Multi-level nursing workforce planning considering talent management in healthcare with a dynamic quantitative approach

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shila Monazam Ebrahimpour ◽  
Fariborz Rahimnia ◽  
Alireza Pooya ◽  
Morteza Pakdaman
Keyword(s):  
Optimal Control ◽  
Dynamic Model ◽  
Health Sector ◽  
Workforce Planning ◽  
Talent Management ◽  
Optimal Number ◽  
Linear Quadratic ◽  
Planning Period ◽  
Linear Quadratic Optimal Control ◽  
Content Type

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.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

scholarly journals Two Inverse Problems Solution by Feedback Tracking Control

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 137
Author(s):  
Vladimir Turetsky
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Feedback Linearization ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Linear Quadratic Tracking ◽  
Ill Posed ◽  
Quadratic Optimal Control ◽  
Quadratic Tracking

Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

scholarly journals A Hida–Malliavin white noise calculus approach to optimal control

2018 ◽  
Vol 21 (03) ◽  
pp. 1850014
Author(s):  
Nacira Agram ◽  
Bernt Øksendal
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
White Noise ◽  
Backward Stochastic Differential Equation ◽  
Second Order ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Alternative Approach ◽  
Quadratic Optimal Control ◽  
White Noise Calculus

The classical maximum principle for optimal stochastic control states that if a control [Formula: see text] is optimal, then the corresponding Hamiltonian has a maximum at [Formula: see text]. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida–Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

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