This paper addresses a scheduling problem which handles urgent tasks along with
existing schedules. The uncertainty in this problem comes from random situations of
existing schedules and arrival of upcoming urgent tasks. To deal with the uncertainty,
this paper proposes a stochastic integer programming (SIP) based aggregated online
scheduling method. The method is illustrated through a study case from the outpatient
clinic block-wise scheduling system which is under a hybrid scheduling policy
combining regular far-in-advance policy and the open-access policy. The COVID-19
pandemic brings more challenges for the healthcare system including the fluctuations
of serving time, and increasing urgent requests which this paper is designed for. The
SIP model designed in the method can easily accommodate uncertainties of the
problems, such as: no-shows, cancellations and punctuality of previously scheduled
patients as well as random arrival and preference of new patients. To solve the SIP
model, the deterministic equivalent problem formulations are solved using the
proposed bound-based sampling method.