Reducing Disruptive Effects of Patient No-shows: A Scheduling Approach
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Appointment scheduling systems have been studied for nearly 60 years. From a decision making point of view, related problems can be classified into two categories: static and dynamic. In a static scheduling problem, all decisions are made before a clinic session starts; in a dynamic scheduling problem, the schedule of future arrivals is revised constantly during the clinic session. I categorize my problem as static. Within the research field of static appointment scheduling, little attention has been paid to patient no-show until the past decade. As an important aspect of patient arrival behaviors, the phenomenon of patient no-show has resulted in huge economic loss industry wide. I aim to explore static scheduling approaches to alleviate negative effects of patient no-show, with consideration of nonhomogeneous patients, overbooking, and nonconventional patient waiting cost structure. One primary contribution of this dissertation is a static analytical model I developed for the problem of scheduling patients to queues with consideration of quadratic patient waiting costs, nonhomogeneous patient no-show probabilities, and nonhomogeneous patient waiting cost ratios. By relaxing the assumptions of constant and identical no-show probabilities and waiting cost ratios, Hassin and Mendel's  model becomes a special case of my model. Another major contribution lies in my study on a set of heuristics that sequence patients based on their no-show probabilities. My numerical studies on three heuristics suggest scheduling patients with higher no-show probabilities in front of patients with lower no-show probabilities. It achieves best overall system performance as well as patient waiting performance. Last, I integrated the static model with a nonconventional overbooking strategy to formulate a problem with a hybrid overbooking model which not only determines number of patients to schedule but also determines scheduled inter-arrival times. It enables outpatients, inpatients, and emergency patients to be considered within a static scheduling environment. By comparing performances of three booking heuristics, I recommend scheduling inpatients first when no-show probability is low, while scheduling outpatients first when no-show probability is high. Patient waiting is reported to be an important index of patient satisfaction in various surveys. Almost all appointment scheduling studies assume a linear relationship between patient waiting cost and patient waiting time, which might not be correct. The waiting cost of a system with one patient waiting for 40 minutes is not equal to another one with 20 patients each waiting for 2 minutes . Furthermore, it also involves issues of goodwill, service, and "costs to the society", which place a value on patients' waiting time . Therefore, a nonlinear cost structure of patient waiting is desired. To control the complexity of target problems, a majority of the static scheduling literature assumes homogenous patients, which might be oversimplified. For the same amount of waiting time, waiting cost varies from one patient to another, due to various occupations held by different patients. Similarly, no-show probability needs to be patient specific as it's determined by various patient level attributes (Age, sex, marital status, income, appointment delay, etc.). I solve a static scheduling problem with patient no-show probability varied among patients. To represent the nonlinear nature of the relationship between waiting cost and patient waiting time, I formulate the objective function as a total of quadratic patient waiting cost and linear sever idle cost. By comparing it to a model with linear waiting cost, I find quadratic waiting cost may change my decision of sequencing patients when no-show probability is nonhomogeneous. I solve another problem with both patient no-show probability and patient waiting cost ratio varied among patients, and compare the performance of three no-show probability based booking heuristics: lower no-show first, higher no-show first, and higher no-show in the middle, with the purpose of providing simplified heuristics to medical scheduling practices. Next, I address a daily scheduling problem of allocating relatively flexible diagnostic capacities among three categories of patients: inpatients, who have low level of no-show probability and waiting cost ratio; outpatients, who have medium level of no-show probability and waiting cost ratio; and emergency patients, who usually show up as walk-in, with extremely high waiting cost ratio. To incorporate walk-in emergency patients into the model, I employ an overbooking strategy with server overtime allowed. The objective is to maximize system performance in terms of net revenue which consists of service revenue, server idle cost, patient waiting cost, and patient deny penalty cost. I analyze the model from three perspectives: behavior of optimal schedules, overall system performance, and customer experience. To make the model easy to apply, I analyze the model performances under three heuristic booking strategies: all outpatient, inpatient first and outpatient first, with three environmental factors (outpatient no-show probability, equipment hourly idle cost, and inpatient service fee) are varied. The system is found to perform better when server hourly idle cost is greater. This phenomenon is more significant when outpatient no-show probability is relatively low. For clinics which also schedule inpatients, I recommend using the inpatient first policy when outpatient no-show probability is low; and using outpatient first policy when outpatient no-show probability is high. To a certain extent, overbooking can alleviate the negative effects brought by patient no-show, but system performance still decreases as no-show probability increases.