Spine surgeries tend to be lengthy (mean time of 4 hours) and highly variable (with some surgeries last-ing 18 hours or more). This variability along with patient preferences driving scheduling decisions resulted
in both low operating room (OR) utilization and significant overtime for surgical teams at Mayo Clinic. Inthis paper we discuss the development of an improved scheduling approach for spine surgeries over a rollingplanning horizon. First, data mining and statistical analysis was performed using a large data set to iden-tify categories of surgeries that could be grouped together based on surgical time distributions and could becategorized at the time of case scheduling. These surgical categories are then used in a hierarchical optimiza-tion approach with the objective of maximizing a weighted combination of OR utilization and net profit. Theoptimization model is explored to consider trade-offs and relationships among utilization levels, financial per-formance, overtime allowance, and case mix. The new scheduling approach was implemented via a customweb-based application that allowed the surgeons and schedulers to interactively identify best surgical days withpatients. A pilot implementation resulted in a utilization increase of 19% and a reduction in overtime by 10%.
Keywords : operating room scheduling; surgery scheduling; mixed-integer programHistory : Received: February 28, 2014; accepted: August 24, 2015. Published online in Articles in Advance.
1. IntroductionFor spine surgeries, large medical centers like MayoClinic generally face more patient demand than avail-able capacity. One reason is the relatively long surgi-cal times for spine patients. Data from Mayo Clinicshows that 50% of spine surgeries are over four hoursin length. Thus, on most days a spine surgeon is ableto do only one or at most two surgeries (within regu-lar working hours).
The length and variability of spine surgeries ad-versely impact patient access, effective operations,and financial performance (Dexter et al. 2010). AtMayo Clinic, 38% of surgical days went past thedesired end time of 5 p.m. At the same time, operat-ing room (OR) utilization during normal hours wasless than desired, limiting patient access and reducingpotential financial performance. Overtime is a con-cern at Mayo Clinic due to the importance of qual-ity of life for the surgeons and the surgical teams.
In addition, as noted in Espin et al. (2006), safety forboth the patient and surgical staff may be an issue ifsurgical days run long. Emergency cases, short-termcancellations, teaching requirements for surgeons onspecific weekdays, and complex cases that requiremore than one surgery per patient further complicatescheduling and OR management.
In this paper, we describe a data-driven hierarchi-cal modeling approach for scheduling spine surgeriesthat tackles multiple aspects such as surgery vari-ability (by better classification), OR utilization, over-time, payer mix, and financial performance. We use aseven-year data set consisting of 2,500 spine surgeriesto parameterize our models. We also quantify howthis scheduling approach performed in a pilot imple-mentation. Many of the concepts and approaches dis-cussed in this research are relevant to other surgicalpractices and particularly those in spine surgery.Nonetheless, the orthopedic spine surgery practice at
Mayo Clinic has many unique characteristics. In whatfollows, we discuss the specific problem setting.
1.1. Mayo Clinic Spine Surgery SchedulingApproach
Mayo Clinic’s core value is the “needs of the pa-tients come first.” This influences surgical schedulingbecause patient timing preferences are important tofinal scheduling decisions. This is in contrast to manysurgical settings where patients are simply told whento show up. Thus, at Mayo Clinic the patient negoti-ates with the surgeon and their team, when to sched-ule their surgery. This is also in part because spinesurgeries often have significant impact on patients’lives for extended periods and a lengthy recoveryprocess.
However, this approach leads to problems in dailysurgical loads; for example, when a patient requeststo have their surgery on a particular day when severalother surgeries are already scheduled. This is due tothe difficulty in simply “squeezing in” another spinesurgery because of their length and variability. Con-versely, other days and weeks are underutilized. Inthe absence of good information regarding the currentstatus of their schedule, surgeons and schedulers areoften driven to make decisions influenced too muchby patient preferences.
Scheduling surgeries at Mayo Clinic is further com-plicated by the fact that dedicated OR time is avail-able to most surgeons, thus there is a specific timepreallocated to each surgeon. This is a positive in thatit allows the surgeons a great deal of autonomy inmanaging their cases both in the OR and the clinic.However, it is problematic in that the organizationcannot pool OR time and balance loads across all ORs.Rather each surgeon’s load must be balanced acrosstheir surgical days. These surgical days are assignedvia the “blue and orange” system at Mayo Clinic. Thisharkens back to the system developed by the Mayobrothers, Dr’s. Will and Charlie, who performed surg-eries every other day, in complementary fashion. Inthe first week, one surgeon (“blue”) performs surg-eries on Mondays, Wednesdays and Fridays, whilethe other surgeon (“orange”) is active on Tuesdaysand Thursdays. In the next week, the orange surgeonperforms surgeries on Monday, Wednesday, and Fri-day while the blue surgeon does so on Tuesday andThursday. This alternating cycle is then repeated. Ondays that surgeons are not operating, they have clin-ical consultations with patients. This creates a sim-ple management system for clinic and surgery daysthat continues today, but results in some restrictionsin scheduling flexibility and can make short-term caseload imbalances worse as some surgeons get over-loaded and others underutilized. A nontrivial 10%of spine patients require multiple surgeries that need
to be scheduled within days of each other. Further-more, even on surgical days, surgeons have teachingand seminar responsibilities, leading to a late start forsurgeries. Thus weekdays get characterized as “earlystart” or “late start” days, which has an impact onaccess as well as overtime.
Although Mayo Clinic is a nonprofit organization,financial viability and sustainability are still impor-tant considerations. Profits from clinical practice sup-port research, education, and ongoing improvementinitiatives, all of which are important to Mayo Clinic’smission. With limited capacity to allocate to the highdemand for spine surgeries, some control of whichsurgeries are performed and when, can be impor-tant to net operating income (NOI). Given specificrevenue reimbursements and Mayo’s cost structure,some types of spine surgeries are more profitable thanothers, for example patients with government payers(e.g., Medicare and Medicaid) generally have lowerprofitability. However, there is no desire to reduce thenumber of such patients.
Furthermore, the overall patient profitability toMayo Clinic, including their hospital stay, is affectedby the timing of surgeries, specifically the day of week(DOW) that the surgery is performed. Thirty-four per-cent of spine surgery patients require discharge to askilled nursing facility (SNF). These facilities gener-ally do not accept patients on weekends and there-fore if a patient requires a SNF and their planneddischarge is on a weekend, Mayo often incurs theadditional costs without compensating revenue. Thisis due to the fact that government insurance payersgenerally have a fixed reimbursement for each proce-dure type. Even though it may be difficult to a pri-ori determine the probability of a patient requiringa SNF at discharge, it is known that older patientshave a higher risk. Because such patients are gener-ally covered by Medicare, special attention is paid towhen these patients are scheduled. In general theyare scheduled on Mondays and Fridays with theassumption that this results in the least number ofdelayed discharges. Although all the above factors areimportant when scheduling patients, the Mayo sys-tem needs to have the flexibility to ensure that theneeds of the patients always come first.
1.2. Objectives and ApproachThe primary objective of our research is to createschedules that improve patient access as a resultof increased utilization of surgical capacity, whilekeeping the practice financially sustainable. It is alsoimportant to ensure that overtime levels are not toohigh, the proportion of government payer patientsremains at historical levels, and Mayo-specific DOWconstraints discussed above are met. To address thisproblem, the following research approach was used(see Figure 1 in §3).
• Data mining and statistical analysis were per-formed using Mayo Clinic’s database. Surgeries werecategorized based on surgical time distributions,using patient characteristics known in advance ofscheduling.
• Using the surgical categories, Simulation Model 1was used to identify combinations of surgeries thatcan feasibly be performed within one surgical dayand to calculate the outcomes (overtime, utilization,and NOI). Since spine surgeries are long and highlyvariable, only combinations consisting of one or atmost two surgeries need to be considered. The sim-ulation uses the relevant time distributions derivedfrom the data set.
• The feasible surgical combinations and their out-puts are used as an input to the hierarchical optimiza-tion approach, consisting of three stages:
a. Optimization Model 1: A mathematical pro-gram was formulated and implemented to maximizea weighted function of OR utilization and NOI, con-sidering changes to surgical case mix, limiting over-time, and downstream inpatient length of stay (LOS).The surgical combinations and their outcomes areused as inputs. This stage generates the optimal casemix over a planning horizon.
b. Optimization Model 2: The second-stage opti-mization model creates the optimal schedule for eachday in the horizon using the results of the first stagemodel and maximizes available slots for patients whoneed to have multiple surgeries within a short period,typically two days.
c. Optimization Model 3: The last stage of theoptimization creates a surgeon schedule by incorpo-rating Mayo Clinic specific scheduling requirements(the blue–orange surgical template).
• Another simulation model (Simulation Model 2in Figure 1) is used to test the impact of urgent surg-eries and cancellations on the optimal schedule.
• As a last step, our optimization framework wasimplemented in Mayo Clinic and the results of theintervention were evaluated in a controlled pilot, witha pre and post evaluation as well as using a controlgroup (with two surgeons) and a test group (with twosurgeons).
2. Literature ReviewSurgical scheduling is an extensively studied area,and a full review is beyond the scope of this paper.Instead, we split up our literature review into twoparts: literature on prediction of surgical times and ashort review on surgical scheduling. These two partsbroadly revolve around our two major contributions:a new method for classifying spine surgeries based ontheir durations, and the pilot implementation.
2.1. Literature on Prediction of Surgical TimesAccurately estimating surgical durations is crucial forsurgical case scheduling (May et al. 2011). Currently,the surgical duration in Mayo Clinic spine practiceis estimated using historical data based on the lastfive similar surgeries—a widely used estimation toolcalled the “last 5 case estimate” (Macario and Dexter1999). This is a poor estimation tool especially whenthere are too few historical cases, as it is very sur-geon specific (Zhou et al. 1999). In fact, a recent studyhas shown that OR times for similar surgeries in eightdifferent hospitals vary significantly from each other(Dexter et al. 2006). Other common methods for surgi-cal duration estimation are surgeon estimates, histori-cal averages, a combination of historical average withsurgeon estimate, adjustments with case complexities,and regression models to develop predictive models(Schult et al. 2011).
There are many factors that impact the surgicalduration, like type of anesthesia, age, gender, surgeon,and American Society of Anesthesiologists (ASA) riskclass (Strum et al. 2000). We investigate all of the fac-tors that are known in advance of surgery to find thebest categorization that is also clinically relevant. Log-normal distribution is typically the best fit and is oftenused in the literature to represent highly variable pro-cedure times (Spangler et al. 2004). However, besidesestimating a single surgery, for scheduling purposes,it is essential to predict an entire surgical day or anOR block’s duration (Dexter et al. 1999). This is why,as discussed in Strum et al. (2003, p. 232) we thenuse the surgery duration predictors “ 0 0 0 for buildingsimulation models of surgical environments and fordecision analysis based on such simulations.”
Surgery durations exhibit high variability andwhen multiple cases are performed back to back thisvariability accumulates. Research in this field has pro-posed various ways to estimate the end of day (EOD)in the face of high variability. Wang and Yang (2014)suggest using Type 4 Pearson distribution to approx-imate the EOD distribution for a list of cases.
Alvarez et al. (2010) develop a method to accuratelydetermine the EOD for multiple cardiovascular oper-ations, considering the turnover times as well. Theauthors suggest using the sum of the average casedurations from historical cases and turnover timesto estimate the time to complete a series of surgicalcases, supporting Dexter et al. (1999).
We have analyzed the convolution of lognormalvariables to predict the EOD distributions for differ-ent surgical combinations. For instance, Gao et al.(2009) study the asymptotic behavior of a probabil-ity density function for the sum of two lognormallydistributed random variables. They approximate boththe left and right tails with simple functions. How-ever, these models get intractable when we are con-sidering the tail probability density function of more
than two lognormally distributed random variables(which is the case when we are characterizing eachof the surgical steps with a lognormal distribution).Thus, we have turned our focus to using simulationmodels that mimic the ORs in Mayo Clinic based onsampling from historical data. And instead of directlyusing the empirical values for the surgical combina-tions, we have created a simulation model due tothe fact that not all of the combinations were rep-resented in the data-set. We were able to derive theresults of interest (overtime, normalized NOI, utiliza-tion) using a simulation model for all feasible surgicalcombinations.
2.2. Literature on Surgical SchedulingSurgical suites’ management impacts costs, thepatient flow, and resource utilization throughout thewhole hospital (Nan and Li 2011). Various approacheshave been used to optimally schedule surgeries toORs like, integer programming (Blake and Donald2002; Denton et al. 2007, 2010; Vissers et al. 2005;Adan et al. 2009), stochastic optimization models(Denton et al. 2010, Batun et al. 2011, Oostrum et al.2008, Testi et al. 2007), goal programming (Rohlederet al. 2005), discrete event simulation (Adan et al.2009), and heuristics (Denton et al. 2010, Oostrumet al. 2008, Testi et al. 2007). For detailed reviewson surgical scheduling, we refer to May et al. (2011),Guerriero and Guido (2011), and Cardoen et al. (2013).Here, we only emphasize studies that are relevant tothe unique features of our study.
Although there has been research on addressing thefinancial implications of surgical scheduling (Wachtelet al. 2005, Dexter et al. 2002), we not only con-sider the financial differences between patient groups,but also the profitability of patients’ entire encounterrelated to their surgery. This would include post-surgery hospitalization and the effects of unnecessaryhospital stays (and associated costs) for patients likelyto require a SNF upon discharge. In addition, it wasa vital part of our project that there was no deteriora-tion in care, thus we did not limit access to OR time,inpatient beds, or surgical expenses to reduce ourcosts as suggested in some papers (Dexter et al. 2002).
A major shortcoming in the literature is the lackof research on implementations. To the best of ourknowledge, Blake and Donald (2002) is one of thefew papers that mention the implementation of adeterministic model without considering the vari-ability in surgical durations. Recently, Turner et al.(2013) discuss how operations research was usedto improve the education and training of surgi-cal trainees at the Northwestern University FeinbergSchool of Medicine. Cardoen et al. (2013, p. 142) notein their detailed review of the surgical schedulingliterature that “even if implementation of research
can be assumed, authors hardly provide details onthe process of implementation.” A major missingpiece, the paper notes, are “the behavioral factors thatcoincide with the actual implementation” (p. 142).Furthermore, it notes that “identifying the causes offailure or the reasons that lead to success, may be ofgreat value to the research community” (p. 143). Weattempt to fill this crucial gap in surgical schedulingresearch.
2.3. ContributionsIn summary, our paper contributes to the literature inmultiple ways. The suggested approach is applicableto any institution with surgical specialties that havelong and variable durations, such as spine, cardio-thoracic, neurosurgery, and plastic surgery. The clas-sification of surgeries based on time required forsurgery using clinical information known at the timeof case scheduling is also unique and can be appli-cable to other surgical areas. We consider variousaspects of surgery scheduling such as costs of thedownstream hospital stay, payer type, and DOWeffects. These are questions surgical specialties in alllarge academic medical centers have to grapple with.The specific details may differ. For example, the ideaof surgical days and consultation days (which inMayo results in the blue–orange system) may exhibita different pattern; or the teaching responsibilities,which result in late start surgery days, may occur dif-ferently; or the payer mix may follow a different pro-portion. This is why we have kept the formulationsand indices as general as possible.
Finally, by creating a scheduling interface basedon our optimization models, implementing it in apilot, and measuring the outcomes of the implemen-tation, this research provides a template that otherinstitutions could adapt based on their own specificrequirements. The combination of objectives and con-straints considered in our models, supported by anactual pre/post implementation and test and controlgroup comparison, and a discussion of the lessonslearned from the pilot implementation, sets the paperapart from other purely modeling-based efforts in theliterature.
3. Optimization ModelsAs described in §1.2, we follow a hierarchicaloptimization approach; if all stages are consideredtogether as an integrated model, tractability becomesan issue. The interactions between different stages isvisualized in Figure 1. The first stage decides on theoptimal patient case mix in a time horizon to maxi-mize a weighted function of utilization and estimatedprofitability (via NOI). With this optimal surgery mixas input, the second stage allocates cases to specific
days in the time horizon, while ensuring that multi-ple surgeries performed on the same patient can becarried out within a few days. The third stage deter-mines which exact days the surgeons will work andthe specific surgical combinations they will perform.
Before describing the three stages, we define indicesand parameters used in the model. The index l refersto surgery category. Surgeries are statistically catego-rized based on the length of their durations. In ourcase study, there are 10 surgical categories (l = 10010).The index r indicates payer type: “1” for govern-ment (G), in our case typically Medicare; and “2” forprivate (P).
The index i refers to a surgical combination. A sur-gical combination is a set of surgeries, and eachsurgery in the set is defined by: (a) the category itbelongs to, and (b) the payer or insurance type. Forexample, 41P16G5 is a two-surgery combination: thefirst is a surgery from category 1 with a private payer;and the second is a surgery from category 6 with agovernment payer. Other examples of surgical combi-nations are as follows: 44P5, a combination that con-tains only one privately insured category 4 surgery;and 43G13G5, a combination that contains two gov-ernment insured category 3 surgeries.
Because spine surgery durations are long, we needto consider only combinations involving one or twosurgeries for a given day. By linking surgery cate-gories and payer type we get a finite number of fea-sible surgical combinations, which are indexed by i.The operational consequences of scheduling a partic-ular combination on a surgical day are precalculatedby simulation. For example, the combination 41P16G5scheduled on a particular day will result in a certain
amount of average operating room utilization, createsome probability of overtime, and produce a certainaverage NOI. These parameters become inputs to thefirst stage of the optimization model.
In the formulations, the parameter Milr denotesthe number of category l surgeries insured by payertype r in combination i. For the combination i =
41P16G5, l = 11 and r = P , the value Milr will be equalto 1. For the combination i = 43G13G5, l = 3 and r =G,the value Milr will be equal to 2; for the same combi-nation, if l = 3 and r = P , Milr will be equal to 0 sincethere are no privately paid category 3 surgeries in thecombination. We use Milr in constraints relevant to thenumber of surgeries in each category and the numberof Medicare surgeries.
Additionally, we note that there are three sets ofindices for days in the formulation: k, d, and t. Eachindex serves a unique function. Index k representswhether a particular weekday is a late or a regularstart day. Late starts happen because of teachingresponsibilities on specific weekdays, which influ-ences overtime and utilization if a certain surgicalcombination i is scheduled on a late start day. DOW(M, T, W, T, F), which is important for schedulingMedicare surgeries is represented with d. In our for-mulations, we impose that Medicare surgeries arescheduled on specific days of the week, since thisminimizes downstream LOS costs by reducing unnec-essary weekend stays. The DOW also helps differenti-ating hospital-specific dynamics such as blue–orangesurgical days (described in §1.1). Parameter Dkd, con-nects the DOW index d with the start of the dayindices, k in the formulation. Finally, the index t =
1121 0 0 0 1 T is for days in the time horizon (in our casestudy, 120 days), which is required to schedule thesurgeries to specific days in the rolling horizon.
3.1. First Stage: Maximizing Utilization andNet Operating Income
The main decision variable in this stage is the totalnumber of surgical combinations of type i to be per-formed on day type k in a time horizon consistingof T days. The decision variable thus gives us the casemix for the time horizon. The objective is to maxi-mize a weighted combination of normalized NOI andutilization with Equation (1). This is constrained by:(a) number of surgeries from each category (mini-mum and maximum limits determined by the prac-tice); (b) minimum number of Medicare surgeries;(c) overtime limit; (d) available number of operatingrooms; and (e) DOW in which Medicare surgeries canbe performed. Recall that average NOI, average oper-ating room utilization, and probability of overflow foreach surgical combination performed on a particularday are precalculated via simulation, and serve as an
w40111 0 0 0 1W − 15: Where W is the number of weeksin the time horizon
t411 0 0 0 1 T 5: Days in the planning horizon
Parameters Obtained from the SimulationOTik: Simulation derived parameter representing
the average probability of finishing after theEOD (5 p.m.) when surgery combination i isperformed on day group k.
EOik: Simulation derived parameter for averageovertime after EOD (5 p.m.) when the surgerycombination i is performed on day group k.
�ik: Simulation derived parameter for the averageovertime probability after 11 p.m. for surgerycombination i on day group k. (Variable costsstart to be incurred after 11 p.m. because of theshift change.)
Uik: Simulation derived parameter for the averageOR utilization for surgery combination i onday group k.
NOIi: Simulation based average NOI for surgerycombination i. NOI is a measure of theprojected revenue less operating and fixedallocated costs.
Parameters Determined by the Practiceo: Practice imposed limit on the proportion of
overtime after 5 p.m.e: Practice imposed limit on the expected
overtime after 5 p.m.f : Practice imposed limit on the percentage of
overtime after 11 p.m.b: The case-mix bound width represented as a
fraction between 0 and 1 (i.e., allowedflexibility in changing the case mix).
m: Minimum percentage of Medicare surgeries tobe performed.
Pl: Average number of surgeries from surgicalcategory l, calculated per OR room.
T : Number of working days in the planninghorizon.
Jt : The open number of ORs on day t.
�: Weight assigned to utilization in the objectivefunction (i.e., relative importance of utilizationin comparison to NOI).
Parameters that Link IndicesFld: Binary parameter with a value of 1 if DOW d
is the best surgical day for category lMedicare patients; 0 otherwise.
∑
d Fld = 1 andFld binary ∀ l1 d.
Dkd: Binary parameter with a value of 1 if DOW dis a type k day (i.e., if it is a regular start orlate start day); 0 otherwise.
∑
kDkd = 1 ∀d andDkd binary ∀k1d.
Milr: The number of category l surgeries in eachsurgical combination i with payer r .
Decision Variablesxik: Total number of surgery combinations of type
i performed on day group k over the timehorizon T .
�ld: Output variable representing the number ofMedicare surgeries from surgical category lscheduled on DOW d.
First-Stage Model
max{
�·∑
k
∑
i
Uik ·xik+41−�5·∑
k
∑
i
NOIi ·xik
}
(1)
s.t∑
t
Pl ·41−b5·Jt ≤∑
k
∑
i
∑
r
Milr ·xik
≤∑
t
Pl ·41+b5·Jt1 ∀l1 (2)
∑
k
∑
i
xik ·Mil1 ≥∑
i
∑
k
∑
r
xik ·Milr ·m1 ∀l1 (3)
∑
k
∑
i
xik ·Mil1 ≤∑
t
Pl ·41+b5·Jt ·m1 ∀l1 (4)
∑
i
∑
k
OTik ·xik∑
t Jt≤o1 (5)
∑
i
∑
k
EOik ·xik∑
t Jt≤e1 (6)
∑
i
∑
k
�ik ·xik∑
t Jt≤f 1 (7)
∑
i
∑
k
Dkd ·xik =∑
w
J5·w+d1 ∀d1 (8)
�ld =∑
i
∑
k
xik ·Mil1 ·Fld ·Dkd1 ∀l1d1 (9)
∑
i
∑
k
xik ·Dkd ·Mil1 ≤B ·Fld1 ∀l1d1 (10)
xik ∈�≥01 ∀i1k0 (11)
There are four main groups of constraints in thisstage: case-mix and payer-mix calculations (Equa-tions (2)–(4)), overtime restrictions (Equations (5)–(7)),
open OR restrictions (Equation (8)), and DOW restric-tions for Medicare surgeries to minimize the num-ber of weekend discharges (Equations (9)–(10)). Weexplain these in more detail below.
To build a realistic model, the surgical scheduleneeds to create a surgical case mix that is similar toobserved levels in the current practice. Thus, Equa-tion (2) ensures that number of patients from surgi-cal categories (11 0 0 0 1L) deviates from the current casemix within a prespecified bound width, b. Medicaresurgeries are enforced to constitute at least m% of theoverall number of surgeries with Equation (3). Sumof Medicare patients from each surgical category iswithin the ±m% range of the empirically observednumber of these patients (Equation (4)).
The percentage of overtime (after 5 p.m.) is enforcedto be less than the overtime limit based on the clinic’sthreshold, “o” (Equation (5)). Expected hours of over-time after 5 p.m. is kept less than the observed averageovertime hours, “e” (Equation (7)). Similarly, the pro-portion of days with overtime after 11 p.m. is forced tobe less than the historical average, “f ” (Equation (6)).
Equation (8) ensures that the total number of surg-eries that will be performed on each DOW d in thehorizon must be equal to the total number of operat-ing rooms available on such weekdays in the horizon.
In Equation (9), �ld represents the number of Medi-care surgeries from category l scheduled on DOW d,that is the product of the binary variable that indi-cates the best day to perform category l Medicaresurgery and the sum of all Medicare surgeries for thatspecific surgery category. With Equation (10), Medi-care patients are assigned to their best day of surgery,based on their category so that the Medicare weekendstay is minimized. This has financial impact, whichwill be discussed later in the case study.
3.2. Second Stage: Maximizing Multiple DaysStaged Surgeries
In the first stage the surgery combinations are not yettied to a specific day t in the time horizon consistingof T days. The second stage assigns surgery combina-tions to each day t in the horizon, while meeting con-straints imposed by the first stage outputs. Note thatthis stage has no impact on NOI or utilization, sincethey have already been optimized in the first stage.
The objective in the second stage is to maximize theability of the spine practice to accommodate surgerieson the same patient conducted over multiple days. Wecall such surgeries on the same patient “multiple daysstaged surgeries” (MDSS). MDSS result when someof the very long surgeries are broken down into twoor more surgeries with feasible durations by the sur-geons. The components of surgeries need to be carriedout within two to five days.
For example, a patient may need to undergo a cat-egory 6 surgery followed by a category 8 surgery
within two days. This would be the MDSS pair 6_8,where MDSS are indexed with s. If t is the day ofthe first surgery on the patient, then this means that acombination containing surgery 6 must be scheduledon day t and a combination containing surgery 8 onday t + 2. One of the ways this would be possible is ifcombination 1_6 is scheduled on day t and combina-tion 1_8 is scheduled on day t + 2; thus MDSS pair 6_8spans two days. To ensure MDSS constraints are metin the formulation, we use a binary parameter �ics thattakes on the value of 1 if for surgery combination i =41_65 contains one element of the MDSS pair s = 46_85in cth position; for this example if c = 11�ics = 0, butif c = 21�ics = 1.
Indicesi411 0 0 0 1 I5: Combination of surgeriess411 0 0 0 1 S5: MDSS pair indexc411 0 0 0 1C5: Position in the sequence in which
the MDSS pair is performedw401 0 0 0 1W − 15: Weeks in the planning horizon
Parameters�ld: Number of Medicare surgeries from surgery
category l scheduled on DOW d. (Derived fromthe first stage.)
�s : Weight of MDSS pair s in the objective function,based on the empirically observed proportion ofpair s.
�: Coefficient for balancing the workload over theweekdays.
�ics: Binary parameter that takes on the value 1, ifsurgery combination i contains one element ofthe MDSS s in cth position; 0 otherwise.
Decision VariablesYit : Integer decision variable representing the
number of surgery combination i’s performedon day t as a part of MDSS pair.
Zit : Integer decision variable denoting the numberof surgery combination i’s performed on day tnot as a part of MDSS (rather as a singlestand-alone surgery combination).
Lts : Integer decision variable denoting the numberof surgeries on day t performed as the firstcomponent of the MDSS pair s.
Qid: Number of surgery combination i’s to beperformed on DOW d.
The objective function maximizes the weighted sumof MDSS performed (Equation (12)). Detailed analysisis presented in §4.1.2.
Constraints. Equation (13) links the first stage output(the optimal surgery case mix), to the second-stagedecision variable (number of surgeries scheduledfrom each surgery category on specific days of week).Equation (14) ensures that number of combination isurgeries performed on each DOW matches with thefirst stage results, via the Qid decision variable. Next,Equation (15) enforces that the Medicare surgeries areperformed on the right DOW.
There can be at most Jt number of combinationsscheduled each day (Equation (16)); recall that Jt is thenumber of open/available operating rooms on day t.Equations (17) and (18) ensure that for a MDSS pair sto take place, the second surgery of MDSS pair needsto be arranged within two working days after the firstsurgery. Equation (19) spreads MDSS evenly over theworkdays, using a lower bound �. This ensures thatnot all of the MDSS pairs, which place significant bur-den on the surgical team, are performed on the samedays of the week.
3.3. Third Stage: Determining Surgeon SchedulesAt the end of the second stage, surgical combinationshave been assigned to specific days in the time hori-zon. In this last stage, each surgeon in the practiceis assigned the exact days when they will operateand the surgical combinations they will perform. Inour pilot implementation, we only had two spine sur-geons with predetermined alternating schedules (theblue–orange alternating template discussed earlier).Since spine surgeries tend to be long and variable, anoperating room is dedicated to each surgeon on eachday that he/she operates. Thus the two surgeons cre-ate an alternating schedule that covers surgical casesassigned to each each day in the horizon. See Table 3in §4.3.3 for an example. Other hospitals may havemore surgeons in the practice and greater flexibilityin assigning surgical days to cover their cases duringa horizon. This in itself is an optimization question.For such a general case, we provide a formulation
to balance the workload across surgeons for differentsurgery types and payer mix.
Only the additional relevant indices are describedhere. The main decision variable �hit is a binary vari-able denoting if surgeon h performs combination i onday t (1 if yes, 0 otherwise). The objective is to balancethe workload between the surgeons so that the abso-lute difference in the surgery categories and payertypes performed by surgeons relative to the practiceaverage is minimized.
Indicesh411 0 0 0 1H5: Surgeon index
Decision Variables�hit: Binary decision variable denoting if surgeon h
performs combination i on day t.�lhr: Absolute difference in workload for surgeon h,
from the average number of category lsurgeries scheduled over the planning horizonwith payer r .
Wlhr: Number of category l surgeries with payer rscheduled for surgeon h over all weeks.
Third-Stage Model
min∑
l
∑
h
∑
r
�lhr (23)
s.t Wlhr =∑
t
∑
i
�hitMilr1 ∀h1 l1 r1 (24)
�lhr ≥Wlhr −
∑Hh′=1 Wlh′r
H1 ∀ l1 h1 r1 (25)
�lhr ≥
∑Hh′=1 Wlh′r
H−Wlhr1 ∀ l1 h1 r1 (26)
∑
h
�hit = Yit +Zit1 ∀ i1 t1 (27)
∑
i
�hit ≤ 11 ∀h1 t1 (28)
�hit ∈ 0111 ∀h1 i1 t1 (29)
�lhr ≥ 01 ∀ l1 h1 r1 (30)
Wlhr ∈�≥01 ∀ l1 h1 r0 (31)
Constraints. Each surgeon’s workload over theplanning horizon is calculated using Equation (24).�lhr is calculated as the absolute difference between theworkload of each surgeon and the average numberof surgeries from each surgical category, in a linearfashion with Equations (25) and (26). Equation (28)ensures that combinations scheduled on a particularday t are covered by the surgeons in the practice.Equation (29) ensures that each surgeon has at mostone combination scheduled on a particular day t. Thisconstraint can be relaxed for specialties where a sur-geon may perform more than one case per day.
4. Case StudyThe optimization model was developed and evalu-ated based on the operations and data from the ortho-pedic spine practice at Mayo Clinic, Rochester, MN.Model development and evaluation occurred overmuch of 2012 with a live implementation target set asDecember 2012. We have set the planning horizon Tto 120 days, with a surgical day length of 10 hours.This is a sufficiently large horizon to represent all thesurgery categories, including those that are sparselyobserved. We consider two types of surgical days: reg-ular and late start days. The latter occurs on Mondaysto allow for teaching seminar, resulting in reductionof the surgery day by one hour. As discussed in §1.1,we follow the “blue and orange” system.
4.1. Data and Model AssumptionsSpine surgery related data involves two primary ORrooms with five surgeons performing more than 2,500surgeries over seven years from 2005 to 2011. Dataavailable include patient-related (age, gender, geo-graphical location, ASA scores of patient physical con-dition before surgery, initial diagnosis (ICD9 code),and LOS), surgery-related (surgeon name, OR room,long description of the surgery provided by the sur-geons, surgery durations broken down into OR enterto incision time, incision to closure time, and closuretime to OR exit time), and financial information (pro-cedures performed, cost and revenue for each case) ata very detailed level.
Some of the baseline characteristics of the data setare as follows: average patient age was 57.6, with 45%female patients. Hospital LOS is on average 5.9 dayswith a standard deviation of 6.5 days. The averageOR enter to incision time is 1.5 hours with a standard
Figure 2 Cumulative Distribution of the Surgery Time by Each Patient Category
O
deviation of 0.4, the average incision to closure timeis 4.6 hours with a standard deviation of 2.5 hours.The average closure to OR exit time is 0.5 hours witha standard deviation of 0.3 hours.
4.1.1. Surgery Type. We classified the entire patientpopulation into 10 surgery categories using Classifi-cation and Regression Tree (CART) analysis in JMP(version 9.01, SAS Institute, 2010). This data mininganalysis enabled us to accurately predict how longeach surgery will take and therefore better plan thesurgery days. Table A.1 in the appendix illustrates theproperties of the surgical categories generated as aresult of this analysis. The clinical characteristics usedin this categorization is also explained in the appendix.
Figure 2 shows the cumulative distributions forthe surgical categories and highlights the differencebetween the categories. For example, surgeries fromcategory 1 always take less than four hours to com-plete, although on average only 50% of all cases takeless than four hours to complete.
4.1.2. MDSS Patients. As explained previously,some of the very long surgeries are split on individ-ual patients into two or more procedures with feasi-ble durations. Such surgeries constitute 10% of the allsurgeries and need to be performed within a certainnumber of days (ideally in two days).
Whether a patient will be undergoing a MDSS ornot depends on the ASA scores, anatomical location,surgical approach, and other factors. We also analyzedwhich surgical categories are generally divided intomultiple segments. Table A.2 in the appendix summa-rizes the most commonly observed MDSS pairs. Forinstance, a surgery category 6 followed by an 8 con-stitutes the biggest percentage. These percentages are
Figure 3 Relationship Between NOI and LOS for Medicare and Non-Medicare Patients
then used as weights in the objective function of thesecond stage (�s).
4.1.3. Financial Analysis and LOS. Our financialanalysis is based on the reported NOI values. Datamining was used to derive the cost drivers for theclinic. NOI values are driven by the LOS of thepatients, i.e., the hospitalization period in an inpatientunit post surgery. As well as the LOS, the charac-teristics of surgery like the equipment used (such asmicroscope and CT scanner), fusion and number ofvertebrae segments are an important predictor of NOI(see the appendix for terminology).
We performed the analysis for Medicare and non-Medicare patients separately, because of the differencein reimbursement policies (Figure 3). Regardless oftheir hospitalization period, Medicare patients onlyget reimbursed for four days and the hospital almostalways loses money for Medicare surgeries. How-ever, for non-Medicare patients, the hospital is reim-bursed based on the number of hospitalization days.Thus, as seen in Figure 3 as the LOS increases fornon-Medicare patients so does the NOI. However, theopposite is true for Medicare patients. Only some ofthe patients with small LOS indicate a potential gain,the majority of patients result in loss of NOI. In per-forming this analysis, we only considered first surg-eries of the day, to ensure that the effect of overtimecosts are discarded.
Since Medicare patients often require discharge toaSNF that does not accept patients on weekends, itwas important to schedule surgeries to avoid unnec-essary weekend stays in the hospital. We calculatedLOS in base 7 to analyze their discharge day of theweek after the surgery. For example, a LOS value of8 was equal to 1, meaning the discharge happenedon the following DOW of the surgery. Figure 4 rep-resents the percentage of weekend overflow (patientswho are ready to be discharged on the weekend) ifthey have their surgery on that DOW. This shows
Figure 4 The Percentage of Weekend Overflow by Each PatientCategory and Surgery DOW
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that Mondays and Fridays are generally the best daysto schedule surgeries, when it is important to avoidunnecessary weekend stays. However, this is not truefor all surgery categories. In particular, some of themore complex surgeries were better to schedule inmid-week because of specific LOS distributions.
We integrate the optimal day of Medicare surgeriesinto the first part of our optimization model usingthe Fld parameter, to minimize the weekend overflowsin the optimal solution. Using the results of the dataanalysis, this binary parameter takes on a value of 1 ifthe best DOW to perform category l Medicare surgeryis d and 0 otherwise.
4.2.1. Surgery Steps and Times. Similar to Batunet al. (2011) we divide the surgery durations into threecomponents: preincision, incision to closure, and post-closure activities. Preincision time involves preparingthe patient for surgery, incision to closure time is theactual procedure time, and the postclosure is requiredto close up the incision and prepare the patient forrecovery. Surgeons only need to be present in the ORfor incision to closure; the other activities can be per-formed by other surgical staff.
In addition to the preincision, incision to clo-sure, and postclosure time, we analyzed the surgeonturnover, OR cleaning, and beginning of day (BOD)time distributions as well (see Figure 5). Table 1 sum-marizes the best theoretical distribution fit for theempirical data. The lognormal function typically fitsthe best and is commonly used in the literature to rep-resent similar highly variable procedure times (Span-gler et al. 2004, Choi and Wilhelm 2012). However,in our research we have chosen to use the empiricaldistributions and not theoretical distributions.
The simulation used data for the time distribu-tions of the 10 surgery categories. The distributions
Table 1 Distributions for the Relevant Durations
25% quartile Median 75% quartile Mean Std. dev. Best fit
BOD (hrs) 8:18 (8:34) 8:22 (8:40) 8:28 (8:51) 8:27 (8:52) 0:22 (0:41) Normal 2 mixtureOR enter to incision (hrs) 1.1 104 1.7 104 0047 Johnson SuIncision to closure (hrs) 2.2 307 5.7 402 2077 WeibullClosure to OR exit (hrs) 0.3 0045 0.6 005 0029 Johnson SuOR turnover time (mins) 37 44 55 4805 1803 Normal 2Surgeon turnover time (hrs) 2.4 203 2.7 201 006 Johnson Su
Note. The values in parentheses represent the Monday outputs.
Table 2 Simulation Inputs to the Optimization Model
NNOI for NNOI forCombination Duration EOD % OT after 5 p.m. Hours after 5 p.m. % OT after 11 p.m. Utilization Medicare (%) non-Medicare (%)
Note. The values in parentheses represent the Monday outputs and NNOI stands for normalized net operating income.
Figure 5 (Color online) Stages in OR Time
≡
are derived for: BOD, preincision, incision to closure,postclosure, surgeon turnover, and OR cleaning forthe 10 categories.
4.2.2. Inputs to the Optimization Model. Table 2illustrates the simulation-based outputs for a sam-ple of surgery combinations. These outputs in turnbecome inputs to the first stage optimization. The mea-sures of interest are overtime percentage after 5 p.m.and 11 p.m., expected hours of overtime after 5 p.m.,OR utilization, and normalized NOI for Medicare andnon-Medicare surgeries. The values in the parenthe-ses represent the Monday outputs, as Mondays havedifferent outcomes as a result of late starts.
Note that sequencing does not play a role in ourmodels. A category 1 surgery followed by a cate-gory 2 surgery performed in the same OR will produceidentical results compared to a category 2 surgeryperformed after a category 1 surgery in the sameoperating room. Certain combinations result in 100%overtime and were therefore infeasible; this left uswith 55 feasible combinations. We compared the em-pirical EOD collected over seven years with the resultsof the simulation model. The simulation model accu-rately predicts the EOD values of the empirical distri-bution, with 95% confidence.
4.3. Example Optimization ResultsThe outputs of the simulation model were used to testand evaluate the optimization model. In addition, theoptimization model was explored to consider trade-offs and relationships among utilization levels, finan-cial performance, overtime allowance, and case mix.
4.3.1. First Stage Optimization. An example ofthe optimal surgery mix for a 120 day horizon can beobserved in Figure 6. The figure displays the optimalnumber of surgeries from each combination (y-axis)performed on different day groups. The shorter surg-eries (which are the lower numbered categories) areperformed on Mondays. Fridays are heavily loadedwith longer Medicare procedures. This results fromlate start Mondays and to prevent excessive overtime,long Medicare surgeries are left to Fridays, leadingto greater burden. Note that for profitability reasons,Medicare surgeries are generally best scheduled onMondays and Fridays, however this is not true for allsurgery types.
4.3.2. Second-Stage Optimization. The secondstage creates the optimal 12 week schedule with thefocus on maximizing the availability for MDSS. The
Figure 6 Optimal Surgery Mix
Tue-Fri non-Med all
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schedule assigns more priority to surgeries that havea greater empirically observed percentage (Table A.2in the appendix). The schedule repeats itself every12 weeks.
4.3.3. Third-Stage Optimization. Table 3 is an il-lustration of the final output of the optimizationmodel, for one set of parameter values. Values ineach cell indicate the surgical combination assignedto that day. This specific schedule is created so thatit follows the blue–orange schedule template of MayoClinic. This stage ensures there is a balanced work-load between the blue and orange surgeons.
4.3.4. Simulation for Testing Robustness. Eventhough most of the spine surgeries are scheduled inadvance, there are also some urgent cases. Six per-cent of the patients present infections, which need tobe operated quickly (within 24 hours). These surg-eries generally result in overtime, because infectionpatients need to be operated as the last surgery of theday to prevent the spread of infections. These urgentcases typically take much shorter than regular surg-eries (with an average length of 2 hours). Also, anecdo-tally 5% of the time last minute cancellations happenwhen the insurance company declines the surgery orwhen the health of the patient deteriorates.
We developed a second simulation model to testthe impact of unplanned surgeries (infections) andcancellations. We analyzed the impact of these onEOD when utilizing the optimal schedule. We con-clude that the simulation models and the results ofour optimization model are robust and are not statis-tically different when compared with a year’s worthof data (with a confidence interval of 99%).
4.3.5. Sensitivity Analysis. We performed sensi-tivity analysis to test the impact of parameters and
Table 3 (Color online) Optimal 12-Week Alternating Blue–OrangeSchedule for Two Surgeons
Note. The numbers indicate the surgical combination recommended on eachday. Numbers in bold indicate the combinations for the first surgeon whilenumbers not in bold indicate combinations for the second surgeon.
constraints, including the weight assigned to utiliza-tion in the objective function, case-mix bound width,limit on overtime, and length of the planning horizon.We analyzed the impact on optimal case mix, NOI,expected overtime, total number of surgeries, andutilization, using a multivariate analysis. Since plan-ning horizon did not have a statistically significantimpact on any of the output measures, we focused onbound width, overtime limit, and weight assigned toutilization.
To understand the trade-off between NOI and uti-lization, we generated an efficient frontier (as can beseen in Figure A.1 in the appendix). We altered theweights assigned to these two output measures fordifferent boundwidths and overtime limits. This anal-ysis points to potential gains with the same OR uti-lization, but with a different patient mix. The initialflat line in the curve shows the potential gain in NOIwithout sacrificing from utilization. The underlyingreason is that the surgeries that are creating high uti-lization levels do not necessarily result in higher rev-enue (like long Medicare surgeries).
This sensitivity analysis was used to set the param-eter values used in the optimization model for thepilot study implementation. Some of the main param-eter values used in the pilot are as follows: w (weightassigned to utilization) = 80%, o (overtime percent-age after 5 p.m.) = 25%, e (number of hours past5 p.m.) = 5 hours, f (percentage of days that end after11 p.m.) = 5%, m (Medicare patient proportion) = 30%.
5. ImplementationThe optimized scheduling approach was imple-mented via a custom designed web-based appli-cation that partially integrates with Mayo Clinic’sexisting surgical planning systems. The application,Spine Surgery Scheduling Optimization (SSSO), pro-vides visual cues to promote scheduling surgerieson the appropriate days identified by the optimiza-tion model. If a surgeon or their delegated scheduler
Figure 7 (Color online) SSSO Screenshots
needs to schedule a case on a “nonoptimal” day, thetool provides visual information as to the case loadand the likelihood of going overtime. The applica-tion can be used on any office or tablet computer andis therefore easy to use in an interactive way withthe patient. Figures 7–9 are screenshots from the web-based application.
To evaluate the effectiveness of the optimizationmodel and SSSO application, a pilot study was runfrom December 2012 to June 2013. Two of the fourorthopedic spine surgeons participated in the study. Itshould be noted that other initiatives were going on atthe same time as the pilot. In particular the orthopedicspine practice was working to increase case volumesand improve work processes related to on-time casestarts and room turnover. Therefore, as in an inter-vention to an ongoing process, it is difficult to deter-mine the precise benefit or cost of the implementation.In the following section we will describe the results ofthe pilot and how we attempted to account for pro-cess effects not due to SSSO.
5.1. Results of the Pilot ImplementationIn evaluating the results, the first month of the pilotdata was removed, because surgical cases duringthis period were primarily scheduled using the oldapproach. Figure 10 shows the results for the key per-formance measures during the evaluated pilot period.For all measures we eliminated empty days that weredue to holidays, vacations, and on-call duties. For uti-lization, this was evaluated as the busy percentage ofthe prime time period of 7:30 a.m. to 5:00 p.m. Over-time is defined as the percentage of days that wentover 5 p.m.
Figure 10 shows that, in general, the implementa-tion of the SSSO system provided the desired results.Patient access and utilization were higher and over-time lower for the surgeons participating in the pilot,during the pilot period. In particular, it is interestingto note the significant increase in cases per day for the
Figure 8 (Color online) Question Screen to Categorize Surgical Case
Figure 9 (Color online) Initial Screen that Identifies Optimal Days
surgeons participating in the pilot. It is also impor-tant to note that this was not done by using moreovertime.
Since it may be that the surgeons participating inthe pilot had practices that performed better beforethe pilot, we also compared the pre- and postim-plementation results for all surgeons in Table 3. Itis gratifying to identify that the overall efforts ofthe practice to improve patient access were achievedbecause all surgeons increased their number of casesper day during the pilot evaluation period. The twosurgeons participating in the SSSO pilot togetherincreased their access by a higher percentage (3001%)
versus the nonparticipating surgeons (2406%). Theimprovement in number of cases per day and utiliza-tion during the pilot period was statistically signif-icant compared to the prepilot period for the SSSOgroup, whereas the improvement in the same twomeasures for the two surgeons that did not use thetool was not statistically significant. The increase inovertime was not statistically significant for the SSSOsurgeons or for the non-SSSO group. We now discussresults specific to each surgeon.
In our study, as observed in Table 4, Surgeon 1achieved the kind of results the optimization methodwas intended to return: an increase in cases per
Figure 10 Comparison of Output Measures Evaluated During the Pilot
1.6
80.2%
30.3%
1.19
79.4%
38.7%
Cases per day Utilization Overtime
day, prime-time utilization, and a decrease in daysgoing to overtime. However, only the increase inthe number of cases per day was statistically signif-icant. Surgeon 2, who was also involved in the pilotincreased access and utilization, but also had a sta-tistically significant increase in days with overtime.Thus, we would say that Surgeon 1 used a “workingsmarter” approach and Surgeon 2 a “working harder”approach. Surgeons 3 and 4 also increased their accessand utilization, however, like Surgeon 2, they alsoincreased their overtime. Working hard is, of course,commendable, but the continued strain on the sur-geons and the surgical teams working in this modemay not be sustainable or safe in the long run. Insummary, improvements in comparison to the prepi-lot period were noticed in all surgeons, however, itwas only Surgeon 1 that improved in all measures.
These results also correlate well with the observedcompliance to the SSSO suggested optimal schedule.Surgeon 1 complied exactly with the suggested SSSOschedule on 15 of 42 surgery days during the pilotwhile Surgeon 2 complied exactly on 7 of the 43surgery days during the pilot. Note that this does notmean that the surgeons did not use the SSSO on othersurgery days: the interface allowed surgeons to lookat the overtime probabilities if they chose to override
Table 4 Pre- and Postimplementation Results for All Surgeons(Mean and Standard Deviation of the Mean for theBiweekly Data)
Notes. Surgeons 1 and 2 participated in the SSSO pilot implementation. Bold values show statistical difference at 0.05significance level.
Figure 11 (Color online) Compliance Rate of Surgeon 1
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the suggested schedule with their own choices, andalso the ideal day to schedule Medicare surgeries.
Figure 11 demonstrates Surgeon 1’s compliancerate, where x axis is the day of the surgery and the yaxis represents either full compliance to the schedule(100%) or a lack of compliance (0%) on each surgicalday during the pilot. Note that partial compliancecounts as 0% in the graph. Although compliance itselfis binary, the curve shows a weighted moving aver-age of the percent compliance. The drop in the monthof April represents the detection of a slight error inthe interface (one surgery category was misclassified),which resulted in surgeons not using the interfaceuntil it was fixed at the end of April. After this minorerror was fixed and surgeons were urged to restartusing the interface, the compliance rate once againincreased.
Table 5 shows the (normalized) average NOI percase from July 2012 to June 2013, for the four surgeonssix months before the pilot and during the pilot, splitby the four insurance groups. Numbers in the paren-theses indicate the standard deviation. During thepilot, S1 and S2 performed 138 total cases, comparedto 84 by S3 and S4. S1 and S2 performed 53 commer-cial cases and 65 Medicare/Medicaid cases, compared
to 22 commercial and 50 Medicare/Medicaid casesby S3 and S4. For the surgeons participating inthe SSSO pilot there was a small overall drop in theproportion of government paid patients compared tobefore the pilot; however, the proportion was still wellabove the threshold established by the practice.
It’s clear that both S1 and S2 together either stayedsteady or improved their per case NOI in each cat-egory. Neither surgeon decreased their average percase NOI in any category. S2 improved his NOI con-siderably in all categories. S3 also improved his NOIin all categories; however, average NOI for S4 wentdown in the Commercial and Employee categories.Profitability for Medicare patients increased duringthe pilot period for all surgeons, suggesting that theefforts to do these surgeries on the best days to avoiduncompensated hospital days were effective for thepractice as a whole. It is also likely that the surgeonsnot participating in the pilot worked harder sincethey were aware of the pilot. Together with the over-all increase in access (cases per day) attributable tothe SSSO implementation and other improvement ini-tiatives, the financial sustainability in the orthopedicspine surgery practice has improved and will providebetter access for all patients, regardless of reimburse-ment type, in the future.
In summary, the pilot implementation was deemedsuccessful, but not as comprehensively as desired.As the pilot rolled out, several challenges occurred,including technical issues with the programming ofSSSO, lack of desired flexibility in scheduling patients,and some discomfort by users of the tool with itsreliability. The following section will discuss some ofthe lessons we learned and proposed solutions as thesystem is rolled out more broadly across the surgicalpractice at Mayo Clinic.
5.2. Lessons Learned from the PilotPilot implementations by their nature are intended aslearning experiences. The points below are some ofthe key lessons we learned from our pilot.
• The SSSO application was generally developed inthe classic waterfall approach. The optimization teamhanded off a completed method to the programmingteam. There was some integration and communica-tion, but not as much as desired. This resulted in sometechnical issues with the tool. Some of these issues
were the responsibility of the optimization team andsome the responsibility of the programming team. Forexample, as mentioned in §5.1, in the third monthof the pilot a slight error was identified with regardto the classification of one particular surgery cate-gory; surgeon compliance to the tool reduced duringthis period and picked up again once the error wasfixed. All or most of these issues could have beenavoided by earlier involvement and better integrationof the teams.
• Some assumptions were built into the optimiza-tion method that did not work in practice. In par-ticular, we assumed that case mix could be shapedby how access was controlled at the time of surgeryscheduling. However, for spine surgery, it is commonfor the surgeons to see patients several times beforethe surgery decision is made. Limiting a patient’ssurgical access when they had developed a relation-ship with a surgeon pushed against Mayo Clinic’shigh-quality service philosophy. Thus, this approachis being adapted for ongoing implementations. Effortsat controlling access before patients come to MayoClinic have been implemented and are still under waythat will ensure the best use of our capacity whileensuring the needs of the patient come first.
• As identified in the previous section, Surgeon 1had the most desired performance profile during thepilot. This surgeon and his scheduling team werethe most involved during the optimization and tooldevelopment process. It is not surprising that the staffin this group had the most confidence in and under-standing of what the tool was trying to accomplish.For ongoing implementations of the modified tool weare working to involve more surgeons and staff in thedevelopment process.
• Both surgeons participating in the pilot foundthe ability to see the impact of scheduling a partic-ular case on a day very useful, even if they wereoverriding what was recommended by the optimiza-tion. The visualization shown in the window in Fig-ure 9, was of particular value. As scheduling decisionsevolve from being very patient preference oriented tobeing more system optimized, providing the surgeryschedulers with useful information to guide decisionmaking with flexibility is being incorporated into newversions of the tool.
A great deal was learned from the pilot and spe-cific improvements are being incorporated into newversions that are in development for several surgicalpractices at Mayo Clinic.
6. ConclusionsIn this paper we presented an improved method forscheduling spine surgeries in the orthopedic spinesurgery practice at the Mayo Clinic. Unique aspects ofour model include the incorporation of both resourceutilization and financial objectives. Categorizing surg-eries and developing statistical models for predictingsurgical lengths using clinical factors is a key contri-bution. Furthermore, using input from the surgeonsto categorize case types that led directly to schedulingdecisions assisted in gaining clinical staff engagement.
An implementation using a customized web-based tool that incorporated our optimization modelshowed generally positive results. Patient accessimproved significantly for the surgeons involved inthe pilot and operating room utilization improvedmarginally. For one of the two surgeons participatingin the pilot the access benefits were achieved by alsoreducing the percentage of overtime days. It shouldbe noted that patient access also increased for thesurgeons not participating in the pilot, but not byas much.
Our study has limitations. We consider hospitalLOS implicitly in considering profitability, but theimpact on downstream resource requirements is notinvestigated. We consider the surgeons as bottlenecksand the impact on inpatient or postanesthesia careunit (PACU) beds is not in the scope of this project. Ingeneral, at Mayo Clinic in Rochester, these resourcesare not constraints. Because of lack of informationabout cancellations, we did not directly incorporatethese into our model. Patient waiting time was notconsidered in our models. Lastly, since the surgicaldurations are relatively long, the number of surgicalcombinations is restricted (20 surgical combinations).As the number of possible surgeries in a combinationincreases (for specialties with shorter durations) thecomputational burden will increase as well.
We developed the optimization model using bothExcel’s Open Solver (Mason 2012) and AMPL. Excelwas favored for implementation and the pilot study,and the computational time was around an hourfor each stage with the Open Solver. AMPL, whichshould be favored for research, on the other hand,provides solutions in less than five minutes for eachstage. Exploring the general problem (with a greaternumber of decision variables) will allow us to under-stand the computational complexity of the optimiza-tion model more accurately.
Although this paper highlights a specific case studyapplication, we believe that many of the results and
insights will be of interest more broadly. In particular,the emphasis on considering the trade-offs and effectsof constraint limits may help other similar surgicaloperations gain useful insights. At Mayo Clinic thegeneral approach we developed is being consideredfor other surgical services and would likely benefitother organizations. For this reason, we emphasizedthe underlying ideas and theory of the applicationand show results of experiments that develop man-agerial insight. Other surgical services such as cardio-thoracic, neurosurgery, and plastic surgery that havelong average and highly variable procedure timesmay benefit from our research as well. As reported inAbouleish et al. (2003) these services together (withspine surgery) may make up to about 20% of surgicalvolume in hospitals.
From a literature perspective, we believe our paperis a significant contribution because it does morethan just consider the issues of changing case mixand surgical scheduling (which are prevalent in theconceptual operations management literature). Weextend the research area by considering the multipleobjectives related to utilization (and correspondingly,patient access), overtime, and financial performance.Furthermore, considering the downstream financialissues related to an important class of patients (thosewith fixed reimbursements) is novel and increasinglyimportant, particularly in the UnitedStates wherehealthcare reform is a prominent issue. Finally, to thebest of our knowledge, such pilots (pre and post;and a test and control group) focused on quantify-ing an implementation pertaining to operational andscheduling issues do not exist in the healthcare or sur-gical literature.
AcknowledgmentsHari Balasubramanian’s time on this research was partiallyfunded by the National Science Foundation [Grant CMMI1254519].
AppendixWe provide more detailed information on the inputs of theproblem below.
Spine Surgery TerminologyThis section describes the basics of the spine surgery toincrease the understanding of the problem. Spine anatomyis divided into 4 major sections, which are defined by thenumber of vertebrae. Vertebrae are the bones that make upthe structure of the back bone. Disc is the tough, elasticstructure that is between the bodies of spinal vertebrae. Thedisc and vertebra above and below the disc comprise onesegment of the spine—usually called a spinal level or spinalsegment. The spine is divided into 4 main sections: cervi-cal (neck), thoracic (upper back), lumbar (lower back), andsacral region (bottom of the spine). Because lumbar sectionof the spine bears most of the body’s weight and allows for
the most motion, this is the area associated with most backproblems (Patel et al. 2013).
Surgeons can reach the spine by making an incision (cut)in different places on your body. Incision sites are oftendescribed as: anterior, posterior and lateral. Anterior fusionis done by making an incision in the abdomen (belly). Pos-terior fusion refers to surgeon making the incision in thelower back. Lateral is required as surgeons can reach cer-tain parts of the lumbar spine by making an incision inyour side.
Spinal deformities are typically called scoliosis. Thereare many different types of scoliosis and with that differ-ent types of procedures to correct these spinal deformities.Spinal fusion is surgery to permanently connect two ormore vertebrae in your spine, eliminating motion betweenthem. Bone graft and/or bone graft substitute is needed tocreate the environment for the solid bridge to form. At thetime of the fusion surgery, the use of metal devices, alsocalled implants or instrumentation (e.g., screws and rods)is typically used to provide stability for that section of thespine for the first few months after surgery. In simple termsthere are long spinal fusions (across many levels) and shortsegmental spinal fusions (one or a few levels). Sometimes
Figure A.1 Trade-Off Between Utilization and NOI
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)
Utilization (%)
PB = 200%; OT25% PB = 200%; OT38%
PB = 200%; OT50% PB = 400%; OT38%
Note. PB, case-mix bound width (i.e., allowed flexibility in changing the casemix); OT, overtime.
a fusion is necessary usually in conjunction with a decom-pression, but sometimes alone. Spinal decompression refersto any surgical technique which aims to free the space forthe nerves in the spinal canal (Kuehn 2012).
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