A Stochastic Optimization Approach for Staff Scheduling Decisions at Inpatient Clinics

Abstract

Staff scheduling is one of the most important challenges that every healthcare organization faces. Long wait times due to the lack of care providers, high salary costs, rigorous work regulations, decreasing workforce availability, and other similar difficulties make it necessary for healthcare decision-makers to pay special attention to this crucial part of their management activities. Staff scheduling decisions can be very difficult. At inpatient clinics, there is not always a good estimate of the demand for services and patients can be discharged at any given time, consequently affecting staff requirements. Moreover, there are many other unpredictable factors affecting the decision process. For example, various seasonal patterns or possible staff leaves due to sickness, vacations, etc. This research describes a solution approach for staff scheduling problems at inpatient clinics where demand for services and patient discharges are considered to be stochastic. The approach is comprehensive enough to be generalizable to a wide range of different inpatient settings with different staff requirements, patient types, and workplace regulations. We first classify patients into a number of patient groups with known care-provider requirements and then develop a predictive model that captures patients’ flow and arrivals for each patient category in the inpatient clinic. This model provides a prediction of the number of patients of each type on each specific day of the planning horizon. Our predictive modelling methodology is based on a Discrete Time Markov model with the number of patients of different types as the state of the system. The predictive model generates a potentially large set of possible scenarios for the system utilization over the planning horizon. We use Monte Carlo Simulation to generate samples of these scenarios and a well known Stochastic Optimization algorithm, called the Sample Average Approximation (SAA) to find a robust solution for the problem across all possible scenarios. The algorithm is linked with a Mixed-Integer Programming (MIP) model which seeks to find the optimal staff schedule over the planning horizon while ensuring maximum demand coverage and cost efficiency are achieved. To check the validity of the proposed approach, we simulated a number of scenarios for different inpatient clinics and evaluated the model’s performance for each of them.