Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

The present paper is devoted to modeling and solving the inventory and production planning in a four-echelon supply chain (SC) with reverse logistics, from supplier to after-sales service center and repair center. To the best of our knowledge, this is the first scientific attempt for modeling and resolving the inventory and production planning in an SC with reverse logistics that the problem is modeled by a disturbance optimal control problem (OCP). Both recycling and reworking are assumed in the reverse logistic. There was a disturbance because we considered the demand time-dependent. From the former points the presented model is so close to the real-world problem in the field of SC. The Pontryagin minimum principle is applied to reformulate the OCP into a system of equations. In continuous, the system of equations is solved by an artificial neural network. In the final step, an example and a case study are presented to depict the performance and validity of the model and the method. KeywordsSupply chain planning • Reverse logistic • Service after sale • Optimal control problem with disturbance • Artificial neural network B Alireza Pooya

PurposeWorkforce planning must answer how many workforces, in which positions, and talents, and when each organization is needed. To find the requirements workforce, organizations need to know the organizational position and talents pools. Clarifying the number of workforces required in each pool requires attention to workforce flows, including hiring, promotion, degradation, horizontal movement, and exiting the organization. It is a dynamic issue and must be addressed over several periods over a specific duration, which adds to the complexity. According to the talent management presented in this research, all the above complex questions are answered by applying the optimal control (OC) model according to talent management presented in this research.Design/methodology/approachThis research presents a dynamic model by using a linear-quadratic optimal control model, which was solved by Pontryagin's maximum principle, to achieve an optimal number of workforce requirements for each of the positions of nursing services manager, supervisor, head nurses and nurses in the health sector according to the required talents in each position.FindingsThe results have shown that the target value of workforce numbers has been achieved in the planning period, and the validation test and sensitivity analysis justified the model by reaching the workforce planning targets.Originality/valueThis study provides a dynamic model for achieving quantitative workforce planning targets; the model presented in this manuscript has included an important qualitative factor, namely workforce talents. According to the authors' review, there is no comprehensive research devoted to workforce planning through optimal control models by attention to workforces skills.