Scheduled patient encounters include primary and specialty care visits, as well as elective surgeries. In each of these environments, the process of scheduling appointments (assigning a specific time when the patient is scheduled to start receiving care) is different, which we will describe shortly
The goal of a welldesigned appointment system is to deliver timely and convenient access to health services for all patients. Appointment systems also smooth work flow, reduce crowding in waiting rooms and allow health systems to honor patient and provider preferences while matching supply and demand.
In the primary care setting, the vast majority of patients require services that can be performed within a fixed time length. Therefore, primary care clinics tend to divide available provider time into equallength time slots such that, by and large, patients’ needs can be accommodated in a standard appointment slot. For certain types of visits that require more time, clinics may assign multiple appointment slots. The appointment scheduling problem then reduces to that of finding a suitable match among the available time slots of providers in the clinic, provider prescribed restrictions on how available slots may be filled and patients’ preferences for day/time of week as well as for a particular service provider. (An example of provider restrictions on the use of available slots is the limit that many providers place on the number of physical exams or new patients that can be scheduled in any given session.) Still, the problem of matching supply and demand is not easy because different patients have different perceptions of the urgency of their need and different day-of-week and time-of-day preference patterns
2.1. Primary care appointments scheduling
Physicians divide their available clinic time into appointment slots, which are usually between 15 to 30 minutes long. In addition, providers determine the number of standard slots needed for each category of appointment request. Certain types of appointments, e.g., physical exams, require multiple slots. Other types, e.g., routine follow-up visits, require a single slot. Providers choose start and end times of their work schedule for each day over a pre-specified period of time (say 4 weeks) several weeks in advance of that time period. They also provide schedulers with any restrictions on how available slots may be assigned to incoming requests for appointments. For example, certain appointment slots are reserved each day for physical exams, which makes it easy for schedulers to find contiguous open slots needed for such appointments. This practice also helps physicians plan their day in advance.
Access rules in the primary care environment reserve certain slots exclusively for certain types of patients. Patient types could depend on medical urgency, type of service requested and on whether or not the patient belongs to the physician’s panel. For each physician, his/her panel consists of all those patients who have designated him/her as their PCP. Matching patients with their PCPs is important for continuity (quality) of care and for clinic efficiency because otherwise physicians’ end up spending more time reading medical histories of unfamiliar patients.
However, the implementation of Advanced Access systems remains a challenge because of a variety of reasons. First, even when providers work hard to absorb variations in daily demand, their ability to do so is limited. Therefore, it may not be possible to accommodate all appointment requests on the day they originate. This leads to demand spillover to a future day, limiting the clinic’s ability to meet that future day’s demand. Second, the true demand for same-day service is not captured by the appointments data because it is difficult to tell whether a patient actually preferred to book an appointment on a future date or (s)he did so because a same-day appointment was not available. This makes it difficult for clinic directors to determine approximately how much capacity should be available at the start of each day for that day’s demand. Third, in many clinics, different physicians’ panel compositions and sizes are significantly different, with the result that some physicians have fewer available slots to accommodate same-day demand.
Health service providers struggle to balance supply and demand. Achieving this balance is often difficult on account of the uncertainty in the patient arrival and service times, patient and provider preferences, punctuality, cancelations and no-shows. It is further complicated by the fact that patients’ needs for health services have varying degrees of urgency, and the decision-making process is often dynamic, i.e., some decisions about non-urgent patients must be made in advance of having complete information about urgent and emergency demand. Furthermore, the allocation of rewards and costs in health systems are such that the patient’s, the physician’s and the health system’s incentives may not be aligned. This leads to the additional complexity of deciding whose perspective is appropriate when designing appointment systems.
Late cancelations and no-shows are important in environments where capacity is tight or where no-shows and cancelations constitute a significant proportion of all appointments. The proportion of appointments affected by late cancelations and no-shows is low for clinics that largely serve patients with private insurance or Medicare patients. In contrast, clinics that serve under/uninsured populations, Medicaid recipients, or patients with mental health issues experience significant no-shows. No-shows are also positively correlated with the amount of time patients have to wait to get an appointment (Dove and Schneider, 1981). We discuss opportunities for future work on appointment scheduling with no-shows and cancelations in Section 5.2.
The Unit Process: In this case, booking requests are assumed to occur one at a time and at random time epochs. This corresponds to the situation where the mapped process is identical to the actual appointment-request arrival process. Booking requests can be for different types of services and of different urgency levels. The unit arrival process is commonly assumed for designing appointment systems for primary and specialty care environments.
3.2. The service process Service time requirements can be assumed to be either known (deterministic) or random. In some cases, such as for routine follow-up appointments at primary care clinics it may be reasonable to assume that service times are approximately deterministic. This is in part due the fact that PCPs can more easily influence the time they spend with a patient to fit within a fixed length of time. On the other hand, for some types of surgical procedures, service times can vary significantly from one patient to another. This gives rise to three types of modeling scenarios: constant service times, diagnosis dependent service times, and random service times. Random service times can be either identically distributed or diagnosis dependent. The delivery environments in which each type of service process is most commonly found are summarized in F
3.3. Patient and provider preferences Common examples of patient preferences are as follows. Some patients prefer an appointment on the day they call, or soon thereafter, and the day of the week or the time of the appointment is not particularly important to them. Others prefer a particular day of week and a convenient time. They do not mind waiting for convenience. Patients have different degrees of loyalty toward their designated PCP, or a particular specialist/surgeon. Some book appointments only with a particular provider, even when this leads to an inconvenient appointment time or extra waiting, whereas others switch easily to alternate providers. Providers also vary greatly in their practice styles. Some open up more capacity by double booking, working through lunch and working after hours to take care of urgent demand. Others adhere strictly to their daily schedules. Some place few, if any, restrictions on how their available time is used for appointments. Others have strict guidelines for the use of their time. For instance, many physicians restrict the number and timing of physical exams each day. Some surgeons require office visits and pre-operative evaluation for all referrals. Others may do so only for certain cases, based on medical histories. Hospital data show that surgeons prefer to perform surgeries on certain days of the week. For example, some prefer the first half of the week (Monday to Wednesday) and demand for OR time is typically greater earlier in the week.
The ability to model patient preferences is very important in the primary care setting. It is also important to match patients with their PCPs for continuity of care and revenue/cost considerations. In contrast, in some specialty clinics and surgery scheduling environments, provider preferences take on a greater significance, and patient expectations for scheduling flexibility are lower. Patients needs are often associated with a specific episode of care. Whether or not a patient seeks to be paired with a particular provider can vary significantly depending on the nature of the health service. As a result, in some cases, there is greater opportunity in the specialty care and surgery environments to control the match between supply and demand of appointments by pooling supply
Commonly used approaches fall into four categories: heuristics, simulation, queueing theory, and optimization (deterministic and stochastic). Heuristics are compared either in empirical studies or via computer simulation. The empirical approach is more common in the health services research literature than in the IE/OR literature.
Theme A: Single batch arrival process, random service times, no patient or provider preferences, and a costbased formulation that includes only the direct waiting cost. Theme B: Unit or periodic arrival process, random service times, no patient or provider preferences, and a costbased formulation that includes only direct waiting cost. Theme C: Unit arrival process, deterministic service times, patient and provider preferences, indirect waiting times, and a revenue-based (or cost-based) formulation.
Gupta and Wang (2008) model a primary care clinic’s problem of choosing which appointment requests to accept to maximize its revenue as a Markov Decision Process (MDP). (An equivalent formulation can be obtained in a cost-based setting as well.) They also model patient choices and show that when the clinic is served by a single physician, the optimal booking policy is a threshold policy under a normalformpatient-choice model. The class of normal-form choice models is large, intuitively appealing, and includes all of the commonly used models of discrete choice found in the IE/OR and Economics literatures. Membership in the normal-form class requires that the probability that a patient will select a particular available slot does not decrease when fewer other slots are available When the clinic has multiple doctors, patients may choose a more convenient time with a doctor other than their PCP. This makes the optimal policy more complicated because patient–PCP mismatch lowers physician and clinic revenues (O’Hare and Corlett, 2004). However, Gupta and Wang show that for each physician, there exist computable upper limits on the number of appointments that a clinic should book. These limits depend on: (i) the total number of booked slots in the clinic at the time of call; (ii) the number of booked slots of the physician with whom an appointment is requested; and (iii) on whether or not the requested appointment results in a patient–PCP mismatch. They use the bounds to develop heuristics for appointment booking control, which are tested and found to perform very well in simulation experiments based on real clinic data.
Whereas capacity reservation is also an important aspect of health care access management, there are important differences that make it difficult to simply “tweak” existing models to fit the needs of the health care industry. For example, of the various models suggested for airline RM, comparisons with the Expected Marginal Seat Revenue (EMSR) model (see, Belobaba (1989)) help to highlight the complexity of the health care scenario. In the two fare-class EMSR model, the optimal policy reserves a certain number of seats exclusively for higher fareclass customers. The lower fare-class customers are not allowed to book once a certain number of seats (equal to the booking limit) have been sold. The consumers’ trade-off is between buying a cheaper and inflexible ticket versus a more expensive ticket with greater flexibility. care applications, the patients’ choice function has more elements. A patient chooses a particular service provider (which determines service quality and clinic revenue), a particular day of week (service delay) and a particular appointment time (convenience). Prices are not used to control access to clinic capacity. Instead, clinics and physicians place restrictions on the availability of different slots to different types of patients. These features and the need to accommodate urgent demand make access control more difficult in health care applications; see Talluri and Van Ryzin (2004a) for recent efforts to model consumer choice in airline RM models.
Dynamic demand arrivals are typically not modeled in the machine scheduling context. Instead, the vast majority of work on machine scheduling assumes that the number of jobs to be scheduled is known. This amounts to the assumption of a single batch arrival process in the terminology introduced earlier in this paper. Thus, at best the machine scheduling literature is relevant for a subset of problems encountered in the health care setting. Finally, even though a certain pairing of jobs and machines may be preferred on account of setup and processing time efficiencies, jobs do not exercise their choice in this matter. This minimizes the possibility of independent and competing incentives which patients and providers often have in the health care setting. On account of these differences, research on machine scheduling does not translate directly to the health care setting. In fact, it is the authors’ hope that this paper will encourage new modeling effort to address the specific needs of the health care industry
The medical and IE/OR literature on late cancelations and no-shows (hereafter referred to as no-shows) falls into the following four categories: (i) articles that focus on estimating no-show rates and identifying correlations between no-show rates and patient characteristics (e.g., Dove and Schneider (1981)); (ii) articles that use clinic data to document the time and money effects of no-shows in outpatient clinics