sherali, H.D.:Two-stage workforce planning under demand fluctuations and uncertainty. J. Oper. Res. Soc. 60(1), 94-103(2009)
[17] Vassiliou, P.-C.G., Tsantas, N.:Maintainability of structures in nonhomogeneous Markov systems under cyclic behavior and input control. SIAM J. Appl. Math. 44(5), 1014-1022(1984)
[18] Kipouridis, I., Tsaklidis, G.:The size order of the state vector of discrete-time homogeneous Markov systems. J. Appl. Probab. 38(2), 357-368(2001)
[19] Berman, O., Larson, R.C., Pinker, E.:Scheduling workforce and workflow in a high volume factory. Manag. Sci. 43(2), 158-172(1997)
[20] Gerontidis, I.I.:Stochastic equilibria in nonhomogeneous Markov population replacement process. Math. Oper. Res. 19(1), 192-210(1994)
[21] Vassiliou, P.-C.G.:On the periodicity on non-homogeneous Markov chains and systems. Linear Algebra Appl. 471, 654-684(2015)
[22] De Feyter, T.:Modeling mixed push and pull promotion flows in manpower planning. Ann. Oper. Res. 155, 25-39(2007). https://doi.org/10.1007/s10479-007-0205-1
[23] Guerry, M.-A.:The probability of attaining a structure in a partially stochastic model. Adv. Appl. Probab. 25(4), 818-824(1993)
[24] Chattopadhyay, A.K., Gupta, A.:A stochastic manpower planning model under varying class sizes. Ann. Oper. Res. 155, 41-49(2007). https://doi.org/10.1007/s10479-007-0208-y
[25] Ekhosuehi, V.U.:A control rule for planning promotion in a Nigerian university setting. Croat. Oper. Res. Rev. 7(2), 171-188(2016)
[26] Guerry, M.-A., De Feyter, T.:Optimal recruitment strategies in a multi-level manpower planning model. J. Oper. Res. Soc. 63, 931-940(2012). https://doi.org/10.1057/jors.2011.99
[27] Belis, M., Guiasu, S.:A quantitative-qualitative measure of information in cybernetic systems. IEEE Trans. Inf. Theory 14(4), 593-594(1968)
[28] Guiasu, S.:Weighted entropy. Rep. Math. Phys. 2(3), 165-179(1971)
[29] Girardin, V.:Entropy maximization for Markov and semi-Markov processes. Methodol. Comput. Appl. Probab. 6, 109-127(2004)
[30] Guiasu, S.:Maximum entropy condition in queueing theory. J. Oper. Res. Soc. 37(3), 293-301(1986)
[31] Guiasu, S.:Maximum entropy condition in queueing theory:response. J. Oper. Res. Soc. 38(1), 98-100(1987)
[32] Guiasu, S., Shenitzer, A.:The principle of maximum entropy. Math. Intell. 7(1), 42-48(1985)
[33] McClean, S., Abodunde, T.:Entropy as a measure of stability in a manpower system. J. Oper. Res. Soc. 29(2), 885-889(1978)
[34] Nilakantan, K., Raghavendra, B.G.:Control aspects in proportionality Markov manpower systems. Appl. Math. Model. 29, 85-116(2005)
[35] Feichtinger, G.:On the generalization of stable age distributions to Gani-type person-flow models. Adv. Appl. Probab. 8(3), 433-445(1976)