THE SURGICAL SCHEDULING PROBLEM:
CURRENT RESEARCH AND FUTURE OPPORTUNITIES
Jerrold H. May
The Joseph M Katz Graduate School of Business
University of Pittsburgh
Pittsburgh, PA 15260
William E. Spangler
Palumbo-Donahue School of Business
Pittsburgh, PA 15282
David P. Strum
Department of Anesthesiology and Critical Care
Hospital of the University of Pennsylvania
Philadelphia, PA 19104-4283
Luis G. Vargas
The Joseph M Katz Graduate School of Business
University of Pittsburgh
Pittsburgh, PA 15260
THE SURGICAL SCHEDULING PROBLEM:
CURRENT RESEARCH AND FUTURE OPPORTUNITIES
This article reviews the general problem of surgical scheduling. We organize the literature
based on the time-frame or planning horizon of the schedule into six categories: capacity planning,
process reengineering/ redesign, the surgical services portfolio, procedure duration estimation,
schedule construction, and schedule execution, monitoring and control. We survey past work and
suggest topics for potential future research in each of those areas.
Keywords: surgical scheduling, resource planning
1. INTRODUCTION AND MOTIVATION
Research indicates that of the three major clinical components comprising the health care
system (surgical, medical, and mental health), surgical services is the one most amenable to cost
control by a systematic process of utilization review (Wickizer 1991). According to the National
Heart, Blood, Lung Institute (Mangano 2004) more than 33 million US residents undergo surgery
annually, incurring charges of more than $450 billion, or nearly 10 percent of the entire health care
budget. Integrated scheduling systems are critical to cost containment and collaboration, particularly
with regard to hospital expenditures (Forum 2002). While the actual expenditures for operating
room (ORs) of differently sized hospitals operations is not known with certainty, some estimates
suggest that ORs account for 10 to 30 percent of total hospital expenditures, meaning that hospitals
in the US spend between $30 and $90 billion annually on ORs. These figures indicate that surgical
facilities within hospitals and surgical centers are one of the most costly functional areas in the
We define the surgical scheduling problem as the selection of procedures to be performed,
the allocation of resource time to those procedures, and the sequencing of the procedures within the
allocated time. Resource time includes the surgeons’ time, including block time (an interval of time
over which an individual surgeon or a surgical practice has scheduling control) and the operating
room time. Brick-and-mortar decisions (such as how many operating rooms to construct), as well as
staff scheduling for support personnel (such as anesthesiologists and nurses), constrain and interact
with surgical scheduling, but we view them as being driven by surgical scheduling rather than driving
As expense centers, ORs must be scheduled and run efficiently because they impact on the
financial health of the institution as a whole. Some authors therefore believe that surgical facilities
are similar to other competitive business enterprises, in that they need to be able to deliver services
at a competitive advantage (Gabel et al. 1999). In their view, administrators are required to
determine whether or not a surgical facility is competitive, and if it is not, what actions can be taken
to make it competitive. The former requires the assessment of the current performance of the OR
suites. The latter requires the use of scheduling methods to efficiently manage the resources
available. To be competitive, surgical facilities need to address several problems: (1) How to select
patients to be scheduled for surgery on a given day; (2) How to schedule and sequence patients
according to certain criteria, such as minimizing the number of ORs used; and (3) How to measure
the quality of the schedule. The need for competitiveness may be more typical in the US hospital
environment than it is in a more centralized payer situation such as in Canada (see for example (Pink
and Leatt 1991)).
Admissions rates, OR utilization, and the hospital census depend on a mix of surgical
specialties and unimpeded access to surgical facilities (Stewart 1971). There are two competing and
potentially conflicting goals in the process of implementing an OR schedule: (1) To meet the
demands of surgeons for access to the ORs at suitable times; and (2) To serve the institution’s need
for conserving resources such as people and space, i.e., the schedule should be able to accommodate
as many cases as possible and open only as many ORs as necessary. The complications that may
arise from those two objectives are exacerbated by the type of insurance patients may have.
2. THE SURGICAL SCHEDULING PROCESS
The surgical scheduling process is composed of several problems, which can be defined
based on the time frame or planning horizon they consider. The process entails each of the
decisions required by various stakeholders, including hospital administrators and surgeons (and their
agents), to create and/or upgrade facilities (long term), to allocate surgical time blocks to surgeons
(medium term), to allocate patients to days and times within blocks (short term), to make last minute
adjustments (very short term) and to execute the schedule (contemporaneous), as shown in Table 1.
Very long term decisions, typically performed over a time horizon of 12 to 60 months,
primarily address the issues of capacity planning and allocation, and therefore constrain decisions
that can be made in the medium- and short term. Capacity planning is closely linked to the overall
strategic planning of the institution, including the identification of target markets and customers, the
funding and construction of new facilities, and the reallocation or repurposing of existing facilities.
We do not include such capacity planning problems as part of surgical scheduling, although they
clearly impact what can be done in surgical scheduling.
Table 1. Time horizons involved with the surgical scheduling problem
How far in
Examples of issues to be addressed
(5.1), process re-
How many ORs to construct, layout of
(5.1), Process re-
Patient flow patterns, selection of
surgical providers, block assignment
Few weeks - 6
Staff assignment and scheduling
few days - few
Procedures assigned to ORs (particular
days, parts of days), number of ORs
needed are determined
Last-minute scheduling into released
unused block time; determining ORs to
be opened; start times
Assignment and scheduling of emergency
procedures; reassignment of ORs and
rescheduling of start times as a result of
emergencies, patient no-shows,
cancellations, staff availability, and
procedures taking more or less time than
Once facilities are in place, the surgical scheduling process begins with long term decision
making, typically with a 6 to 12 month planning horizon, which involves allocating specific blocks of
time available within facilities to specialties or to individual surgeons. After the block assignments
are in place, the medium term process of staff assignment and scheduling can take place. A short
term surgical schedule, which is developed anywhere from a few days to a few weeks prior to the
surgery, consists of a set of procedures whose duration is not known with certainty, and a set of
ORs to which they are assigned, satisfying some constraints with respect to the surgeons availability,
room preference (if any), and the type of OR in which the procedure can be performed.
The goal of short term OR scheduling is a predictable workload with adequate time for
emergencies. Among other things, that means the joint and timely meeting of the surgeon,
anesthesiologist, nursing staff, surgical suite, supplies, and special equipment. As noted above, once
a time slot in a particular surgical suite is selected, the use of an inappropriate scheduling
methodology, one that does not permit the timely performance of the procedure, can adversely
impact the availability of the resources necessary to perform the procedure (Hancock et al. 1988).
The very short term perspective is a monitoring and control problem in which the schedule
is referenced and often modified on-the-fly as the inherent variability of the surgical environment
come into play. Once the day starts, it is rare that the schedule remains unchanged. In fact,
deviations from the schedule occur frequently and people expect them to happen.
Surgical scheduling differs significantly from traditional shop-floor scheduling, and so it
requires its own methodologies. Surgical schedules are plans, but are almost never implementable as
designed because (1) emergency cases occur; (2) surgeons do not always know in advance all the
procedures that must be performed on a scheduled patient, such as when the patient undergoes
exploratory surgery or when unexpected findings occur during surgery, the time required to treat the
patient may be much longer than expected, delaying subsequent patients, or much shorter than
expected, possibly creating a hole in the schedule; and (3) even in cases where all procedures are
known with certainty in advance, the time necessary to perform those procedures may vary
significantly, due to characteristics of the operation, the surgical team, and the patient (Eijkemans et
al. 2010, Strum et al. 2000). Although machine scheduling often assumes that an individual operator
works on a large number of jobs per day, common surgical procedures, such as coronary bypass,
require about 4 to 5 hours of surgical time, and thus the surgical team may do only one or two such
procedures in a day. Furthermore, surgery is a non-preemptive activity. The largest variability in the
process occurs during the surgery itself, as opposed to the pre- or post-surgical activities.
The typical script for a patient’s surgical procedure proceeds as follows. In the pre-surgical
phase, the patient arrives at the surgical facility, a nursing history is obtained, the laboratory data are
checked, and the patient is dressed for the procedure. When anesthesia, nursing, and surgery are
ready, the patient is transported to the scheduled operating site and is moved to the operating table,
monitored, and anesthetized.
Post-surgery, the patient is transported to the post-anesthesia care unit, where he/she
recovers before being either moved to a bed at a facility or discharged home. A small number of
patients are sufficiently ill to require admission to an intensive care unit (ICU) following surgery.
The surgery and anesthesia teams make such admission decisions together, and are responsible for
arranging reservations and admissions. Anesthesia must notify the ICU and arrange for beds,
equipment, and personnel prior to the move. In some instances, the patient is taken to the post-
anesthesia care unit and later moved to the ICU.
Several problems may prevent the smooth progression of patients through the system.
These include, but are not limited to, late arrivals of patients or medical records, delays in support
services, acute onset of abnormal medical conditions (infections, chest pain, etc.) requiring delay or
cancellation, inaccurate or inappropriate reservations, lack of a mechanism to enable dynamic
scheduling, and delays that result in lost professional time. These and other problems lead to
variability in the demand for services. As McManus et al. argue:
“…improving the healthcare system’s response to variability represents an
opportunity for simultaneous gains in effective capacity, cost-efficiency, improved
outcomes, and patient satisfaction. A precondition to such improvement, however, is
a deeper understanding of the nature and sources of variation in demand. Without
such understanding and appropriate management of variability, systems such as
healthcare organizations become inefficient, overwhelmed, and frustrating for all.”
(McManus et al. 2003)
3. SURGICAL SCHEDULING
We note that while surgical scheduling often presumes a focus on inpatient procedures,
outpatient surgical scheduling is an important and growing component of surgical scheduling. The
surgical process itself is the same for both inpatients and outpatients. They are both concerned with
the task of setting planned start times when the surgical procedure duration is stochastic. The two
primary differences between surgical inpatients and surgical outpatients are that (1) surgical
inpatients arrive from a hospital ward, so that their arrival is almost certain, whereas surgical
outpatients arrive from outside the hospital, so they may arrive late or fail to arrive (Basson and
Butler 2006), and (2) surgical inpatients return to a hospital ward after the recovery process, whereas
surgical outpatients usually are discharged home the same day as the procedure is performed.
Patients who undergo outpatient surgery may require return visits to the facility with a higher
probability than those patients who have surgery performed on an inpatient basis, for reasons
related to 1) the procedure performed (Coley et al. 2002), 2) the specific characteristics of the
patient, such as the patient’s age and the presence of specific diseases (Fleisher et al. 2007), and 3)
the medical and anesthetic complexity of the case (Dexter et al. 2002b). Therefore, a scheduling
system for an outpatient surgical system may need to be linked to a scheduling system for return
visits. Bowers and Mould (Bowers and Mould 2005) studied the problem of deciding what types of
patients should be served at an ambulatory center. They also analyzed the effect of that decision on
the use of the facilities, and how to allocate capacity between same-day patients and inpatients.
Because the trend toward increasing ambulatory surgery is still evolving, the number of technical
papers in this area is relatively small. The methodologies employed vary from statistical analysis of
data to newer algorithmic techniques, such as simulated annealing. In this paper, we discuss
outpatient surgical scheduling within the context of a broader classification framework, as outlined
in the sections below.
4. PREVIOUS SURVEYS
The past few decades have seen a number of literature surveys pertaining to surgical
scheduling, many of which have characterized the problem in terms of the timeframe considerations
mentioned in the previous section. Magerlein and Martin, for example, organized surgical
scheduling in terms of two processes: advance scheduling, in which patients are given appointments
for a surgical procedure on a particular day, and allocation scheduling, in which the specific sequence
of cases for a particular OR is determined (Magerlain and Martin 1978). In this regard, advance and
allocation scheduling generally correspond to what we term short term and very short term
problems, respectively. Przasnyski’s review of the literature focused on issues of planning, cost
control, utilization, assignment of procedures to OR, and resource management (Przasnyski 1986).
Again, each of these can be characterized with regard to timeframe; in this case, long-, medium-,
short-, and very short term. Blake and Carter combined the Magerlein and Martin dichotomy with
Kennedy’s three-level classification of surgical scheduling problems into strategic, tactical, and
operational levels (Kennedy 1992), while also explicitly addressing external resources necessary to
support surgery at all levels of decision making (Blake and Carter 1997). As such, they framed
surgical scheduling across the entire spectrum from very long term to very short term problems.
Gupta addressed long-, medium-, short- and very short term scheduling by focusing on three aspects
of the problem: 1) Allocation of capacity (i.e., assigning block time) either after expanding capacity
or as a periodic reallocation of existing capacity; 2) Management of elective surgical bookings; and 3)
Optimal sequencing of procedures in an OR (Gupta 2007). Cardoen et al. (2010) present a very
structured framework for classifying papers published since 2000 that explicitly incorporate both
planning and scheduling along six dimensions: Patient characteristics, performance measures,
decision delineation, research methodology, uncertainty, and applicability of research.
This survey updates the previous reviews in the context of a timeframe-based classification
scheme, and extends them by expanding the scope to encompass a number of emerging areas that
have become increasingly critical in the scheduling and management of surgical services. These
areas include process reengineering/redesign, and day-of-surgery scheduling/rescheduling. We also
note that in focusing on those areas, we necessarily emphasize certain areas and deemphasize others.
For example, this review focuses on the various methodologies used to study each area, including
statistical analysis, optimization techniques, simulation, queuing models, inventory theory, data
mining, and artificial intelligence models. Conversely, while human factors and behavioral
considerations are important in schedule construction and execution, we do not consider them in
this review because the methodologies employed are significantly different from the more traditional
management science studies that are of primary interest to the readers of this journal.
5. THE CURRENT STATE OF THE RESEARCH LITERATURE
Although research in surgical scheduling can be classified in numerous ways, we employ two
primary dimensions to define each application: 1) the time horizon to which the results apply and 2)
the specific problem domain studied. Certain problems such as determining the total number of
ORs in a hospital (i.e., capacity planning) are only meaningful in a time horizon that permits the
addition of such rooms. However, other problems, such as scheduling, procedure duration
estimation, and patient selection, tend to transcend time horizons and thus require a multi-
dimensional perspective that considers both the time dimension as well as the problem domain. In
this review, we classify each problem domain within the context of its associated time dimension(s),
as described in Table 1, while also indicating, where appropriate, the specific methodologies used to
study the problem. The methodologies range from statistical analysis to optimization techniques,
simulation, queuing models, inventory theory, data mining, and artificial intelligence models.
Within this context, the classification scheme that follows presents the problem areas along a
time dimension extending generally from long term to contemporaneous, as follows: 1) Capacity
planning (very long term through medium term); 2) Process reengineering/ redesign (very long term
through long term); 3) The surgical services portfolio (long term); 4) Procedure duration estimation
(long term through medium term); 5) Schedule construction (short term through very short term);
and 6) Schedule execution, monitoring and control (contemporaneous). We examine each in the
5.1 Capacity planning
As a long term issue, capacity affects the constraints that limit scheduling decisions, and
many studies simultaneously address both capacity and scheduling. Capacity has three components:
(1) Physical (bricks/mortar), meaning the number of rooms and their equipment, constraining the
number of simultaneous procedures and the types of procedures that can be performed (not
included in this survey); (2) Human resource, meaning the number and type of surgical practices,
anesthesiologists, and other OR staff available, affecting the type and number of procedures that can
be performed in the equipped rooms (also not included in this survey); and (3) Resource availability,
meaning the number of hours the ORs are open and how those hours are parceled out. Although
some papers do consider the ‘parceling out’ and perhaps the ‘time allocation’ part of (3) as
scheduling, the term ‘scheduling’ generally is applied only to case scheduling, the assignment of
patients after all three capacity decisions have been made. Some of the papers address staff
scheduling, which allocates and schedules hospital staff.
On a strategic level, Dexter et al. explored the allocation of OR time at facilities where the
strategic decision had been made to increase the number of ORs. They noted that allocation
typically occurs in two stages: a long term tactical stage, followed by a short term operational stage
(Dexter et al. 2005a). Dexter and O’Neill studied the use of a specific technique, data envelopment
analysis (DEA), in several contexts pertaining to capacity expansion, workload, and external
competition, including the development and implementation of a method to measure market
capture of elective inpatient surgery (Dexter and O’Neill 2004; O'Neill and Dexter 2004).
Subsequently, they conducted a case study showing how results of DEA are linked to financial
analysis for purposes of deciding which surgical specialties should be provided more resources and
institutional support (O'Neill and Dexter 2007).
Other capacity-related issues are shorter-term and tactical. In a review of the literature on
decision making for expansion of OR capacity, Wachtel and Dexter noted that the choice of surgical
subspecialties to receive additional block time and fill the additional OR capacity is a tactical
decision, made approximately once a year (Wachtel and Dexter 2008). Exploring cost reduction,
operating suite utilization, and capacity planning in surgical services, Strum et al. described capacity
planning (optimizing surgical subspecialty block time allotments) using a minimal cost analysis
(MCA) model (Strum et al. 1997b). Dexter et al. employed time-series analysis to predict the total
hours of elective cases performed by a surgical group using data from surgical services information
systems (Dexter et al. 1999b). Strum et al. developed a newsvendor model for measuring operating
suite utilization, analyzing the quality of surgical schedules, and allocating surgical suite budgets
(capacity planning) (Strum et al. 1997b). Blake et al. reported a hospital’s experience using integer
programming to solve the problem of developing a consistent schedule that minimizes the shortfall
between each group’s target and actual assignment of OR time (Blake et al. 2002). Blake and
Donald used an integer-programming model and a post-solution heuristic to allocate OR time to the
five surgical divisions at Toronto’s Mount Sinai Hospital (Blake and Donald 2002).
McIntosh et al. studied the impact of service-specific staffing, case scheduling, turnovers,
and first-case starts on anesthesia group and operating room productivity and found that the most
important step at most facilities is to allocate OR time (i.e., plan service-specific staffing)
approximately 2–3 months before the day of surgery (McIntosh et al. 2006). Epstein and Dexter
recommend that 9 to 12 months of data be used when using a statistical method for adjusting
staffing on a quarterly basis, (Epstein and Dexter 2000). They also noted that moderate uncertainty
in knowing the actual OR in which cases were performed – i.e., up to a 30% uncertainty – had only
a minor effect on OR allocations (Epstein and Dexter 2002).
Van Oostrum et al. specifically addressed the issue of OR scheduling at the tactical level of
hospital planning and control, by modeling the construction of cyclic OR schedules as a
mathematical program containing probabilistic constraints (van Oostrum et al. 2008). Zhang et al.
developed a methodology for allocating OR capacity to specialties consisting of a finite-horizon
mixed integer programming model which determines a weekly OR allocation template that
minimizes inpatients' cost measured as their length of stay (Zhang et al. 2009). Belien and
Demeulemeester proposed and evaluated a number of models, including mixed integer
programming based heuristics, for building surgery schedules with leveled resulting bed occupancy
(Belien and Demeulemeester 2007).
Methodologically, the consensus of the current literature appears to be focused on relying on
simulation modeling for capacity planning; see, for example, VanBerkel and Blake (2007) and
Vermeulen et al. (2009). A potential research focus might be on the development of accurate and
representative simulation models that can be used over a medium to long term planning horizon. In
order to support medium and long term capacity planning, reliable forecasts of surgical demand are
desirable. Strum et al. (2008), for example, use Slepian functions to decompose historical surgical
demand data into a variety of cycles, resulting in a more accurate representation of the demand
patterns. The improved representation may be used to construct more accurate forecasts, which
better support capacity planning models.
5.2 Process reengineering/redesign
Modern approaches to scheduling in many environments consider how to redesign
processes to improve performance, rather than simply how to schedule to make the best use of a
fixed configuration of resources. Research in this area includes physical redesign of operating suites,
such as adding induction rooms, so that parallel processing of patients may be possible in some
circumstances (a longer-term problem), as well as alternatives such as inserting idle time buffers in
schedules so that subsequent procedures are more likely to begin promptly (a shorter-term
problem). Further consideration of flexible manufacturing techniques and methodologies, to
maximize the throughput, minimize the makespan, and achieve resource load balancing, may prove
to be fruitful.
Several papers discuss changes in the layout of the physical resources used for surgery or in
the way patients travel through those resources. A number of papers have explored overlapping and
concurrent anesthesia induction processes. Hanss et al. studied the use of overlapping induction,
finding that it shortened the time of care of regularly scheduled cases, increased the number of cases
performed within OR block time, and decreased nonsurgical time, turnover time, and anesthesia
control time plus turnover time (Hanss et al. 2005). Torkki et al. also reported that overlapping (or
concurrent) induction increased turnover, in this case allowing one additional case to be performed
during the 7-hour working day (Torkki et al. 2005). Sokal et al. used statistical and mathematical
models to develop a system consisting of three parallel processing ORs (concurrent induction and
turnover) with a dedicated three-bed, mini–post-anesthesia care unit (Sokal et al. 2006). Torkki et al.
explored the effects of a process management approach to trauma patient care, with the goal of
reducing the waiting times and increasing the efficiency of the hospital (Torkki et al. 2006). Their
approach followed the Plan-Do-Check-Act cycle and was based on statistical analysis of specific
performance metrics. Stahl studied learning and adaptation to a new system of surgical technologies
and perioperative processes, measuring patient wait time, flow time, and surgery procedure time
(Stahl et al. 2007). Other studies have focused on the use of a) workflow analysis and redesign to
reduce operating turnover time (Cendan and Good 2006) and OR throughput (Sandberg et al. 2005),
b) employment of regional block teams in an orthopedic OR (Eappen et al. 2007), and c) case
sequencing to reduce PACU and OR holding area staffing requirements (Marcon and Dexter 2007).
Redesigning human resource capacity includes changing the mix of surgeons and staff.
Dexter, Lubarsky and Blake explored allocation of resources to surgeons from a financial accounting
perspective, and determined the mix of surgeons’ OR time allocations that would maximize the
contribution margin or minimize variable costs (Dexter et al. 2002a). Belien and Demeulemeester
developed a model to integrate both the nurse and the operating room scheduling process, and
employed the model in developing cost-efficient nurse and surgery schedules (Belien and
Demeulemeester 2008). Exploring whether a facility can accurately estimate the average block time
utilizations of individual surgeons performing low volumes of cases, Dexter et al. concluded that OR
allocations be based on criteria other than only OR utilization, such as OR efficiency (Dexter et al.
2003c). van Ackere (van Ackere 1990) modeled the scheduling process as a game between the
surgeon (the agent) and the scheduler (the principal). Truong et al. (Truong et al. 1996) studied the
causes for late surgical starts and found that only modest improvements can be achieved without
cooperation from surgeons and anesthetists to arrive promptly.
The third capacity component that may be re-engineered is resource availability. Noting that
scheduling a delay between two surgeons’ cases will improve the likelihood that the second
surgeon’s case(s) will start on time, Dexter, Traub and Lebowitz showed that the mathematics of
calculating a scheduled delay between the different surgeons’ cases in the same OR on the same day
entails calculating an upper prediction bound for the duration of the second surgeon’s case(s)
(Dexter et al. 2001). Subsequently, Dexter and colleagues investigated whether moving the last case
of the day from one OR to another could increase OR efficiency (Dexter et al. 2003a). Wachtel and
Dexter compared several possible interventions, and found that creating an auxiliary schedule in
addition to the posted one resulted in the most significant improvement in overall tardiness
(Wachtel and Dexter 2009).
Bhattacharyya et al. found that having an unbooked orthopedic trauma OR reduces
nighttime cases and improves OR flow (Bhattacharyya et al. 2004). Wullink et al found that
reserving capacity for emergency surgery in elective ORs, as opposed to a dedicated emergency OR,
led to an improvement in waiting times for emergency surgery, a reduction in overtime, and an
increase in OR utilization (Wullink et al. 2007). Using a case study from a university hospital in
Finland, Karvonen et al. found that change in a queuing system for open heart surgery, from a
single first-in-first-out queue to a double-queue scheduling system, significantly increased available
capacity (Karvonen et al. 2004).
The information systems requirements for monitoring and control of surgical operations
pose problems that, to some extent, are shared with other disciplines, but nevertheless do not appear
to have been adequately addressed in this field. They include:
Determining overall information requirements, including the content, accuracy and timing of
information flows, from a systems theoretic perspective,
Exploring the use of flexible manufacturing techniques and methodologies in order to
maximize throughput and balance case processing,
Determining the information collection, analysis and communication requirements of the
system and its components. These include: system status tracking, establishing sampling
rates, determining trigger levels for interventions, and determining the criteria and strategies
for replanning based on system information,
Testing the utility of information systems in providing data for use in determining revenues
Building and testing information systems for use in real-time, situation-based replanning and
schedule modification, including the use of data mining of historical data and pattern-
matching on real-time events, and
Exploring the use of leading-edge technologies, such as radio-frequency identification
(RFID), to collect, track and store data.
5.3 The surgical services portfolio
With the pressures of managed care, hospitals must be sensitive to the revenue implications
of their surgical services portfolio. The surgical procedures performed by the portfolio of selected
providers may be determined by competitive and other environmental factors, and influence the
types of patients selected for those procedures (Wachtel and Dexter 2004; Wachtel et al. 2005;
Dexter et al. 2005c). This requires a careful balancing of interests. On the one hand, because
health care institutions should not deny care to a person in need or to an emergency patient, revenue
management tools need to be applied carefully in surgical services. On the other hand, hospitals
may wish to use their scheduling systems to attract desirable surgical practices and patient groups, so
as to achieve particular financial goals. Note that because most patients go to hospitals or
ambulatory centers where their surgeons practice (Wilson et al. 2007), revenue management studies
might need to focus on surgical practices because surgeons, rather than patients, are the hospital’s
primary customers. For example, Kuo et al. used a linear programming technique to optimize
allocation of OR time among a group of surgeons based on professional fee generation (Kuo et al.
Hospitals choose the mix of surgical providers they wish to host by their very long term (1-5
years) and long term (6-12 months) capacity decisions. Exploring patient selection from a longer-
term, strategic perspective, Wachtel and Dexter used a statewide discharge abstract database to
quantify physiologically complex operative procedures performed throughout Iowa in patients aged
80 and older during January through June 2001 (Wachtel and Dexter 2004). Dexter et al. used
inpatient and outpatient data to create market segments consisting of hierarchical combinations of
surgical procedure, then type of payer, and then location of patients’ residences (Dexter et al. 2005c).
They determined the competitive effect of one hospital’s caseload for a given surgical specialty on
the caseload of another hospital from the numbers of patients in each segment.
From a shorter-term, tactical perspective, Gerchak et al. used a stochastic dynamic
programming model to determine the number of additional requests for elective surgery to assign at
the start of a day, so as not to exceed available capacity for the day (Gerchak et al. 1996). Adan and
Vissers studied the mix of patients admitted to a hospital, noting that different categories of patients
within a specialty can be distinguished by their requirements for resources (Adan and Vissers 2002).
They developed a methodology and an integer programming model to generate an admission profile
for a specialty. Vissers et al. further considered the mix of patients in exploring the problem of
cardiothoracic surgery planning involving different resources such as OR time, medium care beds,
intensive care beds and nursing staff (Vissers et al. 2005). They used a master OR schedule to
develop a mixed integer model for the tactical level planning problem of deriving a weekly OR plan.
As noted, the area of portfolio and revenue management – including the related sub-areas of
capacity planning, procedure duration estimation, patient selection and hospital admissions –
contains a number of largely unexplored problems and opportunities for further research.
Opportunities exist to build models connecting long-range capacity planning, forecasting, planning
horizon problems with strategic planning and prioritization. Further opportunities exist for
designing, building and testing medium- and short term models, including game theory and other
economic models, in order to achieve the following objectives:
Establishing surgical services pricing levels,
Estimating the costs of procedures, in part based on better models of procedure durations
and other cost factors,
Selecting surgeons based on their potential contribution margin,
Assigning new time blocks to surgeons or time blocks to new surgeons,
Selecting and scheduling patients within time blocks, in consideration of the uncertainty
regarding revenue potential for each patient a priori, and
Determining the economic feasibility of allowing patients to be self-selecting.
5.4 Procedure duration estimation
In order to apply management science scheduling techniques to case scheduling, accurate
time estimation is essential. However, surgical scheduling is complicated by the fact that even if the
procedures to be performed on a particular patient were known with certainty in advance, and they
often are not, the time necessary to perform the procedures would also be uncertain. Nevertheless,
accurate time estimation would permit case scheduling with fixed start times, as opposed to “to
follow”, permitting optimizing and optimum-seeking scheduling and sequencing approaches to
propose solutions with more efficient use of surgical suites, higher productivity, and lower labor
While the process of estimating procedure durations tends to utilize historical data over an
extended period of time, the impact of those estimates affects scheduling across multiple
timeframes. Specifically, estimates of procedure times potentially can impact the allocation of block
time (long term), staff assignment and scheduling (medium term) the assignment of procedures to
blocks (short term), the allocation of procedures to unused block segments and the determination of
start times (very short term), and the assignment and scheduling of emergency procedures
(contemporaneous). Procedure times tend to follow a probability distribution, with evidence from
historical data indicating that the lognormal distribution best fits the data (May et al. 2000).
Differences among patients and among surgeons result in variability in surgical times, even for the
same procedure (Strum et al. 1999b; Strum et al. 2000). Point estimates are typically used, but the
type of point estimate recommended depends on the decision to be made (Dexter et al. 2004;
Dexter and Ledolter 2005; Dexter et al. 2007a).
The work cited above focuses on time estimation for a single surgery, typically one that
involves only one surgical procedure (the operation is described by a singe CPT code). For
scheduling purposes, it is important to be able to estimate the duration of: 1) an entire time block
that was assigned to a single provider, 2) an entire surgical day in a single operating room, and 3) the
entire surgical day across all of the operating rooms. The literature suggests that a two or three
parameter lognormal distribution is the better model for modeling the time of a single surgical
procedure, so that the time required for a series of procedures might be modeled by the sum of
lognormal distributions, each with different parameters. The times for a series of consecutive
procedures performed by a single surgeon or team are likely to be dependent, because one
procedure done more slowly than normal due to fatigue is likely to be followed by another
procedure, also done more slowly than usual due to fatigue. Alternatively, a surgeon who is
operating behind schedule may also speed up when nearing the end of a block. Nadarajah (2008)
provides a review of the literature on sums of lognormal random variables. The modeling of
correlated two and three parameter lognormals with different parameters has much room for further
development, as does the determination of optimal use of strategies to bound the total length of a
5.5 Schedule construction
As mentioned above, capacity has three components: (1) Physical resources; (2) Human
resources; and (3) Resource availability. The literature reviewed in this section addresses the
allocation of patients to an OR after the three components of capacity planning are addressed. A
number of management science methods and approaches have been applied to the problem of
scheduling surgical suites. They include mathematical programming and optimization techniques,
rule-based heuristic approaches (Dexter and Macario 2002), and simulation. Those studies have
shown significant success in improving overall utilization – both in theory and in practice – and have
shed light on the factors that impact efficient scheduling. Papers in this category range from
classical sequencing and scheduling to bin-packing and optimization algorithms, in order to achieve
objectives such as maximization of OR utilization, maximization of contribution margin, and
minimization of cancellations. The evaluation of proposed methodologies is complicated by the
lack of available raw data and of acknowledged, appropriate general test problems, as well as by the
secular trend toward an increasing proportion of ambulatory surgery.
Those who used mathematical programming and optimization techniques for scheduling
include Sier et al., who formulated the surgical scheduling problem using a mixed integer nonlinear
program and used a simulated annealing heuristic to optimize it (Sier et al. 1997). They tested their
model on simulated data. Using the same data as Sier et al., Velasquez and Melo optimized
preferences for starting times using a binary optimization formulation and solved it using column
generation and constraint branching instead of the traditional variable branching strategy (Velasquez
and Melo 2006). Ozkarahan developed a goal programming model that minimizes idle time and
overtime, and increases satisfaction of surgeons, patients, and staff (Ozkarahan 2000). Also using a
goal programming approach, Ogulata and Erol constructed a set of hierarchical multiple criteria
mathematical programming models to generate weekly OR schedules (Ogulata and Erol 2003).
Exploring the problem of planning surgeries in an OR over a medium term horizon, which they
defined as one or two weeks, Guinet and Chaabane developed an assignment model with resource
capacity and time-window additive constraints (Guinet and Chaabane 2003). Calichman approached
the creation of an OR schedule through a linear optimization model that considered hospital
constraints, as well as historical data, to allocate OR time to specialties attempting to maximize profit
(Calichman 2005). Hans et al. proposed various constructive heuristics and local search methods to
address the robust surgery loading problem (Hans et al. 2008). Denton et al. developed a stochastic
optimization model and some practical heuristics for computing OR schedules that hedge against
the uncertainty in surgery durations, in turn reducing total surgeon and OR team waiting, OR idling,
and overtime costs (Denton et al. 2006). Blake et al. (Blake et al. 2002; Blake and Donald 2002) used
an integer programming model to allocate block time to departments. Jebali et al. developed a two-
step approach for OR scheduling using a mixed integer assignment problem followed by an LP
sequencing problem with and without permitting reassignments. They tested their model on
simulated data (Jebali et al. 2006). Pham and Klinkert proposed a surgical case scheduling approach
based on an extension of the job shop scheduling problem formulated as a mixed integer linear
program to schedule elective and add-on cases (Pham and Klinkert 2008). Lamiri et al. used
stochastic programming to assign elective cases to different periods over a planning horizon and to
take into account emergency cases that arrive randomly and have to be performed on the day of
arrival. Their objective function is to minimize the sum of elective patient related costs and
overtime costs of operating rooms (Lamiri et al. 2008).
Fetter and Thompson were among the earliest to explore the use of simulation of a single
OR as a decision aid for a human surgical scheduler (Fetter and Thompson 1965). Barnoon and
Wolfe later extended the simulation idea to incorporate multiple ORs (Barnoon and Wolfe 1968).
Their program was intended to test the effectiveness of various schedule configurations, as
measured by utilization, rather than to construct a schedule. Goldman et al. used a simulation model
to evaluate three scheduling policies (FIFO, longest case first, and shortest case first) combined with
two expediting rules, and their effects on utilization, overtime, and the average number of delayed
cases (Goldman et al. 1969). They concluded that the longest-case-first approach was superior to
the other two. Kwak et al. used a multi-OR simulation program to explore the impact of different
scheduling procedures on utilization, and tested their approach on actual hospital data (Kwak et al.
1976). Esogbue used a simulation to compare the effectiveness of four scheduling policies used by
hospitals in Southern California with a scheme that used priorities for scheduling, where
effectiveness was measured by expected waiting time and utilization, (Esogbue 1979). Jones et al,
for example, employed a discrete event simulation for the management of surgical suite scheduling
(Jones et al. 1983). Charnetski used simulation to study the impact of a statistical scheduling
technique on two classes of idle times in hospital operating suites (Charnetski 1984). The output of
the model provided capacity/utilization ranges for effective scheduling to either minimize or
equalize the two types of costs. Lebowitz later used a Monte Carlo simulation of ORs scheduled
with various combinations of short and long procedures to develop a strategy for scheduling
procedures in ORs taking into account their variability (Lebowitz 2003). Using a simulation, Dexter
et al. found that for ORs having zero or one add-on elective cases, the best fit descending with fuzzy
constraints strategy maximized OR utilization (Dexter et al. 1999c). Dexter et al. used a simulation
to investigate ways of allocating block time and assigning patients to block (Dexter et al. 1999d).
They found that utilization is optimized when the surgical suite personnel control scheduling and
when patients wait as long as necessary. Dexter et al. used a simulation of a structural equation
model of an OR to evaluate which management interventions can most effectively decrease
variability in underutilized OR time (Dexter et al. 1999a).
With regard to outpatient surgical scheduling, Hsu et al. formulated the patient scheduling
problem as a variant of the no-wait, two-stage process shop scheduling problem, and presented a
tabu search-based heuristic algorithm to minimize the number of post-anesthesia care unit nurses in
an ambulatory surgical center (Hsu et al. 2003). Denton and Gupta developed a two-stage stochastic
LP approach to determine optimal appointment times for a sequence of jobs with uncertain
durations, with the objective of increasing the utilization of resources, matching workload to
available capacity, and smoothing the flow of customers (Denton and Gupta 2003).
Because multiple stakeholders are involved in the surgical process, multiple objectives must
be addressed by the surgical schedule. Surgeons would like to be able to begin their first procedures
on time, and to work uninterruptedly until their last patient. Administrators would like to optimize
surgical suite utilization and also to level the load on upstream and downstream resources. Staff
would like their shifts to begin and end on time. Patients would like fixed start times, predictable
end times, and, if they expect to go home the same day, that their procedures take place early
enough in the day that they are able to do so. The providers would like the patients to arrive
promptly, while patients also would like the providers to arrive promptly. Not all of those objectives
are easily quantifiable, which makes a formulation of the scheduling problem challenging, and if the
problem cannot be formulated, constructing an optimal schedule is difficult. Some aspects of the
overall problem have been addressed in the literature, such as Belien et al., who considered bed
occupancy, surgeons' preferences, and making the schedule repetitive (Belien et al. 2009), and
Cardoen et al. who incorporate six schedule-related objectives and use a mixed integer linear
programming solution method (Cardoen et al. 2009). Summarizing the issues related to schedule
construction, Basson et al. wrote:
“Some authors recommend improving OR utilization in the long term through
better capacity planning, including OR block scheduling, reallocation of time toward
more profitable surgeons, or process benchmarking (comparison to best practices).
Others emphasize shorter-term tactics focusing on timely first case starts, booking
accuracy, turnover time, and speeding surgical procedures themselves. However,
these have all been variably successful in improving utilization. Indeed, superior
utilization may not even be optimal, because too high an OR utilization inevitably
results in delays for urgent cases, overtime, and even delays in elective cases
scheduled too tightly, because the system is necessarily imperfect and chaotic. For
example, despite best efforts at standardization, it is simply not possible to predict
which patients or staff will arrive late, which patients may have their cases cancelled
for medical or other reasons, precisely how long a case will take to perform, or what
unexpected problems may delay care or room turnover." (Basson et al. 2006)
5.6 Schedule execution, monitoring and control
Surgical scheduling can be characterized as a predictive-reactive process because of its
almost certain disruption due to emergencies, uncertainty of procedure times, patient no-shows or
late-shows, and surgeon unavailability. In a manufacturing context, Aytug et al described predictive-
reactive scheduling as follows:
“In predictive–reactive scheduling, scheduling is presented as a two step process.
First, a predictive schedule, representing the desired behavior of the shop floor over
the time horizon considered, is generated. This schedule is then modified during
execution in response to unexpected disruptions. The schedule actually executed on
the shop floor after these modifications is called the realized schedule. The two main
questions are when to initiate a rescheduling action and what that rescheduling action
should be.” (Aytug et al. 2005)
In surgical scheduling, examples of replanning include reallocating block times and changing
the number of open ORs. Examples of rescheduling in turn include changing the start time of a
procedure on the day of the procedure, adding unplanned overtime, opening an additional OR to
accommodate an emergency case, and sending a scheduled patient home.
In addition to the thorough discussion of model formulation issues included in Aytug et al,
Vieira et al. define the strategies, policies, and methods discussed in the rescheduling literature, and
present a framework for understanding them (Vieira et al. 2003). Hozak and Hill, in addition to
surveying the literature, note that while some empirical work appears to show that frequent
replanning and rescheduling produces better results, other research results suggest an opposite
viewpoint (Hozak and Hill 2009). In a review of the literature on same-day OR operational decision
making, Dexter et al. emphasized both the importance of procedure duration estimation, the impact
of uncertainty on those estimates, and the resulting need to obtain measures and indicators that are
relevant to the decision at hand (Dexter et al. 2004).
Replanning and rescheduling in a surgical environment differs from that in a manufacturing
one. In manufacturing, if processing is paused before completion, the item being processed remains
in the same state until work resumes, and the process may be paused for as long as necessary. Aytug
et al. note that the manufacturing literature focuses on machine failure as the typical cause of
schedule disruption; that is, difficulties are caused by resource unavailability. In addition, multiple
instances of the same product are processed equally, products are inanimate, and scheduling
infeasibilities can be tolerated. By contrast, no two patients and no two procedures are exactly the
same, and once a surgical procedure begins it should continue without interruption until it
completes. Furthermore, emergency cases, along with procedures that run longer than expected,
place additional demand loads on the system, indicating that demands on resources rather than the
unavailability of resources are the primary causes of disruptions. Because the mental and physical
well-being patients are of paramount priority, scheduling infeasibilities are typically resolved by
allocating more resources (such as unplanned overtime) at additional cost.
Accurate and timely information and updates are necessary in order to replan and
reschedule. Such information might be provided by a computerized information system such as the
one described in Strum et al. (Strum et al. 1997a), a command line display (Dexter et al. 2007b), an
automatically updated whiteboard (Dexter et al. 2009) or perhaps by RFID technology (Hozak and
Hill 2009), if it could be adapted for use in surgical suites. However, because of the differences
between manufacturing and surgical scheduling noted above, it remains to be seen if the existing
results and observations regarding manufacturing replanning and rescheduling would extend to
Studies of reactive planning and scheduling in outpatient settings have explored the impact
of real-time events, such as cancellations, no-shows and changes in patient status, and many have
suggested compensatory actions that might be taken to mitigate the financial and clinical impact of
those events. Basson et al. studied the impact that surgical cancellations have on OR utilization,
identified preexisting factors predicting the failure of patients to appear for surgical procedures as
scheduled, and found that patient nonappearance can be predicted from patient noncompliance with
clinic visits and other clinical procedures (Basson et al. 2006). Similarly, LaGanga and Lawrence
studied patient no-shows, conducting a series of simulation experiments showing that procedure
overbooking is appropriate when clinics serve larger numbers of patients, no-show rates are higher,
and service variability is lower (LaGanga and Lawrence 2007).
From a clinical perspective, Fleisher et al. developed an outpatient surgery admission index
from independent predictors of immediate hospital admission to determine which patients with
increasing co-morbidities were more likely to be admitted to an inpatient facility after outpatient
surgery (Fleisher et al. 2007). They assigned to a patient one score point for each of the following
characteristics: 65 years or older, operating time longer than 120 minutes, cardiac diagnoses,
peripheral vascular disease, cerebrovascular disease, malignancy, seropositive findings for human
immunodeficiency virus, and regional anesthesia, and two score points for general anesthesia.
Increasing scores were associated with higher odds of admission. Patients with total scores of 4 or
more were about 30 times more likely to require admission than patients with total scores of 0 or 1,
indicating that outpatient procedures on them should be done in hospitals.
This area focuses on schedule execution and the steps required to manage the schedule
within stipulated patient outcome, cost and time constraints. As such, it is analogous to the
implementation phase of project management, including the various monitoring and control
strategies involved. Research issues in this area include:
Measuring the effectiveness and efficiency of surgical schedules, including identifying
appropriate performance measures and comparing surgical schedules ex-ante and ex-
Constructing models for managing and controlling the inherent variability and
uncertainty in the surgical scheduling environment.
Variability and uncertainty occur with regard to the frequency and distribution of patient
arrivals, patient conditions, and procedure durations, as well as ‘add-on’ cases and other
unanticipated changes. Potential models include 1) process engineering and re-engineering models,
including those involving product and patient flow, 2) queuing models, including models of transient
state behavior, 3) the degree of variance in financial and economic factors, and 4) the overall and
specific demand for surgeries.
6. SUMMARY AND CONCLUSIONS
Surgical scheduling is a challenging task, primarily because every detailed-level plan is almost
certain to deviate significantly from what actually transpires in the course of the surgical day.
Emergency patients enter the system, patients (and perhaps staff) either do not arrive or do not
arrive when expected, planned procedures become unnecessary, unplanned procedures become
necessary, and procedures take more time or less time than originally planned. In such an
environment, a schedule is a guide for operational management rather than a statement of precisely
expected outcomes. But the better the guide, the more likely it is that operational management will
be able to use resources effectively and efficiently.
We suggest that the economic and project management aspects of the surgical scheduling
process might be the most promising lines of research in the foreseeable future. Over the past 55
years, a variety of standard operations research models have been proposed for use in hospital
scheduling, but none appear to have had widespread impact on the actual practice of surgical
scheduling. We hope that investigations along the lines suggested in this paper make the next 55
years more productive for operations research work in surgical scheduling.
A primary contribution of this paper is to suggest potentially productive topics that might be
pursued in each part of the literature. In this paper, we categorized the literature into six areas along
a time dimension extending generally from long term to contemporaneous: Capacity planning (very
long term through medium term); process reengineering/ redesign (very long term through long
term); the surgical services portfolio (long term); procedure duration estimation (long term through
medium term); schedule construction (short term through very short term); and schedule execution,
monitoring and control (contemporaneous). Because of the wide variety of approaches used in each
of those areas, we believe that segmenting the literature along a time axis provides a particularly
useful view of past research, and provides an effective framework in which to identify areas that are
particularly attractive for future work.
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