Nurse allocation in hospital: hybridization of linear regression, fuzzy set and game-theoretic approaches

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Sufficient numbers of staff are required for any hospital for providing better services to patients with satisfactory treatment. In most hospitals, the patient's treatment and care depend on the availability of nurses. Less number of nurses are a reason for average care and treatment to patients, whereas more than the required number of nurses may cause wastage of expenditure and manpower. More importantly, an additional number of nurses may be assigned to some hospitals where a sufficient number of nurses are not available. Moreover, nurses are of different categories such as qualified nurses having experience in providing service to patients, qualified nurses without having experience, and nurses without qualification but have experience. The expenditure also depends on categories of nurses' appointments. To reach an equilibrium point in appointing nurses, we propose a hybridization model using linear regression, fuzzy set theory and game-theoretic approaches. Regression analysis is implemented for prediction based on different fuzzy membership values of independent variables. We implement two concepts of game theory, the Nash equilibrium and the perfect Nash equilibrium. Implementing the Nash equilibrium, different equilibria values are generated and by implementing perfect Nash equilibrium, a subgame is generated to reach one equilibrium value. We have illustrated the proposed approach using a case study in which the linear regression approach is implemented to predict the patients’ arrival rate based on the monetary standard of the patient, communication facilities, patients curing chances, and patient choice towards the hospital, where these four features are quantified using fuzzy membership values. Nash equilibrium decides all possible ways of the nurses' allocations and perfect Nash equilibrium assist to reach an appropriate allocation. Thus, the hybridization of the regression approach, fuzzy membership and game theory approaches finalize the exact allocation of nurses. Finally, a comparative analysis is given to demonstrate the effectiveness of the proposed approach.