A robust optimization approach for the Advanced Scheduling Problem with uncertain surgery duration in Operating Room Planning - an extended analysis

We consider the Advanced Scheduling Problem (ASP) in the operating room block scheduling, taking into account stochastic patient surgery duration. A surgery waiting list, a set of Operating Room (OR) blocks, and a planning horizon are given. The problem herein addressed is to determine the subset of patients to be scheduled in the considered time horizon and their assignment to the available OR blocks. The problem aims at minimizing a measure of the waiting time of the patients. To this purpose, we introduce a penalty function associated to waiting time, urgency and tardiness of patients. We propose a robust optimization model to solve the ASP with uncertain surgery durations. The proposed approach does not need to generate a set of scenarios, and guarantees that solutions remain feasible for some variations of the surgery length parameters. We solve the problem on a set of real-based instances to test the behavior of the proposed model. The solution quality is evaluated with regards to the number of patients operated and their tardiness. Furthermore, assuming lognormal distribution for the surgery times, we use a set of randomly generated scenarios in order to assess the performance of the solutions in terms of OR utilization rate and number of cancelled patients.