Overbooking for physical examination considering late cancellation and set-resource relationship

Late cancellations of physical examination has severe impact on the operations of a physical examination center since it is often too late to fill vacancy. A booking control policy that considers overbooking is then one natural solution. Unlike appointment scheduling problems for clinics and hospitals, in which treating a patient mostly requires only one type of resource, a physical examination set typically requires multiple types of resources. Traditional methods that do not consider set-resource relationship thus may be inapplicable.

We formulate a stochastic mathematical programming model that maximizes the expected net reward, which is the examination revenue minus overage cost. A complete search algorithm and a greedy search algorithm are designed to search for optimal booking limits for all examination sets. To estimate the late cancellation probability for each individual consumer, we apply logistic regression to identify significant factors affecting the probability. After clustering is used to estimate individual probabilities, Monte Carlo simulation is conducted to generate probability distributions for the number of consumers without late cancellations. A discrete-event simulation is performance to evaluate the effectiveness of our proposed solution.

We collaborate with a leading physical examination center to collect real data to evaluate our proposed overbooking policies. We show that the proposed overbooking policy may significantly increase the expected net reward. Our simulation results also help us understand the impact of overbooking on the expected number of customers and expected overage. A sensitivity analysis is conducted to demonstrate that the benefit of overbooking is insensitive to the accuracy of cost estimation. A Pareto efficiency analysis gives practitioners suggestions regarding policy determination considering multiple performance indications.

Our proposed overbooking policies may greatly enhance the overall performance of a physical examination center.