Healthcare delivery, even for outpatients, requires the use of expensive and many times scarce resources, which can range from physicians and nurses to MRI and dialysis machines. Therefore, it is essential that these resources are used efficiently, in a way they are highly utilized but are not overworked to the point of negatively impacting the quality of service or adding significant financial costs. At its core, this is a problem of matching patient demand with service supply. Just to illustrate the main idea, consider an outpatient clinic with a single physician. Patient demand is typically random and non-stationary and although service capacity is more or less fixed, there is some control over how many patients can be seen every day. For example, a clinic can work overtime with some additional cost or overbook patients and see more patients during regular working hours possibly in the expense of service quality. The clinic would also typically try to regulate the fluctuations in day-to-day patient demand by offering appointments in the future. However, while appointments help smooth out the demand, a very common problem is no-shows and no-shows, while depending on many factors, are typically more likely the longer the patients have to wait for their appointments to arrive. The question then is how the clinic should simultaneously decide what capacity to offer, how to schedule patients within a day, and how to schedule appointments into the future. Further complexities arise if one were to consider multiple providers working at the same clinic, patient preferences for appointment dates and times as well as providers and continuity of care, patients requiring multiple appointments (as in the case of physical therapy or dialysis) etc.

Kulkarni and Ziya, along with their graduate students, have been using discrete-time stochastic models and simulation to provide insights into these complex decision problems and develop methods that inform decision making in practice. They have primarily used queueing and Markov decision processes (MDPs). The complexity of the systems modeled led to MDPs having large state spaces and as a result the focus of their research has been to a large extent on the development of heuristic methods.  They have used simulation to test the results of their analysis and their proposed methods on models that are constructed using data from UNC outpatient clinics.

Students who have been involved in this research project include Aaron Ratcliffe (Masters student), Nan Liu, Jianzhe Luo, Yu Zhang, and Siyun Yu (Ph.D. students). If you are interested in being involved in this research project, please send an email to Kulkarni or Ziya for any potential opportunities.

Selected Publications:

1 – Liu, N, S. Ziya, V. G. Kulkarni, “Dynamic scheduling of outpatient appointments under patient no-shows and cancellations,” Manufacturing and Service Operations Management 12 (2010), 347-364.(supplement).

2 – Luo, J., V. G. Kulkarni, S. Ziya, “Appointment scheduling under patient no-shows and service interruptions,” Manufacturing and Service Operations Management, 14 (2012), 670-684. (supplement)

3 – Liu, N., S. Ziya, “Panel size and overbooking decisions for appointment-based services under patient no-shows,” Production and Operations Management, 23 (2014) 2209-2223. (supplement)

4 – Feldman, J., N. Liu, H. Topaloglu, S. Ziya, “Appointment scheduling under patient preference and no-show behavior,” Operations Research, 62 (2014) 794-811. (supplement)