A Two-Stage Method of Dimensioning and Scheduling Service Providers under Patient Demand Uncertainty

Many researchers have studied the problem of dimensioning service providers and making shift schedules and have proposed various methods to solve it. Considering the importance and complexity of health care, this research is conducted through the integrated dimensioning and scheduling of service providers under patient demand uncertainty. In the first stage, a robust approach is adopted to determine the minimum number of required service providers. In the second stage, a monthly schedule is devised for service providers, and a two-stage stochastic program is used to solve the problem. To this end, an improved sample average approximation method considers different contracts and skills to determine a near-optimal schedule by minimizing the service providers' regular working hours, overtime, and penalties for idle hours. In the first stage, considering the highest level of conservatism, equal to 7.6, a 19.38% cost increase is created compared to the nominal problem. In the second stage, by applying different clustering methods in the SAA algorithm and comparing them, the k-means++ algorithm obtains a good upper and lower bound and achieves a near-optimal solution in the shortest time. This research deals with the Iranian Health Control Center as a case study. The proposed method can yield the appropriate number of service providers based on monthly workloads and make the least undesirable schedules for service providers. Hence, managers can overcome patient issues' uncertainty by assigning various service providers to each scheduling period.