Modeling Strategic Walk-in Patients in Appointment Systems: Equilibrium Behavior and Capacity Allocation

Abstract

We consider an outpatient clinic with strategic patients. Based on the level of available information, patients either take an appointment and wait until the appointment day or they select walk-in and eliminate the indirect waiting cost. Those patients who prefer walking-in face the risk of not receiving service if there are more walk-in patients than the available slots for walk-ins. Patients make their decision by taking other patients' choice into consideration. Considering the equilibrium behavior of patients, the clinic should determine the optimal number of slots reserved for walk-ins. We conduct our analysis under two different levels of information: un-observable (patients know expected waiting time only) and observable (patients know their exact waiting time). In each case, we investigate the optimal capacity reserved for advanced patients that minimizes the expected daily cost for the society, considering strategic customer case and comparing it to the centralized decision maker case. We show that for the un-observable case either all-appointment or all walk-in policy is optimal, while for the observable case no such structure exists. We also analyze value of information and coordination via numerical examples and show that providing waiting time information is most valuable for hybrid systems sharing capacity between walk-ins and advanced patients. We also show that not accounting for strategic behavior may lead to sub-optimal capacity allocation policy and increase costs.