Equitable Appointment Scheduling at a Healthcare Clinic : A Data-Driven Markov Chain Approach

We develop an appointment scheduling model for a healthcare clinic that includes an upper bound on expected patient wait times. We refer to the schedule it produces as an equitable schedule. The operating environment of our focal clinic included three complicating features, all of which are addressed by our model: heterogeneous treatment times; significant no-show rates; stochastic patient arrival times. We show that using a fixed amount of time between patients, as done in many clinics, is a predictably poor method for managing equitable wait times. Instead, the spacing must be calculated sequentially depending on all previously scheduled treatment types. Using a simple discrete time Markov chain to model the state of the clinic, we show how to calculate the optimal spacing between patients. A schedule where the longest waits are reduced by 40-50% (and the average waits are reduced as well) is achievable by adding roughly 1%-2% to the minimum makespan produced by a traditional penalty cost model. Because the transition matrix is exceptionally sparse, our schedule can be computed exceptionally fast. If we assume patients arrive on time, it is computed in O(m^2n^2) (where m is the input length of the longest discrete treatment distribution and n is the number of patients). When patient arrivals are stochastic, it is computed in O(m^3n^2). This makes our approach effective as either a stand-alone model or embedded in a larger model as a numerical sub algorithm