A distributionally robust optimization approach for outpatient colonoscopy scheduling

We consider the outpatient colonoscopy scheduling problem, recognizing the impact of pre-procedure bowel preparation (prep) quality on the variability in colonoscopy duration. Data from a large academic medical center indicates that colonoscopy durations are bimodal, i.e., depending on the prep quality they can follow two different probability distributions, one for those with adequate prep and the other for those with inadequate prep. We therefore define a distributionally robust outpatient colonoscopy scheduling (DROCS) problem that seeks optimal appointment sequence and schedule to minimize the worst-case weighted expected sum of patient waiting, provider idling, and provider overtime, where the worst-case is taken over an ambiguity set (a family of distributions) characterized through the known mean and support of the prep quality and durations. We derive an equivalent mixed-integer linear programming formulation to solve DROCS. Finally, we present a case study based on extensive numerical experiments in which we draw several managerial insights into colonoscopy scheduling.