Appointment scheduling with delay tolerance heterogeneity - WANG, Shuming (Institutional Knowledge at Singapore Management University, 2024)
In this study, we investigate an appointment sequencing and scheduling problem with heterogeneous user delay tolerances under service-time uncertainty. We aim to capture the delay-tolerance effect with heterogeneity, in an operationally effective and computationally tractable fashion, for the appointment scheduling problem. To this end, we first propose a Tolerance-Aware Delay (TAD) index that incorporates explicitly the user-tolerance information in delay evaluation. We show that the TAD index enjoys decision-theoretical rationale in terms of Tolerance Sensitivity, Monotonicity, Convexity and Positive Homogeneity, which enables it to incorporate the frequency and intensity of delays over the tolerance in a coherent manner. Specifically, the convexity of TAD index ensures a tractable modeling of the collective delay dissatisfaction in the appointment scheduling problem. Using the TAD index, we then develop an appointment model with known empirical service-time distribution that minimizes the overall tolerance-aware delays of all users. We analyze the impact of delay-tolerance on the sequence and schedule decisions, and show that the resultant TAD appointment model can be reformulated as a mixed-integer linear program (MILP). Furthermore, we extend the TAD appointment model by considering service-time ambiguity. In particular, we encode into the TAD index a moment ambiguity-set and a Wasserstein ambiguity-set, respectively. The former captures effectively the correlation among service-times across positions and user-types, while the latter captures directly the service-time data information. We show that both of the resultant TAD models under ambiguity can be reformulated as polynomial-sized mixed-integer conic programs (MICPs). Finally, we compare our TAD models with some existing counterpart approaches and the current practice using synthetic data and a case of real hospital data, respectively. Our results demonstrate the effectiveness of the TAD appointment models in capturing the user delay-tolerance with heterogeneity and mitigating the worst-case delays.