Outpatient appointment scheduling with walk-ins in fixed arrival periods

Abstract

Abstract We study the problem of determining the optimal appointment scheduling decision in the presence of patient’s no-show behavior and random walk-ins arriving in a specified time window. We propose a two-stage optimization model to determine the optimal time window for the arrival of walk-ins and corresponding optimal appointment schedule for regular patients, to minimize the total cost of patients’ waiting time, and physician’s idleness and overtime. We demonstrate that the objective function for the first stage optimization problem is multimodular and propose a variable neighborhood descent (VND) algorithm to solve the proposed model. The VND algorithm performs well compared with some common local search algorithms. Our analysis suggests that the policy that stipulates an optimal time window for the arrival of walk-ins performs better than the general random walk-in arrival (open walk-in) policy when the arrival rate of walk-ins is moderate relative to the clinic’s capacity. In particular, utilizing the optimal time window policy can lead to a fair reduction in system cost and preservation of an increased level of patients’ access to care.