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A continuous-time optimal control model for workforce planning considering human resource strategies (HRS)

Alireza Pooya (Ferdowsi University of Mashhad, Mashhad, Iran)
Morteza Pakdaman (Climatological Research Institute, Mashhad, Iran)
Shila Monazam Ebrahimpour (Ferdowsi University of Mashhad, Mashhad, Iran)


ISSN: 0368-492X

Article publication date: 28 September 2020

Issue publication date: 13 July 2021




This paper aims to present a continuous-time workforce planning model in which workforce flow occurs in terms of internal and external recruitment considering human resource strategies (HRS). The proposed model is a linear optimal control model in which promotions occur by inside appointment and outside employment of the system considering a cost leadership or a differentiation strategy and whether organizations have an internal or an external recruitment orientation. In other words, in the model and its solution procedure, this paper could determine any arbitrary function for the demand of the workforce with each HRS.


The proposed model contains five main sections, namely, applicants, newcomers, workforce who are doing sensitive-simple jobs, expert workforce and supervisors (or managers) that have a different orientation in different HRS. Each of these sections has a target value that this paper tries to attain it by applying appropriate control variables, such as recruitment, layoff, degradation, promotion and retirement. To reach this purpose, this paper formulated an optimal control problem using a linear system transition equation with a quadratic cost function.


Based on the proposed model, it was found that the optimal control model can interpret the managerial aspects. This model could be useful for different firms with different types of workforce demands. This paper has tried to have a comprehensive view of different flows of the workforce in an organization that concern to workforce planning.


Despite the considerable amount of research published, and the importance of following a human resources strategy from organizational strategy, in the knowledge, there is no comprehensive study dedicated to human resources strategy and workforce planning by optimal control models for workforce planning.




Funding: This work was supported in part by Research Deputy of Ferdowsi University of Mashhad, under Grant No. 48299 (dated November 26, 2018).

Conflicts of interest Competing interests: The authors declare that there is no conflict of interest regarding the publication of this study.

Availability of data and material: Not applicable.

Code availability: Not applicable.


Pooya, A., Pakdaman, M. and Monazam Ebrahimpour, S. (2021), "A continuous-time optimal control model for workforce planning considering human resource strategies (HRS)", Kybernetes, Vol. 50 No. 7, pp. 2106-2133.



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