A two-stage stochastic programming approach for care providers' shift scheduling problems

Due to the importance of the health field, the problem of determining the shift scheduling of care providers has been addressed in many studies, and various methods have been proposed to solve it. Considering different skills and contracts for care providers is one of the essential issues in this field. Given the uncertainty in patients' demands, it is a crucial issue as to how to assign care providers to different shifts. One area facing this uncertainty is the provision of services to cancer patients. This study develops a stochastic programming model to account for patient demand uncertainty by considering different skills and contracts for care providers. In the first step, care providers are assigned to work shifts, then, in the second step, the required overtime hours are determined. The sample average approximation method is presented to determine an optimal schedule by minimizing care providers' regular and overtime costs with different contracts and skills. Then, the appropriate sample size is 100, determined based on the Monte Carlo and Latin Hypercube methods. In the following, the lower and upper bounds of the optimal solution are calculated. As the numerical results of the study show, the convergence of the lower and upper bounds of the optimal solution is obtained from the Latin Hypercube method. The best solution is equal to 189247.3 dollars and is achieved with a difference of 0.143% between the upper bound and lower bounds of the optimal solution. The Monte Carlo simulation method is used to validate the care provider program in the next stage. As shown, in the worst case, the value of the objective function is equal to 197480 dollars.