Perioperative process improvement using discrete event simulation

by

Solmaz Azari-Rad

A thesis submitted in conformity with the requirements

for the degree of Masters of Applied Science

Graduate Department of Mechnical and Industrial Engineering

University of Toronto

c© Copyright by Solmaz Azari-Rad 2010

Perioperative process improvement using discrete event simulation

Masters of Applied Science, 2010

Solmaz Azari-RadGraduate Department of Mechnical and Industrial Engineering

University of Toronto

Abstract

A discrete event simulation was applied to model the perioperative process in the gen-

eral surgery service at Toronto General Hospital, aiming at reducing the number of surgical

cancellations and improving the perioperative process. This model includes emergency case

interruptions with two types of emergency cases with different levels of urgency, and takes

into account the availability of three types of post-surgical beds: medical surgical intensive

care unit, step-down unit and ward beds in decision making level. The effect of three types of

scenarios on the number of surgical cancellations was explored: 1) applying effective schedul-

ing rules based on the utilization of post-surgical beds, 2) sequencing the surgical operations

based on the length of surgeries and the variance of surgery durations, 3) increasing the

number of post-surgical beds. The results indicated that scheduling the surgeons in a weekly

schedule based on their patients’ average lengths of stay in the ward reduced the number of

surgical cancellations. Sequencing the surgeries in increasing order of the length of surgeries

and the variance of surgery durations reduced the number of cancellations, and adding beds

to the surgical ward reduced the number of surgical cancellations as well. The interactions

of all these scenarios were compared against the current system and against each other to

provide basis for decision making.

ii

Acknowledgements

This research project could not have been completed without the encouragement and

assistance of numerous people.

I would like to give my sincere thanks to my supervisor, Professor Dionne Aleman for

her guidance, advice and support throughout the entire process, and for providing me with

such a great research opportunity. I would also like to thank my co-supervisor, Dr. David

Urbach for guiding me through this research.

I would like to acknowledge the help and cooperation of the surgical and administrative

staff at Toronto General Hospital.

My special thanks go to my friends Somayeh Sadat, Daphne Sniekers and Pedram Sahba

for the help, encouragement and caring they provided.

A big thank goes to my morLAB buddies for making the lab such a friendly place to

work, and a special thank to Hamid Ghaffari for his pointers on various matters.

Finally, I am forever indebted to my parents for their understanding, endless patience

and encouragement when it was most required, and for uplifting me through my difficult

times. I also thank my brother Vahid for always being there for me.

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Contents

1 Introduction 1

2 Literature review 4

2.1 General issues in OR efficiency and patient flow . . . . . . . . . . . . . . . . 4

2.2 OR scheduling problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Assignment of surgical cases to OR time blocks . . . . . . . . . . . . . . . . 7

2.4 Sequencing of surgical cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Resource planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Unpredictability of surgical procedure length . . . . . . . . . . . . . . . . . . 12

2.7 Emergency case planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.8 Contributions to the literature . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Perioperative process for general surgery patients at the Toronto General

Hospital 15

3.1 Overview of TGH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Pre-surgical process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Patient flow on surgical day . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4 Post-surgical process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Model development 24

4.1 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Flow of patients through the surgical process . . . . . . . . . . . . . . . . . . 27

4.3 Modelling patient arrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.4 Determining the patient path through the model . . . . . . . . . . . . . . . . 29

4.5 Determining the first patients of the any OR day . . . . . . . . . . . . . . . 30

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4.6 Decision making process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.7 Model limitations and assumptions . . . . . . . . . . . . . . . . . . . . . . . 33

5 Results 34

5.1 Warm-up period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 “What if” analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3.1 Modifying the surgeons’ weekly schedule . . . . . . . . . . . . . . . . 37

5.3.2 Scheduling rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3.3 Sequence of surgical operations . . . . . . . . . . . . . . . . . . . . . 41

5.3.4 Increasing the number of ward beds . . . . . . . . . . . . . . . . . . . 43

5.4 Pairwise comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Conclusion 46

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1 Introduction

No private industry would survive with the level of waste and inefficiency commonly seen in

the healthcare industry [Carter, 2002]. The fact that the healthcare industry could be more

efficient has encouraged the use of operations research to improve healthcare systems. Some

examples of use of operations research in healthcare industry are patient waiting list man-

agement (e.g., surgical waiting list, MRI, etc.), emergency department planning, operating

room scheduling and staff scheduling (e.g., surgeons, nurses, etc.).

This study will focus on the operating room planning and scheduling problem. Since

operating rooms (ORs) use scarce resources such as surgeons, nurses and pre-operative and

post-surgical beds, they are among the costly facilities in hospitals. Therefore, creating

an efficient OR schedule that improves the throughput and the OR time utilization is an

important issue in hospitals, and several studies have been performed to address this matter.

This research was performed in collaboration with Toronto General Hospital (TGH),

and the objective of this research was to identify the potential improvements in the flow of

patients through the surgical process, to reduce the number of surgical case cancellations,

and to make more efficient use of hospital resources such as post-surgical beds.

A discrete event simulation (DES) model was built to model the flow of patients through

the surgical process in the general surgery service at TGH, and used to test the impact

of different scheduling and sequencing rules as well as the number of available resources

(e.g., number of beds in post-surgical units) on the surgical case cancellations. The arrival

of emergency cases were taken into consideration as well. Patients arrive to the system

from different points and follow certain paths. DES allows us to observe the behaviour of

the system under different situations and analyze the results of running different scenarios.

Specifically, we seek to observe the impact of applying scheduling rules on the weekly schedule

of surgeons, applying sequencing rules on surgeons’ daily cases and adding beds to post-

1

surgical units on the number of surgical cancellations.

Simulation modelling can be thought of as virtual representation of a system or a pro-

cess where the goal is to mimic, or simulate, a real system in order to explore it, perform

experiments on it, understand it, and to identify the bottom line opportunities for system

improvement without spending substantial resources in the examination process [Hauge and

Paige, 2001]. Simulation is an approach used when the system is considered too complex to

be abstracted into strict mathematical relationships. Instead, simulation models conform to

the direct representation of the system’s structure, logic and the available data [Standridge,

1999].

Simulation models have been extensively used to model healthcare systems, and many

papers in the literature outline the appropriateness of the simulation models in healthcare

problems. Van Berkel and Blake [2007] state that “the complex nature of healthcare sys-

tems often makes analytical models intractable; researchers must decide between simple, but

tractable models, or opt for complex but realistic models”.

The main advantage of simulation over other modelling techniques, such as linear pro-

gramming, is its capability to model complex systems and perform “what-if” scenarios by

changing the model’s rules and assumptions. Everett [2005] argues that the function of a

model is not only to provide information to managers but also to engage them in the devel-

opment process so as to allow them to use the model independently as a decision support

tool.

DES is a technique in which a system is modeled as it evolves over time and the state

variables change at separate points in time [Law, 2007]. At these points in time, events occur

that may change the state of the system. DES is designed to model detailed processes that

consist of entities, resources, and control elements (elements that determine the states of the

entities and resources), and generally relies on transaction-flow approach to model systems.

2

Examples of such processes could be call centers, factory operations and healthcare systems.

In operational level problems in healthcare, usually patients are modelled as entities with

specific attributes such as their gender, age, urgency of treatment, etc. These entities pass

through a series of queues and discrete event activities that influence their journey through

the system. The activities that the patients undergo provide basis for estimating the resource

use and the time they spend in queues provide the basis for estimating wait times [Koelling

and Schwantdt, 2005].

OR planning and scheduling is a complex problem, and simulation modelling has been

widely used to address this problem. Yang et al. [2000] regard computer simulation as a

powerful management tool that can be applied to medical scheduling. They provide several

examples of studies that have been successfully done by simulation in emergency depart-

ments, pharmacy departments, operating rooms and out-patient departments, and conclude

that traditional approaches to scheduling such as mathematical programming are of limited

usefulness in medical scheduling due to the complexity and involvement of human factors.

The OR scheduling at TGH is challenging due to the involvement of several units in the

surgical process. For instance, shortage of beds in post-surgical units is a bottleneck in the

smooth flow of patients. Accurate prediction of surgical case durations, pre-operative and

post-surgical lengths of stay are necessary to reach an efficient OR schedule. Occurrence of

emergency cases is an important factor resulting in surgery delays and cancellations in TGH.

Delays in the start of surgeries may result in running the ORs into overtime, and running

the ORs into overtime has financial and non-financial consequences. Financial consequences

include the cost of overtime staff in ORs and post-surgical care units; the non-financial

consequences include staff dissatisfaction due to long working hours and patient anxiety due

to long wait times.

In Section 2, some related studies in OR efficiency, patient flow through the surgical

3

process, and OR scheduling with different perspectives and goals are discussed. Section 3

explains in detail the perioperative process in the general surgery service at TGH. Section

4 describes the challenges of model development for the perioperative process at TGH,

limitations and assumptions. Section 5 includes the model validation and results, and Section

6 includes the conclusions and the area of future work.

2 Literature review

Since operating rooms (ORs) are generally a hospital’s both largest cost centres and great-

est revenue sources [HFMA, 2005], OR management is an area with significant potential for

recognizing higher efficiencies within hospitals [Denton et al., 2006]. Managing ORs is a com-

plex task due to the conflicting priorities and preferences of its stakeholders [Gelauberman

and Mintzberg, 2001], and scarcity of costly resources. In addition, healthcare managers

need to predict the increasing demand for surgical services caused by an aging population

[Etzioni et al., 2003], and developments in surgeries [Marjamaa et al., 2008]. In order to

achieve higher efficiency in ORs, numerous resources must be synchronized. For instance,

surgeon availability, operating team availability, bed and staff availability in post-surgical

care units, equipment and support services must be carefully synchronized.

2.1 General issues in OR efficiency and patient flow

Improving OR efficiency is of great importance to the economic viability of the healthcare

institutions. Several works have described the problem of OR efficiency by addressing the

common goals in OR efficiency and by depicting the various factors affecting the flow of

patients and consequently the efficiency of the OR.

4

Marjamaa et al. [2008] state that improving OR efficiency means “shorter surgical case

durations, rational scheduling of various types of surgeries, and minimization of the non-

operative time by reorganizing the OR tasks”. Strum et al. [2000] define the OR efficiency

in terms of under-utilized and over-utilized hours of OR time. The efficiency of OR use is

maximized by minimizing the sum of two products: (1) under-utilized OR hours multiplied

by the cost per hour of under-utilized OR time; and (2) over-utilized OR hours multiplied

by the cost per hour of over-utilized OR time.

Efficient OR scheduling is essential in achieving OR efficiency. OR scheduling is not an

isolated problem; several factors need to be taken into consideration in order to achieve an

efficient schedule. Harper [2002] states that dynamics governing a hospital system demand

a need for capacity models, which reflect the complexity, uncertainty, variability and limited

resources. Factors such as rules governing patient admissions into a hospital, constraints

imposed by other hospital services, variability of patients’ lengths of stay in different surgical

specialties and limited resources (e.g., beds, nurses) need to be taken into consideration.

Cendan and Good [2006] estimate that for every operative month, the equivalent of five

working days are wasted through a combination of factors including inappropriate patient

preparation, insufficient staffing (e.g., surgeons, anaesthesiologists and nurses), emergency

case arrivals, congestion in the post-anaesthesia care unit and, of particular importance,

OR turnover time, the time required to prepare the OR for the next case. Marjamaa et al.

[2008] enumerate the key factors for operating room efficiency as streamlining processes with

other departments, patient flow and its coordination, timely patient preparation, efficient

patient reception, parallel processing by use of induction area, recovery room, intensive care

unit and ward capacity, number of professional skilled personnel, flexible facilities, patient

focused processes and continuous process improvement.

Cendan and Good [2006] improve the daily workload by analyzing the routine tasks of

5

an operating team and minimizing the inefficiencies. By observing and studying their as-

signed tasks and workflow patterns, a re-designed workflow diagram for each function was

created. Inefficiencies were identified by analyzing the interactions among the anaesthesiolo-

gists, scrub technicians and circulatory nurse assistants. Acting on inefficiencies to improve

the process and redesigned flow reduced the turnover time and allowed the surgeons to sched-

ule additional cases without working overtime. Baumgart et al. [2007] propose a conceptual

framework to use computer simulations in different stages of business process management

(BPM) lifecycle for operating room management. Computer simulation supports process

engineering in perioperative processes and shows potential process improvements.

Poorly designed perioperative processes, change reluctance, lack of motivation and finan-

cial incentives for stakeholders, lack of clearly defined responsibilities and discipline seem to

be common problems associated with OR management [Marjamaa et al., 2008].

2.2 OR scheduling problem

Schedule development for ORs is a three-stage process. The first stage is assigning the

available OR time to different services in a hospital. The total OR time available in a

hospital is a function of hospital’s budget and available resources such as number of ORs,

OR nurses, etc. Once the total OR time is determined by hospital administrators, the next

stage is to develop a master surgical schedule (MSS). Blake and Donald [2002] describe

the MSS as a “cyclic time table that defines the number and type of ORs available in an

institution, the hours that the rooms will be open and the surgical unit associated with each

OR block time”. A new MSS is created whenever the total amount of OR time changes.

After development of the MSS, in the third stage the OR time available in each service is

distributed among its surgeons, elective cases are scheduled in each allocated time block and

the sequence of surgical cases is determined.

6

The OR time assignment to different departments in a hospital can be based on different

criteria such as total cases per allocated time block (e.g., historical utilization), costs and

gains per allocated block (e.g., financial criteria) and demand for different services (e.g.,

waiting lists), etc. [Testi et al., 2007].

In order to select the number of sessions to be scheduled for each ward on a weekly basis,

Testi et al. [2007] solve a bin packing-like problem. They use an updated priority score

taking into account the waiting list of each ward and reduction of unsatisfied ward demand

for operating time sessions. Then, using a blocked booking method, they determine an

optimal MSS, which maximizes surgeon preference (e.g., available days). Blake et al. [2002]

apply an integer programming model to allocate total OR hours to different departments in

a hospital as close as possible to their target. The produced MSS, with a one week time

period, is then extended to cover all the weeks in a certain time period. Blake and Donald

[2002] also use integer programming to distribute the OR time among different departments

of a hospital aiming at reducing the conflict between departments.

The distribution of the OR time available in each service among its surgeons is usually

performed based on the policies and rules governing different hospitals such as waiting lists,

seniority, etc.

Most studies in OR scheduling have focused their attention to techniques that involve

the scheduling and sequencing of surgical cases into OR time blocks in order to reduce the

OR hours of overtime, number of case cancellations, staff cost, etc.

2.3 Assignment of surgical cases to OR time blocks

A variety of planning and scheduling techniques have been applied to assign the surgical

cases to the OR time blocks. Jebali et al. [2005] model the operation assignment problem

as a mixed integer program, and consider the recovery room beds as a bottleneck aiming

7

at minimizing the total overtime for ORs. However, this study does not take into account

the occurrence of emergency cases and the priority that exists among some operations.

Van Houdenhoven et al. [2007] use a bin-packing approach with a different planned slack

for each department to assign the surgical cases to ORs. To deal with the unpredictability

of the case durations they exploit the portfolio effect and minimize the planned slack. This

technique is applicable to hospitals that set their surgical schedule a few weeks in advance.

Hans et al. [2008] also use a general bin-packing problem for robust surgery loading. They

choose the amount of slack so that the probability of overtime is approximately 30%, and

minimize the total planned slack by using the portfolio effect.

Fei et al. [2006] build an efficient weekly OR schedule through two phases: first the OR

weekly scheduling problem is solved with a heuristic procedure based on column generation;

then, the OR daily scheduling problem is solved with a hybrid genetic algorithm, based on

the results from the first phase. To study the impact of uncertainty on strategic design and

OR scheduling, Denton et al. [2006] start with a single OR optimization model and then

expand it to a multi-OR optimization model. They use a computer simulation to model the

three stages of patient intake, surgery and recovery, attempting to reduce the patient wait

for intake and surgery as well as the OR overtime. They have applied simulated annealing

to find a schedule that simultaneously improves waiting and overtime.

Dexter et al. [1999] use a computer simulation to model the OR scheduling and to evaluate

the four standard algorithms (Next Fit, First Fit, Best Fit and Worst Fit) to maximize the

OR time utilization. This study makes use of waiting lists; the longer the patients wait

for surgery, the greater the percentage of OR block time used. Since most serious surgeries

cannot be delayed, this approach is not feasible in all circumstances. In addition, there is no

clear strategy for handling the emergency cases. Testi et al. [2007] apply a simulation model

to identify the best admission rule for selecting patients to be scheduled in each OR session.

8

However, other resources involved in the process such as recovery and intensive care unit

beds and staff do not define bottlenecks. Dexter and Traub [2002] assess the application of

two heuristics on OR time utilization, while scheduling a new elective case in ORs: (1) latest

start time (LST); (2) earliest start time (EST). This approach considers elective cases in

hospitals with specific characteristics (e.g., surgeons and patients choose the day of surgery,

cases are not turned away, etc.). They show that neither EST nor LST is preferable to the

other in terms of OR efficiency.

2.4 Sequencing of surgical cases

Once the surgical cases are assigned to the OR time blocks, the sequence of the surgical cases

must be determined. The sequencing of the surgical cases impacts the risk of OR overtime,

number of case cancellations and the resource requirement in the post-surgical care units.

Therefore, it is important to identify an effective sequencing rule.

Denton et al. [2007] applied a two-stage stochastic programming model to determine

the optimal surgery schedule. Based on numerical experiments using real surgery duration

data, they compared optimal schedules with actual schedules and showed that sequencing

decisions also play an important role in scheduling decisions, and concluded that the common

practice of scheduling longer and more complex cases earlier in the daily schedule may have

a significant negative impact on OR performance measures. After assignment of surgical

cases to ORs, Jebali et al. [2005] first assign the surgical cases to the ORs, and then test two

strategies regarding the sequence of surgical cases to reduce the OR overtime. The strategies

are: 1) sequencing is done on surgical cases of every OR and the operation assignment to

ORs, obtained in the assignment step, is not reconsidered; 2) operation assignment to ORs

is redefined in order to be less constrained.

Using a simulation model, Testi et al. [2007] select the patients from the surgical list

9

based on different priority rules: longest wait time (LWT), longest processing time (LPT)

and shortest processing time (SPT), and examine different sequencings of surgical cases to

improve the OR time utilization. They showed that the SPT is the best admission rule.

Marcon and Dexter [2006] employ a simulation model to compare the outcomes of different

sequencing rules on PACU staffing, and over utilized OR time, while applying the same

sequencing rules to lists of individual surgeons.

2.5 Resource planning

Since hospital resources are limited and costly, hospital administrators seek to find alterna-

tives to maximize the resource utilization in hospitals. This problem can be considered at the

level of admission profile planning. Admission planning decides on the number of patients

admitted to a specialty each day and also on the mix of patients admitted. Within each

specialty, patients can be categorized depending on their requirement of resources. The type

of resource required for an admission may involve ward beds, OR capacity, nursing capacity,

etc.

Adan and Vissers [2002] model the case mix planning in the form of linear integer pro-

gramming, taking into account the planning period, patient categories, resources and their

capacity, target patient output and target utilization of resources. The outcome provides

evidence that the model does what it should do, but the serious limitation of the model

is that it excludes the emergency surgeries. Blake and Carter [2002] use two linear goal

programming models to allow decision makers to set case mix and case costs in a way that

the hospital is able to break even, while preserving physician income and minimizing dis-

turbance to practice. The validity of the model was tested through a three-phase process.

Harper [2002] proposes a generic framework for modeling hospital resources, considering the

user needs and the real life processes. The key differentiator between this work and other

10

studies that produce practical capacity planning and management tools is this framework

includes patient classification techniques to define statistically and clinically meaningful pa-

tient groups. Then, these classified patient groups can be fed into developed simulation

models.

Since ORs function in synchrony with other units such as pre-operative care units, in-

tensive care units, recovery rooms and wards, efforts to improve OR time utilization may

affect the functioning and efficiency of other departments. Consequently, even after deter-

mining the case mix for hospitals at a more detailed level, OR planning and scheduling has

to satisfy various resource constraints such as number of beds and professional staff for ORs,

post-anesthetic care units and wards. Some studies particularly focus on OR scheduling to

achieve higher efficiencies in resource utilization.

Marcon and Dexter [2006] use discrete event simulation to study the impact of surgery

sequencing on PACU staffing, over utilized OR time resulting from delays in PACU admis-

sions and hourly number of patients staying in PACU. In order to reduce the number of

surgery cancellations, Calichman [2005] reviews the hospital’s bed use statistics. The key

is to schedule surgical procedures on different days to minimize and balance the number

of beds required each day. The efficient OR schedule should result in a balance between

the demand and the supply of ward beds during the week. Marcon et al. [2003] develop a

simulation model to calculate the minimum number of beds required in the PACU, and to

evaluate the relationship between overall performance of ORs and number of staffed PACU

beds and porters. Using a simulation model, they showed that in their particular system,

the porters seem to play a role of bottleneck in the flow of the patients in the operating

process.

Van Berkel and Blake [2007] use discrete event simulation model for capacity planning and

management of patient wait times for general surgery department. After the model validation

11

the sensitivity analysis is performed, and they conclude that the bed resource rather than the

OR available time is the bottleneck of the system, and redistribution of beds between sites,

in their particular hospital, help them to achieve their emergency operational requirements

with the minimum number of beds possible. Due to the type of surgical operations done in

their particular system, they exclude the intensive care unit beds from their study.

2.6 Unpredictability of surgical procedure length

Unpredictability of surgical procedure length is an important issue in OR planning and

scheduling [Tyler et al., 2003, Wright et al., 1996]. Numerous studies have focused their

attention on a realistic prediction of the surgical case durations to produce a more reliable

OR schedule. The identity of the surgeon and the type of surgical procedure are the two

most important determinants of surgical time [Zhou et al., 1999]. Lebowitz [2006] identifies

that approximately half of the subsequent surgical cases (after the first of the day) will

not start on time because of procedure duration overruns by preceding procedures. Using

reliable historical data about a specific surgeon and procedure combinations can minimize

these overruns. However, statistical variability of surgical durations implies that half of

surgical operations will run longer than the mean calculated, resulting in wait time for the

patients and surgeons. Lebowitz uses a Monte Carlo simulation model to examine different

statistical variations in order to maximize the OR surgical throughput.

Zhou et al. [1999] use a statistical model containing three effects: procedure (effect of

the type of procedure on surgical time), surgeon (effect of the particular surgeon on surgical

time), and case (remaining variation in surgical time after specification of procedure and

surgeon) to study the effectiveness of using historical data to predict lengths of surgical

operations. In the Monte Carlo simulation, the behaviour of these effects is represented by a

probability distribution to calculate the surgical time for millions of hypothetical cases. They

12

concluded that relying solely on previous cases’ surgical time is unlikely to reduce the average

amount of time cases finish late. The reason is for many cases there are no historical data

for a combination of particular procedure and particular surgeon, and when the historical

data are available, increasing the number of previous cases does not significantly affect the

average length of time that cases finish past their scheduled finish time.

Dexter [2003] states that “even one month of historical data can be used to for the analysis

and still provide better OR time allocations than those developed by hand or by experienced

OR managers”. This review shows the effectiveness of information management systems in

more efficient OR time allocation and of sharing allocated time between different services

in a hospital. Dexter and Ledolter [2005] suggest a practical way to calculate Bayesian

prediction bounds and compare the OR times of the cases even when there are few or

no historic data for the surgeon and the scheduled procedure. Dexter and Traub [2000]

propose a statistical method to predict whether one case will last longer than another case.

The rationale to develop this method was based on the need to share resources such as

equipment and personnel. The major limitation of this method is that it only performs

pairwise comparisons. This method cannot be used when limited resources will be shared by

three or more ORs on the same day. Tyler et al. [2003] and Wright et al. [1996] also consider

the case duration and its variability as an important factor that affects the OR utilization,

and attempt to provide more accurate time durations by applying statistical modeling.

2.7 Emergency case planning

Arrival of the emergency cases in hospitals is an inevitable fact. Emergency cases, depending

on their severity, may demand immediate action. Occurrence of emergency cases disrupts

the daily OR schedule and causes surgical delays and cancellations. Most OR scheduling

studies in the literature overlook the effects of such cases in their elective schedule planning.

13

However, emergency cases are one of the important issues that need to be taken into account

in creating an efficient OR schedule.

Davenport et al. [2001], Herroelen and Leus [2005], and Wullink et al. [2005] state that a

buffer of extra time (slack) and/or resources can be used to deal with the disruptions caused

by emergency cases on the daily elective schedule. Lovett and Katchburian [1999] stress that

assigning dedicated ORs to urgent cases can decrease overtime and the number of urgent

surgeries served after working hours. However, Barlow et al. [1998] and Brasel et al. [1998]

conclude that setting ORs aside for emergency cases is costly, due to low utilization rates of

ORs.

Wullink et al. [2007] adopt a discrete event simulation model to evaluate two different

policies for reserving operating room capacity for emergency surgeries to reduce waiting time

and staff overtime, and to improve OR time utilization. They compare: 1) concentrating all

reserved OR capacity in dedicated emergency ORs with 2) evenly reserving capacity in all

elective ORs. Outcomes of the simulation model shows that the second policy has overall

better results in terms of performance measures.

Van der Lans et al. [2005] state the need for constructing a robust surgical schedule that

anticipates urgent surgeries, while minimizing the urgent surgery wait time and overtime

and maximizing OR utilization. They consider two levels of planning and control. At the

first level they study the allocation of slack to dedicated ORs to emergency surgeries versus

distributing the slack among all available ORs, and at the second level they try to sequence

the elective cases in a way that their completion time, which are break-in moments (BIM)

for emergency cases, spread as equally as possible during the day to reduce the wait for start

of the emergency surgeries. They refer to the second phase as a BIM optimization problem.

Lamiri et al. [2008] formulate the elective case planning problem as a stochastic mathe-

matical program, taking into account the emergency cases. A solution method combining the

14

Monte Carlo simulation with mixed integer programming is proposed and successfully tested.

Although, this work does not consider the availability of resources in the OR planning.

2.8 Contributions to the literature

The literature in OR planning and scheduling mostly focuses on the scheduling of elective

cases into time blocks. Many studies have not considered the existence of emergency cases,

and those studies that have considered emergency cases, did not distinguished between dif-

ferent types of emergency cases with different urgencies.

Even though the availability of post-surgical resources such as post-surgical beds is an

important matter in achieving higher performances, it has not been addressed in the litera-

ture extensively. Most studies that consider post-surgical resources in their planning usually

focus on utilization of resources in a particular unit.

This work considers emergency case interruptions, and distinguishes between the two

types of emergency cases (more urgent and less urgent). We also take into account the

availability of three types of post-surgical beds: medical surgical intensive care unit, step-

down unit and ward beds. Additionally, we attempt to improve the surgical process by

applying effective scheduling (based on the utilization of post-surgical beds) and sequencing

rules (based on the length and variance of surgical operations) and identifying the bed

requirements in post-surgical units.

3 Perioperative process for general surgery patients at

the Toronto General Hospital

Perioperative generally refers to three phases of surgery: pre-operative, intra-operative, and

post-operative. The perioperative period is the time period that describes the duration

15

of patient’s surgical encounter. This commonly starts when the patient is scheduled and

consequently is admitted to the hospital for the surgical procedure, and ends when the

patient is discharged from the hospital or alternative level of care (ALC) facilities.

The purpose of this section is to describe in detail the perioperative process for general

surgery patients at the TGH. Different types of patients, units and resources involved in the

perioperative process will be explained, and the flow of patients through it will be described.

3.1 Overview of TGH

TGH, a part of the University Health Network (UHN), is a major teaching hospital in

downtown Toronto. There are 19 ORs, and approximately 9,000 surgical cases per year.

TGH is affiliated with the University of Toronto, and has been serving the community with

acute care patient services for more than 165 years. TGH provides many complex services,

including cardiac care, organ transplantation and the treatment of complex patient needs.

TGH is composed of 406 in-patient beds, and the emergency department at TGH servers

30,000 patients annually.

The perioperative services for general surgery patients at TGH includes the pre-admission

clinic, pre-operative care unit (POCU), ORs, post-anesthetic care unit (PACU), step down

unit (SDU), medical surgical intensive care unit (MSICU), medical day unit (MDU) and the

surgical ward:

• Pre-admit clinic: is the clinic that performs the patients’ pre-operative tests approx-

imately two weeks prior to their surgery.

• Pre-operative care unit (POCU): prepares patients physically and psychologically

for the surgical operation according to their needs. The preoperative period runs from

the time the patient is admitted to the hospital to the time that the surgery begins.

16

This area is also called the “holding area”.

• Post-anesthesia care unit (PACU): where surgical patients are transferred for

nursing assessment and care while recovering from anesthesia. Vital signs, adequacy of

ventilation, level of consciousness, surgical site, and level of pain are carefully monitored

as the patient recovers consciousness. This unit is also called the “recovery room”.

• Medical surgical intensive care unit (MSICU): specialized unit containing the

equipment, medical and nursing staff, and monitoring devices necessary to provide

continuous and intensive care to acutely ill patients.

• Step down unit (SDU): designated to provide intermediate care for the patients

who need less monitoring than those in the intensive care unit, but still require more

monitoring than those in the hospital ward.

• Medical day unit (MDU): which admits the same day patients from PACU, and

prepares them to be discharged. This unit also serves outpatients with a wide variety

of medical conditions, from transplantation to blood disorders. For instance, adminis-

tering intravenous antibiotics, iron infusions and blood transfusions are performed in

this unit.

• Ward: is a suite of rooms shared by patients who need a similar kind of care. Patients

are taken to the ward from PACU, MSICU or SDU when they need a lesser level of

care and monitoring by medical staff, but are still not well enough to be discharged.

• Alternative level of care (ALC) facilities: provide care for patients who no longer

require the intensity of resources or services provided in their current settings. An

example of ALC facilities is long-term care facilities.

17

Depending on the surgery type and the level of care required, patients are taken to a com-

bination of these units alternatively.

The type of decision making and the journey of patients through the perioperative process

depend on the type of patients. The three main types of surgical patients at TGH are:

1. Same day patients: elective patients who arrive at the hospital on the scheduled

date for the surgical procedure. These patients are intended to be admitted to and

discharged from hospital the same day. Same day patients usually have short lengths

of stay in PACU, and then are taken to the MDU to be returned home.

2. In-patients: are elective patients who are admitted to the hospital on the scheduled

date of the surgery, but meant to be hospitalized for one or more nights depending

on the severity of their case and the level of care they need. These patients require

longer recoveries under the supervision of medical staff, and may stay in a mix of highly

monitored (e.g., MSICU) and less monitored (e.g., surgical ward) post surgical units.

3. Emergency patients: patients who visit the emergency department (ED), and re-

quire surgery within a few hours to a few days of their arrival depending on the urgency

of their case. These patients generally wait for their surgical procedure in the ED or

the ward or the intensive care unit beds, depending on their health condition and the

availability of resources.

Emergency general surgery patients at TGH that require surgery can be categorized into

two groups: (1) emergency type A patients; (2) emergency type B patients. Emergency type

A patients require surgery within 0 to 2 hours of their arrival to hospital, and emergency

type B patients require surgery within 2 to 8 hours of their arrival to hospital.

Another type of emergency patients, rare to general surgery, are emergency type C pa-

tients. These patients are the ones that are already admitted to the hospital, and require

18

surgery. These patients may need to be prioritized ahead of the elective patients, since they

are already in the hospital using resources.

3.2 Pre-surgical process

Elective patients are referred to surgeons by their family physician for specialist care. Then,

patients meet with the surgeon, and the surgeon decides whether the patient needs a surgical

operation. Each surgeon’s office, which is composed of a surgeon and one or more assistants,

manages its own patients’ waiting list, clinic visits and scheduling decisions.

Currently, there are no explicit or formal rules for scheduling the elective patients. Each

surgeon’s office decides how to prioritize the patients in the waiting list, and when to schedule

their surgeries. However, there are some constraints imposed by TGH to respond to resource

constraint of the hospital and wait time guarantees set by the Ontario Ministry of Health

and Long Term Care (MOHLTC).

Through interviews with general surgeons and their assistants at TGH, it was determined

that they normally schedule the patients in the first available time block. However, the

preferences of patients (e.g., travelling considerations for remote patients) and the availability

of the pre-admission clinic are taken into consideration as well.

Some patients may be prioritized ahead of other patients due to the severity of their

case or their health status. Such cases may result in reshuffling the surgeon’s schedule

to accommodate these patients. One important constraint that needs to be taken into

consideration while scheduling and ordering the surgical cases is that the longest cases have

to be scheduled as the first cases of the day. The rationale behind this constraint is the

fact that long cases are typically done for patients whose health status is more critical, and

scheduling these cases as first cases of the day reduces the risk of cancellation.

Patients who are cancelled on the day of the surgery are sent to the surgeon’s office to be

19

rescheduled for the surgery. Normally these cases are scheduled in a free time block within

the next week, but if there is no free time block, depending on the seriousness of the case

and the patient’s health status, the case is given priority over all other cases and is moved

to the front of the waiting list, or is booked in a free time block later than a week. The

surgeon’s office generally attempts to book the cancelled cases in a time limit so that these

patients do not need to re-do the required tests in the pre-admission clinic. If a patient has

been cancelled once or twice, his or her case is usually booked as the first case of the day to

avoid another cancellation.

Before booking the date of the surgery, the surgeon’s office needs to ensure that the

patients are booked for their required visit to the pre-admission clinic approximately two

weeks prior to the day of surgery. However, in some cases, if patients are being scheduled for

their surgical cases in a few days (e.g., the urgent cases), the visits with the pre-admission

clinic can be booked for even 24 hours prior to the surgery. Once the appointment with the

pre-admission clinic is booked, the surgeon’s office immediately sends the electronic patient

record (EPR) to the pre-admission clinic, and the patient file is also sent to the pre-admission

clinic. The surgeon’s office must submit the elective OR schedule at least 48 hours in advance.

This schedule includes the type of surgical procedures, their sequence, expected procedure

length, type of patient (e.g., same day patient, in-patient), equipment needs and required

resources (e.g., MSICU bed, SDU bed). The weekly schedule must be confirmed with the

nurse manager with regard to the lengths of surgeries booked, their sequence, and required

resources. If the length of a surgical procedure for a specific surgeon and specific procedure

type does not seem to be realistic based on the historical data available, or the sequence of

surgical procedures does not conform the hospital’s policy (longest cases first), the schedule

will be returned to the surgeon’s office to be revised. Any scheduled OR time block that is

not used by the assigned surgeon must be returned one week in advance.

20

3.3 Patient flow on surgical day

Elective patients are scheduled to arrive at the hospital two hours prior to their surgery.

Once patients arrive at the hospital, they report to the surgical administration desk to check

in, and then they wait to be taken to the holding area by a nurse. In the holding area, the

nurse performs all the necessary tests to ensure that the patient is prepared for the surgery,

and his or her health status allows proceeding with the surgical operation. The patient then

remains in the holding area until called to the OR or cancelled. Meanwhile, the surgeon will

visit with patient to ensure that he or she is ready for the surgery, mark the surgical site

and discuss any final details with the patient. Emergency patients do not go through the

holding area. They remain wherever they are admitted to be called to an OR.

Depending on the length of surgical procedure and the type of resources that the patient

needs, numerous checks are to be performed prior to calling the patient to the OR. These

checks are necessary in order to ensure that the patient can proceed to the next destination

after the surgery is performed.

The surgical control station is the unit that manages the daily elective schedule as well as

the emergency patients. Nurse managers working in this unit play an important role in the

operations of the surgical department; they make critical decisions with regard to cancelling

the elective cases, handling the emergency cases and deciding to run the ORs into overtime.

In some situations, they may need to consult with the surgeon in charge and/or other nurse

managers to decide upon a situation. For instance, when only one resource (e.g., MSICU

bed) is available and two patients with almost the same situation need that resource, which

case should be cancelled?

Every morning, the surgical control station reviews the daily elective schedule, and eval-

uates the number of required resources. Based on the situation in ORs, emergency cases

arrived, number of resources available and the surgical time left; the surgical control station

21

decides which surgical cases must be held or cancelled. For instance, an emergency patient

who is taken to the OR at midnight, and requires a MSICU bed affects the availability of

MSICU bed resource. Occurrence of such cases may cause elective case cancellations.

As mentioned previously, emergency type A patients require surgery within two hours of

their arrival and have priority over all other elective and emergency patients. Upon arrival

of emergency type A patients, the first available OR of the same service is assigned to that

patient and all other patients of that OR are to be held in the holding area. Emergency type

B patients require surgery within 2 to 8 hours of their arrival, and do not usually disrupt

the daily elective schedule. These cases are held until all elective patients of an OR are

finished (either have surgery or are cancelled) for the day. After the regular hours, ORs are

kept open for certain hours for the emergency type B patients. However, if an emergency

type B patient cannot be operated on during these hours, and waits for surgery for more

than 48 hours, his or her case becomes urgent. Such cases are given priority to daily elective

patients, and have to be done as the first cases of the next day.

When the surgical control station determines that the OR is turned-over, the surgical

team is ready, enough time is available and the required resources are expected to be available

upon surgical finish time, the patient is called to the OR. The same checks are to be performed

for emergency type B patients during the hours that ORs are kept open for emergency type

B patients (and sometimes a part of elective hours). However, emergency type A patients

have to go through the surgical process regardless of the time or resource availability.

Once the patient is called to the OR, he or she will be taken to the OR, anesthesia

(if required) will be induced and the procedure will start. When the procedure is nearly

complete, the OR nurse will call to notify the surgical control station of the remaining time

of the surgical process. The nurse will also call the PACU or MSICU (depending on patient’s

next destination) to inform them that the patient is being transferred.

22

3.4 Post-surgical process

Critically ill patients are directly sent to the MSICU rather than being sent to the PACU.

Patients transferred to the MSICU, generally stay there for one or more days. Due to

instability of their health status, these patients require intensive care and close monitoring

by the medical staff. Thus, the ratio of nurse to patients in this unit is one to one. MSICU

patients are eventually transferred to the SDU or ward depending on the stability of their

health status.

Patients transferred to the PACU are either same day patients, who are to be discharged

through the MDU the same day; or in-patients, who are to be sent to the SDU or the

surgical ward to continue recovering. The amount of time that a patient spends in the

PACU depends on the length of surgery, type of surgery, status of regional anesthesia (e.g.,

spinal anesthesia), and the patient’s level of consciousness. Patients stay in PACU until their

health status is stable enough to be transferred to the subsequent unit.

Same day patients are transferred to the MDU, and stay there until they are well enough

to be returned home. Medical staff in the MDU educate the patients about the medication

and the care they need. This unit operates from 7am to 6pm and stops accepting patients at

4pm. Therefore, the same day patients who finish their necessary lengths of stay at PACU

later than 4pm cannot be taken to the MDU for discharge. These patients stay longer in

PACU, and are discharged from this unit. This causes inefficiencies as these patients consume

bed and nurse resources in the PACU. Moreover, the PACU staff is not trained to educate

the patients about their needs after being discharged from hospital.

Sometimes, patients meant to be transferred to the MSICU are temporarily moved to

PACU until a bed is made available in MSICU. Although the ratio of nurses to patients in

PACU is one to two, such patients require one on one care as their health status is not stable

enough. Patients who require a higher level of monitoring than that of a surgical ward but

23

less monitoring than that of the MSICU, are transferred to SDU. These patients stay in the

SDU for one day or more until they are stable enough to be transferred to the ward.

The final destination for the in-patients in the hospital is a ward bed. Patients first

transferred to PACU, MSICU, SDU or a combination of these units. Then, they are trans-

ferred to the ward and stay in the ward to continue their recovery until they are well enough

to be discharged from the hospital. Most patients in the general surgery department are

discharged home; however, there are some patients who are to be sent to the alternative

level of care (ALC) facilities. Shortage of resources in destination facilities may cause longer

unnecessary lengths of stays for these patients in the ward.

4 Model development

In order to capture the complexity of this process and to construct a flexible and reliable

model that can represent the real processes, a DES model, using software package Simul8

made by Visual8 Corp., Mississauga, Ontario L5G 3H7 , was constructed. This model makes

an extensive use of visual logic codes to create modules that can be used to mimic the real

complex tasks. Three types of patients were modelled: 1)elective, 2)emergency type A and

3)emergency type B. Various decision making points with regard to patient status (e.g., hold,

cancel) were modeled. Decision making takes into account the type of patients, their priority,

expected length of surgical operation, bed requirements, and patients’ expected lengths of

stay (LOS) in MSICU, SDU and the surgical ward. This section will describe the rationale

behind the main modules that were used to develop this simulation model.

24

4.1 Scheduling

The general surgery service at TGH is generally assigned two or three ORs per day, during

the week days. The regular hours of ORs are from 8:00 am to 3:30 pm, and every service has

one late day which is from 8:00 am to 5:30 pm. As mentioned in Section 3, after the regular

hours, the ORs are kept open until 11:00pm, for emergency type B patients. However, one

OR is kept open for 24 hours with on call staff to accommodate the emergency type A

patients.

The MSS determines which surgeon performs surgery in which day of the week and in

which OR. In the MSS, every surgeon is assigned at least a time block of 7.5 hours, which

is a full day. Thus, one OR is assigned to one surgeon per day, and surgeons rarely switch

ORs in one day. Therefore, we only allowed an OR day to be assigned to one surgeon in the

model.

As mentioned in Section 3, other than some constraints that are put in place by hospital

administrators, explicit rules with regard to scheduling of surgical cases do not exist, and

each surgeon’s office manages the scheduling of their own set of patients. Therefore, in order

to reasonably represent the daily surgeons’ schedule, schedule sampling from real schedules

of particular surgeons was done.

Every day, before start of the day, the model creates the schedule for the coming day.

First, the model determines the day of the week. Second, using the MSS, it determines how

many ORs run for that day, and which surgeons are assigned to the ORs. Third, for every

surgeon, a random day from historical data is selected. This random day represents the

actual cases that the surgeon scheduled previously in terms of number, type and sequence

of the surgical cases. Table 1 demonstrates what the daily schedule looks like.

The model can determine the patient path using the daily schedule. For instance, if the

PACU field is zero, it means that the patient is not intended to go the PACU. Therefore,

25

Patient ID 1Status 2Show 1Case Number 444580Case Description Whipple ProcedureAge/Gender 61/FSurgeon ID 7OR Number 1Booked length of case 460Actual length of case 520PACU 0PACU LOS 0MSICU 1MSICU LOS 2880SDU 0SDU LOS 0Ward 1Ward LOS 5760MDU 0

Table 1: Sample of daily schedule sheet for one patient

26

the PACU length of stay is zero too. Also, using the status field, the model can indicate the

status of patients during the simulation time (e.g., cancelled).

4.2 Flow of patients through the surgical process

Figure 1 shows a screen shot of the simualtion model. Patients flow through the surgical

process, depending on their patient path, and their lengths of stay in PACU, MSICU, SDU

and ward beds are specified from the historical data. Since no data were available with

regard to the same-day patients’ lengths of stay in MDU, and patients are booked to stay in

MDU for an hour, patients’ lengths of stay in MDU beds is considered one hour in the model.

As mentioned previously, MDU stops accepting patients at 4:00pm; thus, some patients have

to be discharged directly from PACU.

4.3 Modelling patient arrivals

Depending on their type, patients arrive to the system from two different points. Elective

patients arrive to the model from surgical administration area, and emergency type A and

B patients arrive to the model from the emergency department (ED). Elective patients are

expected to arrive to the surgical administration area at their scheduled time, which is two

hours prior to their surgery time. However, patients often arrive earlier or later than their

scheduled time, or some patients do not present at all.

Using the percentage of patient no shows and scheduled arrival times, the model calculates

patient tardiness and probability of patient no shows, and sets the inter-arrival times of the

patients accordingly.

Emergency type A and B patients enter to the model from two different entry points at

ED. Historical data from one year were used to fit a distribution for arrival rate of emergency

type A and emergency type B patients. Emergency type A patients arrive based on a Weibull

27

Fig

ure

1:Sim

ula

tion

Model

Scr

eensh

ot

28

distribution with parameters (25, 0.91, 2.9e+003) and emergency type B patients arrive based

on a Gamma distribution with parameters (10, 0.866, 3.36e+003).

4.4 Determining the patient path through the model

Patients may follow five different post-surgical paths in the general surgery at TGH. Based

on their knowledge about the type of surgical procedure, severity of the case, and patient’s

health status, surgeons determine the patient path while scheduling a patient for the surgery

or deciding upon an emergency patient.

Patient paths are specified, in order to determine the required resources in the decision

making process and to determine the patient’s next destination in every post-surgical unit.

The five pre-defined patient paths are:

1. OR → PACU → MDU

2. OR → PACU → Ward

3. OR → PACU → SDU → Ward

4. OR → MSICU → Ward

5. OR → MSICU → SDU → Ward

However, some patient paths may change due to the unavailability of resources in the

post-surgical units. Whenever an emergency patient enters the model, a random sample of

the same emergency type is selected from the historical data that determines the surgical

case type and the patient path for that emergency patient.

29

4.5 Determining the first patients of the any OR day

After being admitted to the hospital at the surgical administration desk, patients are taken

to the POCU area by a nurse. The ratio of nurses to patients in this area is one to four, and

the availability of the nurse resources to carry out the pre-surgical tasks has been taken into

consideration in the model.

Then, patients stay in POCU beds until they are called to the OR. The model checks for

the first patient of a particular OR in the POCU area. If the first patient has arrived but

is not in the POCU area yet, the model does not check in the second patient of that OR.

However, the second patient is checked in to the OR, if the first patient has not arrived yet.

ORs open at 8:00am for elective patients. Before opening the ORs, the model checks whether

there is an emergency type B patient who has waited more than forty eight hours. If such a

patient exists, this patient has priority to all elective patients, and has to be checked into the

OR first, regardless of the availability of post-surgical resources. If not, the model checks for

the availability of the required resources for the first elective patients of the free ORs, and

decides accordingly to either check in the patients or cancel them. At all time, emergency

type A patients have priority to all other patients, and are taken to the first available OR

regardless of the availability of post-surgical resources.

4.6 Decision making process

The surgical control station manages which patients can go through the surgical process,

and which ones have to be cancelled. Every time a surgical operation ends, and the OR is

turned over, the surgical control station calls the next patient for the OR.

To mimic the operations of surgical control station, the model first checks for emergency

type A patients. If an emergency type A patient is waiting for an OR, the priority is given

to that patient. Otherwise, the model checks the elective patients in the POCU to find the

30

next patient for that particular OR. If there is no patient in POCU for that OR, the model

checks for emergency type B patients to be sent to the OR.

Elective surgeries should be done by cut-off time which is 3:30pm. However, in some cases

surgical control stations allows ORs to close, up to 45 minutes later if they can finish a case

by that time. This is called allowed overtime. Once the patient is chosen, the model decides

whether the OR time available is enough to finish the surgical operation. If the surgical

operation can be finished before the cut-off time plus the allowed overtime, the model starts

checking the availability of the post-surgical resources upon the expected surgical finish time,

otherwise the surgical case is cancelled.

Assuming that the surgery can be finished before the cut-off time plus allowed overtime,

the model checks for the availability of the required resources, and based on the availability

of resources decides whether or not the patient can be checked into the OR.

The PACU is a very dynamic unit in terms of patient arrivals and departures, and the

patients are not meant to stay in PACU for a long time. The high turn-over rate of PACU

indicates that it is realistic to expect that a PACU bed will be available at the end of surgery,

if the patient is being transferred to PACU. In such cases, the availability of the bed in the

next destination (SDU or ward) should be taken in consideration as patients’ lengths of

stay are short in PACU. However, if the patient is being sent directly to the MSICU, the

availability of bed in MSICU must be checked.

If the patient is to be sent directly to the MSICU but the MSICU bed will not be available

right after the surgery (but will be available in a reasonable amount of time), the patient

is temporarily sent to PACU until a bed is made available in MSICU. The model takes

advantage of patient path to determine the post-surgical resources that a patient needs. For

instance, if the patient path is four, it means that the patient’s destination after OR is a

MSICU bed, and then a ward bed. Therefore, the availability of a MSICU bed needs to be

31

taken into consideration. The model keeps track of bed available times using track sheets,

and decides whether to check in or to cancel a patient.

For a MSICU bed, if the bed will be available within two hours of expected surgery

finish time, the bed is considered available. Although, if the wait time is greater than OR

tolerance time, which is 15 minutes, the patient should be temporarily sent to PACU, until

a bed is available in MSICU. Thus, two new patient paths that are result of this change can

be defined: OR PACU MSICU ward OR PACU MSICU SDU ward

These paths are not pre-defined paths and are created based on dynamics governing the

model. If the bed will be available, the model books the bed for the patient to avoid double

booking of the bed. If the bed available time is greater than two hours, the bed is not

considered available, and the patient’s surgery must be cancelled.

For a SDU or ward bed, if the bed will be available by 8:00pm, the bed is considered

available. In this case, the model books the bed for the patient to prevent double booking.

If the bed is not considered available, the patient’s surgery will be cancelled.

The same procedure is performed for emergency type B patients once all elective patients

of an OR are either completed or cancelled. The cut-off time for emergency type B patients

is 11:00pm and no allowed over time is considered.

If an emergency type B patient cannot be admitted to the OR during these hours, and

waits more than 48 hours for the surgery; this patient should be operated on as the first case

of the next day, prior to elective patients. These patients are called expired emergency type

Bs in the model.

In order to represent the real system, the model uses the booked surgical times for the

purpose of decision making, but the actual lengths of surgery for the processing time of the

ORs.

32

4.7 Model limitations and assumptions

Due to a lack of available data and to simplify some aspects of the model, the following

assumptions were made:

• The model includes the elective and emergency patients of the general surgery service

at TGH. However, it does not take into account the transplant cases or the emergency

case interruptions from other services.

• The model assumes that surgeons and nurses in ORs and post-surgical units are avail-

able at all times. This assumption is reasonable, since only three surgery cancellations

occurred due to the unavailability of surgeons, and no cancellations occurred due to

the unavailability of nurses in one year (2008-2009).

• The surgeon’s weekly schedule is assumed to be fixed over the period of one year.

However, in reality the schedule may change every four or six months.

• The model does not take into account the patients who die in the OR or any of the

post-surgical units.

• The model does not include emergency type C patients, as these patients are rare in

the general surgery service.

• When there is more than one emergency patient who requires surgery, the model does

not take into account any priority due to the severity of the case.

• In the model, all in-patients are assumed to be sent home from the surgical ward. In

reality, some in-patients may be transferred to ALC institutions from the surgical ward

and the unavailability of resources in those institutes may cause delays in discharge of

patients from ward.

33

• The number of PACU, MSICU and SDU beds assigned to general surgery service is

chosen based on the average number of bed occupancy by this service.

5 Results

5.1 Warm-up period

The warm up period is the time required for the model to cycle from the beginning to

achieve a steady state before we can start collecting the results for the simulation model.

The warm-up period should be specified in order to ensure that the initial simulation period

is representative of the steady state operation of a system. We can only start tracking the

states and counters once this steady state period is reached.

The most general technique for determining the warm up period is the graphical proce-

dure of Welch Law [2007]. In this model, all the beds are empty at the beginning. Since

patients stay in ward beds longer than other post-surgical beds, the number of occupied

ward beds is representative of the steady-state behaviour of the system. Hence, we chose

the number of occupied ward beds as the steady-state random variable of interest.

The model was run for one year. Over 10 replications, the average number of occupied

ward beds per day was calculated. The moving average using a window size of 10, 20, 30

and 40 shown in Figure 2 , and we can see that after 45 days, the graph starts smoothing

out, meaning that the system reaches steady-state behaviour.

5.2 Model validation

Once the model is functional, we need to validate it to determine that it is a reasonably

accurate representation of the real system. The underlying structure of the model should

correspond to the actual system, and the output statistics should appear reasonable.

34

Fig

ure

2:C

alcu

lati

ng

the

war

m-u

pp

erio

d

35

The most definitive test of a simulation model’s validity is to establish that its output

data closely resemble the output data that would be expected from the actual system [Law,

2007]. If the two sets of data compare closely, then the model of the existing system is

considered valid.

In this model, the number of surgery cancellations was chosen as a measure for the

purpose of validation. As the number of surgery cancellations takes into account the available

time required for the surgical operation, the availability of post-surgical resources such as

MSICU, SDU and ward beds and the interruptions caused by emergency cases, it is an

appropriate measure to summarize the operation of the overall system.

Historical data for the number of surgery cancellations were available on monthly basis

for a period of one year, and were used to validate the simulation model. To consider the

autocorrelation existing among the surgery cancellations, the number of surgery cancellations

were counted per month as the simulation progressed over a one year period. We performed

10 replications of one year (excluding the warm-up period) to obtain satisfactory values.

Since there is no a priori correlation between the actual data and the simulation output,

we employed a modified two-sample-t or Welch’s confidence interval. Welch’s approach has

the advantage that it does not require the data sets have equal variances [Law, 2007].

We constructed 95% confidence intervals for the difference between the actual and simu-

lated number of surgery cancellations using Welch’s approach. Since the interval around the

difference between the number of cancellations is (−1.191, 2.008), and it contains zero, so

the observed difference between the actual data and the simulation output is not statistically

significant, and we conclude that the simulation model is valid.

36

5.3 “What if” analysis

This section presents the “what-if” scenarios and the recommendations for reducing the

number of surgery cancellations. Based on the performance of the system, three types

of scenarios were chosen. First, we tried to reduce the number of surgery cancellations

by altering the weekly schedule of surgeons. Second, we explored the effect of different

sequencing rules, such as sequencing based on the length of surgeries on the number of

surgery cancellations. Third, we examined how adding beds to the surgical ward influences

the number of surgery cancellations. The interactions among these scenarios were explored,

and these results are presented as well.

5.3.1 Modifying the surgeons’ weekly schedule

The weekly schedule of surgeons is assumed to be fixed over the period of one year. As the

surgeons perform different types and numbers of surgical operations, modifying the surgeons’

weekly schedule may reduce the number of surgery cancellations.

As mentioned in previous sections, two major causes of surgery cancellations are surgical

case overload and shortage of beds in post-surgical units. The availability of MSICU, SDU

and ward beds were taken into account in the model. Shortage of MSICU beds does not

seem to be a bottleneck in this system as only a few surgeries are cancelled annually because

of the shortage of beds in MSICU. However, a high number of surgery cancellations occur

due to the shortage of beds in the SDU and ward. Since all in-patients’ final destination is a

ward bed and patients stay in ward beds longer than other post-surgical beds, we sought to

identify whether modifying the surgeons’ weekly schedule to make better use of ward beds

will reduce the surgery cancellations.

37

OR1 OR2 OR3

Monday 2 (11) 3 (6)Tuesday 11 (9) 9 (4) 1 (2)Wednesday 10 (1) 6 (8) 5 (5)Thursday 12 (3) 4 (10)Friday 7 (12) 8 (7)

Table 2: Base surgeons’ weekly schedule, surgeons are represented by their ID number inthe schedule, and the values in parentheses show the surgeons’ ward LOS rank.

5.3.2 Scheduling rules

To determine how to schedule different surgeons in different days of the week, we observed

that the average lengths of stay (LOS) in ward beds for patients of every surgeon is a key

characteristic. Patients’ ward LOS determines how a particular surgeon affects the bed

occupancy in the ward. Here, we demonstrate that assigning the surgeons with short ward

LOS and same-day discharge patients OR days at the start of the week and the surgeons

with long ward LOS to the end of the week reduces the chance of surgery cancellations. This

is mostly because the patients with long ward LOS take advantage of ward beds during the

weekends. We also used another key characteristic, average number of surgeries per day, to

add flexibility to the schedules.

To schedule surgeons based on the ward LOS, we used historical data to calculate the

average ward LOS for patients of each surgeon and ranked the surgeons according to the

average ward LOS such that surgeons with longer ward LOS had a higher rank. Then, we

scheduled the surgeons throughout the week from the lower to the higher rank and obtained

the modified schedule. Table 2 shows the surgeons’ existing weekly schedule that will be

referred as the base schedule, and Table 3 shows the modified schedule.

The output variable of interest is the number of surgery cancellations. Common random

numbers (CRN) are used to provide more accurate comparisons between scheduling scenarios

38

OR1 OR2 OR3

Monday 10 (1) 1 (2)Tuesday 12 (3) 9 (4) 5 (5)Wednesday 3 (6) 8 (7) 6 (8)Thursday 11 (9) 4 (10)Friday 2 (11) 7 (12)

Table 3: Modified surgeons’ weekly schedule, surgeons are represented by their ID numberin the schedule, and the values in parentheses show the surgeons’ ward LOS rank.

Law [2007]. Using CRN, we can compare the scenarios under similar experimental conditions

and be more confident that any observed differences in performance are due to the differences

in the changes made to the system rather than to fluctuations of the experimental conditions.

These experimental conditions are the generated random variates that are used to drive the

model through the simulation time [Law, 2007].

We used CRN over 20 replications of one year, and then used a paired-t approach to

construct 95% confidence intervals for the difference between the number of surgery can-

cellations in the base model and those of the models with the modified schedule. Since

the mean value (-17.55) and the confidence interval (-29.043, -6.056) are negative and the

interval excludes zero, we conclude that the number of surgical cancellations is reduced.

As mentioned before, the average number of surgeries performed by every surgeon per day

is another key characteristic that can be used along with the average ward LOS to allow some

flexibility in switching the surgeons in the weekly schedule, and still reduce the number of

surgical cancellations comparing to the base model. As a post-processing heuristic, surgeons

may be switched in the weekly schedule provided that they are not farther than three time

windows in ward LOS rank and their average number of surgeries rank is close. Figure 3

demonstrates every surgeon’s average ward LOS and the average number of surgeries per

day. Figure 4 shows the percentage of days that surgeons have 1, 2, 3 or 4 surgeries that

39

Figure 3: Surgeon’s average ward LOS and average number of surgeries per day

demonstrates which surgeons are similar in terms of the number of surgical cases they do.

We switched surgeon number 8 with surgeon number 6 and surgeon number 4 with

surgeon number 2, and then used a paired-t approach to construct 95% confidence intervals

for the difference between the number of surgery cancellations in the base model and those of

the model with the switched modified schedule. The mean value of -18.05 and the confidence

interval of (-34.307, -1.792) shows that the modified schedule and the switched modified

schedule perform almost the same in terms of the number of surgical cancellations. Surgeons’

average ward LOS and the average number of surgeries can be updated on regular basis to

produce more efficient weekly schedules.

To confirm the validity of scheduling based on the average ward LOS, we considered the

reversed order of surgeon ranking to create the reverse modified schedule and showed that

the reverse modified schedule does not reduce the number of surgical cancellations and may

even increase the number of cancellations. Using CRN and paired-t approach, we constructed

95% confidence intervals around the difference between the number of surgery cancellations

in the base model and those of the model with reverse modified schedule. The mean value

of 0.45 and the confidence interval of (-14.266, 15.166) verified that the reverse modified

40

Figure 4: Percentage of days each surgeon has 1, 2, 3 or 4 surgeries

schedule statistically does not reduce the number of surgery cancellations.

5.3.3 Sequence of surgical operations

The sequence of surgical operations for every surgeon’s daily schedule is another important

determinant of the number of surgical cancellations. We explored the effect of two sequencing

rules on the number of surgical cancellations. First, we ordered the surgeries with regard

to the booked lengths of the surgical operations in both increasing and decreasing order.

Second, we ordered the surgeries based on the variance of the surgical operation time in

both increasing and decreasing order.

We used CRN over 20 replications of one year, and then used a paired-t approach to

constructed 95% confidence intervals around the difference between the number of surgical

cancellations in the base model and those of the model with short to long (SL), and then long

to short (LS) sequence of lengths of surgeries. We observed that sequencing the surgeries

from short to long durations reduced the number of surgical cancellations. In contrast,

sequencing the surgeries from long to short durations did not make any improvement and

41

Schedule

Base Modified Reverse Modified

SL -10.45 (-14.83, -6.0636) -19.7 (-30.89, -8.50) -3.5 (-19.12, 12.12)LS 4.2 (-3.18, 11.58) -10.9 (-26.34, 4.54) 18.35 (-2.65, 39.35)LH -14 (-19.46, -3.73) -28.3 (-42.55, -14.04) -15 (-23.12, 21.32)HL 6.65 (3.41, 9.88) -4.25 (-16.42, 7.92) 14.85 (-0.343, 30.04)

Table 4: Mean values and 95% confidence intervals for the reduction (negative values) orincrease (positive values) in the number of surgical cancellations in a one year period com-pared to the base model. SL: short-to-long lengths of surgeries, LS: long-to-short lengths ofsurgeries, LH: low-to-high variance of surgery durations, HL: high-to-low variance of surgerydurations

even could have increased the number of surgical cancellations. Then, we investigated the

effect of these sequencing rules with the modified and the reverse modified schedule. The

results of these interaction scenarios can be seen in Table 4.

As mentioned above, the variance of surgery durations was used as the second sequencing

rule. We calculated the average of the difference between the actual and the booked lengths

of surgeries for every type of surgery. Then, surgeries were ranked based on the average

variance, and we sequenced the surgeries once in increasing order of their variance rank, and

once in decreasing order of their variance rank.

We used CRN over 20 replications of one year, and then used a paired-t approach to

constructed 95% confidence intervals around the difference between the number of surgery

cancellations in the base model and those of the model with the low to high (LH) variance and

then with the high to low (HL) variance of surgery durations. We observed that sequencing

the surgeries from low to high variance reduced the number of surgery cancellations. On

the other hand, sequencing the surgeries from high to low variance could even increase the

number of cancellations. We applied these sequencing rules to the modified and the reverse

modified schedule as well. The results of these interaction scenarios can be seen in Table 4.

42

As we can see, sequencing the surgeries in increasing order of lengths of surgical operations

and variance of surgery durations reduced the number of surgery cancellations. Moreover,

sequencing based on the variance of surgery durations has a bigger effect on the number of

surgical cancellations than the sequencing based on the lengths of surgeries. The same results

were observed by applying the same sequencing rules to the modified schedule. Additionally,

by applying the sequencing rules to the modified schedule we can further reduce the number

of cancellations. But when the sequencing rules were applied to the reverse modified schedule,

the change observed was not statistically significant at the 95% confidence level.

5.3.4 Increasing the number of ward beds

After case over-load, the unavailability of the post-surgical beds such as MSICU and ward

beds is an important cause of surgery cancellations. MSICU beds do not seem to be a

bottleneck in this system, since only a few surgeries are cancelled annually because of the

shortage of beds in MSICU. However, the high utilization rate of ward beds (over 85%) and

the high number of surgery cancellations due to the shortage of beds in the ward suggest

that adding a few beds to the ward may reduce the number of surgery cancellations.

In this scenario, we explored how adding two beds to the ward affected the number of

surgery cancellations. We used CRN over 20 replications of one year, and used a paired-t

approach to construct 95% confidence intervals around the difference between the number

of surgery cancellations in the base model and those of the model with two extra beds.

We observed that the number of surgical cancellations reduced. Then, we examined how

modifying the weekly schedule and applying different sequencing rules at the same time

influenced the number of surgical cancellations in the model with two extra beds. The

results of these interaction scenarios are presented in Table 5.

As we can see, adding two beds to the ward even without changing the schedule reduced

43

Schedule

Base+2beds Modified+2beds Reverse Modified+2beds

Base sequence -27.5 (-34.29, -21.40) -38.10 (-49.62, -26.57) -13.3 (-36.40, 9.80)SL -34.65 (-42.56, -26.73) -40.7 (-52.49, -28.90) -24.4 (-42.24, -6.55)LS -27.94 (-33.67, -22.21) -35.66 (-44.47, -26.85) -11 (-34.30, 12.30)LH -44.4 (-50.48, -38.31) -47.88 (-68.95, -26.82) -28.9 (-51.34, -6.82)HL -19.7 (-33.89, -5.50) -24.8 (-36.69, -12.90) -4.4 (-21.40, 12.60)

Table 5: Mean values and 95% confidence intervals for the reduction (negative values) orincrease (positive values) in the number of surgical cancellations in a one year period com-pared to the base model. SL: short-to-long lengths of surgeries, LS: long-to-short lengths ofsurgeries, LH: low-to-high variance of surgery durations, HL: high-to-low variance of surgerydurations

the number of surgical cancellations. Modifying the weekly schedule and adding two beds at

the same time further reduced the number of surgical cancellations. Adding two beds to the

ward with reverse modified schedule did not reduce the number of surgical cancellations.

Sequencing the surgical operations in increasing order of the length and variance of

surgeries in the base and the modified schedule further reduced the number of cancellations.

Applying these sequencing rules to the reverse of modified schedule also reduced the number

of cancellations.

Sequencing the surgical operations in decreasing order of the length surgeries and variance

of surgery duration in the base and the modified schedule reduced the number of cancella-

tions; however, this reduction was attributable to increasing the number of ward beds rather

than the sequencing rule. Applying these sequencing rules to the reverse of the modified

schedule did not reduce the number of cancellations.

44

5.4 Pairwise comparisons

In the scenarios presented, we observed that the reverse modified schedule did not perform

better than the base schedule, and sequencing the surgical operations in decreasing order of

length of surgeries and variance of surgery durations did not reduce the number of surgical

cancellations. Therefore, we chose the base and modified schedules as our preferred schedules,

and sequenced the surgical operations in increasing order of length of surgeries and variance of

surgery times. Once, we ran the base model with all possible combinations of the preffered

schedules and sequences, and then we ran the same scenarios in a model with two extra

ward beds. We compared each scenario with every other scenario to detect and quantify

any significant pairwise differences. Table 6 demonstrates the mean values and the 95%

confidence intervals around the difference between the number of surgery cancellations in a

period of one year in two scenarios.

Table 6 allows us to compare the scenario in the column with the scenario in the row in

terms of the number of surgical cancellations in one year with 95% confidence level. When

comparing the scenario in the column against the scenario in the row, if the confidence in-

terval excludes zero and the mean value is negative, we can conclude that the scenario in

the column performs better than the scenario in the row in terms of the number of surgical

cancellations. If the confidence interval includes zero, the number of surgical cancellations in

the scenario in the column is not statistically different from the number of surgical cancel-

lation in the scenario in the row. If the confidence interval exclude zero and the mean value

is positive, the scenario in the column does not perform better than the scenario in the row

in terms of the number of cancellations. We also calculated the confidence level at which

we can say that the scenario in the column performs better than the scenario in the row in

terms of the number of cancellations. Table 7 shows these confidence levels. For instance,

we are 61.40% certain that the scenario with two extra beds, base schedule and short to long

45

sequence of length of surgeries performs better than the scenario with modified schedule and

low to high variance of the surgery time or we are 99.9% confident that the scenario with

two extra beds and modified schedule performs better than the base schedule with short to

long sequence of length of surgeries.

6 Conclusion

The objective of this research was to identify potential improvements in the perioperative

process, to reduce the number of surgical cancellations, and to make better use of hospital

resources such as post-surgical beds. We built a DES model to follow the patients through

the perioperative process in general surgery at TGH, and used it to analyze the impact

of specific scheduling and sequencing rules on the number of surgical cancellations. The

availability of MSICU, SDU and ward beds were taken into considerations, and two types of

emergency case interruptions were taken into account as well.

We found that scheduling the surgeons in a weekly schedule based on the average length

of stay of their patients in the ward affected the number of surgical cancellations. When

surgeons are scheduled in increasing order of their patients’ average ward LOS, from the

start to the end of the week, the number of surgical cancellations decreased. Surgeons can be

switched in the schedule provided that they are similar with respect to their patients average

ward LOS and the average number of surgeries per day. In contrast, when surgeons scheduled

in decreasing order of their patients’ ward LOS, the number of surgical cancellations did not

reduce and in fact in some cases increased.

We explored the effect of two sequencing rules on the number of surgical cancellations:

sequencing based on the length of surgical operations, and sequencing based on the variance

of surgery duration. We concluded that sequencing the surgical operations in increasing

46

MB

-SL

M-S

LB

-LH

M-L

HB

edB

ed/M

Bed

/B

-SL

Bed

/M

-SL

Bed

/B

-LH

Bed

/M

-LH

B(-

29,-6.1

)(-

14.8

,-6.1

)(-

30.9

,-8.5

)(-

19.5

,-3.7

)(-

42.6

,-14)

(-34.3

,-21.4

)(-

49.6

,-26.6

)(-

42.6

,-26.8

)(-

52.5

,-28.9

)(-

50.5

,-38.3

)(-

63,-22.7

)-1

7.5

5-1

0.4

5-1

9.7

-11.6

-28.3

-27.8

5-3

8.1

-34.6

5-4

0.7

-44.4

-42.8

5M

(-5.8

,20)

(-9.2

,4.9

)(-

10,21.9

)(-

21.3

,-.2

)(-

21.1

,.5

)(-

28.1

,-12.9

)(-

28.2

,-6)

(-31.2

,-15.1

)(-

38.8

,-14.9

)(-

39.8

,-10.8

)7.1

-2.1

55.9

5-1

0.7

5-1

0.3

-20.5

5-1

7.1

-23.1

5-2

6.8

5-2

5.3

B-S

L(-

21.9

,3.4

)(-

11.3

,9)

(-34.1

,-1.6

)(-

24.4

,-10.4

)(-

40.1

,-15.2

)(-

31.5

,-16.9

)(-

43.1

,-17.4

)(-

41.6

,-26.3

)(-

52.9

,-11.9

)-9

.25

-1.1

5-1

7.8

5-1

7.4

-27.6

5-2

4.2

-30.2

5-3

3.9

5-3

2.4

M-S

L(-

6.5

,22.7

)(-

17.8

,.6

)(-

18.5

,2.2

)(-

22.5

,-14.3

)(-

26,-3.9

)(-

25.6

,-16.4

)(-

36.2

,-13.2

)(-

39.9

,-6.4

)8.1

-8.6

-8.1

5-1

8.4

-14.9

5-2

1-2

4.7

-23.1

5B

-LH

(-33.6

,.2

)(-

26.1

,-6.3

)(-

42.9

,-10.1

)(-

34.1

,-12)

(-45.6

,-12.6

)(-

40.2

,-25.4

)(-

57.3

,-5.2

)-1

6.7

-16.2

5-2

6.5

-23.0

5-2

9.1

-32.8

-31.2

5M

-LH

(-13.5

,14.4

)(-

19.9

,.3

)(-

21.3

,8.6

)(-

22.3

,-2.5

)(-

30.5

,-1.7

)(-

35.2

,6.1

)0.4

5-9

.8-6

.35

-12.4

-16.1

-14.5

5B

ed(-

21.4

,.9

)(-

10.1

,-3.5

)(-

24.3

,-1.4

)(-

20.8

,-12.2

)(-

34.4

,4.4

)-1

0.2

5-6

.8-1

2.8

5-1

6.5

5-1

5B

ed-M

(-8.4

,15.3

)(-

5.7

,.5

)(-

19.1

,6.5

)(-

19.6

,10.1

)3.4

5-2

.6-6

.3-4

.75

Bed

/B

-SL

(-18.1

,6)

(-14.8

,-4.7

)(-

27.8

,11.4

)-6

.05

-9.7

5-8

.2B

ed/M

-SL

(-16.2

,8.8

)(-

17.1

,12.8

)-3

.7-2

.15

Bed

/B

-LH

(-19.8

,22.9

)1.5

5

Tab

le6:

Mea

nva

lues

and

95%

confiden

cein

terv

als

for

the

diff

eren

cein

the

num

ber

ofsu

rgic

alca

nce

llat

ions

ina

one

year

per

iod

when

com

par

ing

the

scen

ario

sin

the

colu

mn

agai

nst

the

scen

ario

sin

the

row

.T

he

neg

ativ

eva

lues

show

dec

reas

e,an

dth

ep

osit

ive

valu

essh

owin

crea

sein

the

num

ber

ofsu

rgic

alca

nce

llat

ions.

B:

Bas

esc

hed

ule

,M

:M

odifi

edSch

edule

,SL

:Surg

ery

lengt

hsh

ort-

to-l

ong,

LS:

Surg

ery

lengt

hlo

ng-

to-s

hor

t,L

H:

Surg

ery

vari

ance

low

-to-

hig

h,

HL

:Surg

ery

vari

ance

hig

h-t

o-lo

w,

Bed

:M

odel

wit

htw

oex

tra

war

db

eds

47

MB

-SL

M-S

LB

-LH

M-L

HB

edB

ed/M

Bed

/B-S

LB

ed/M

-SL

Bed

/B-L

HB

ed/M

-LH

B99

.50%

99.9

9%99

.80%

99.3

0%99

.90%

99.9

9%99

.99%

99.9

9%99

.99%

99.9

9%99

.90%

M73

.60%

46.6

0%55

.50%

95.3

0%94

.00%

99.9

9%99

.50%

99.9

9%99

.90%

99.8

0%B

-SL

85.6

0%18

.40%

96.7

0%99

.99%

99.9

0%99

.99%

99.9

9%99

.99%

99.6

0%M

-SL

73.8

0%93

.40%

88.2

0%99

.99%

98.9

0%99

.99%

99.9

0%99

.00%

B-L

H94

.70%

99.7

0%99

.60%

99.9

0%99

.80%

99.9

9%97

.80%

M-L

H5.

30%

94.3

0%61

.40%

98.2

0%96

.90%

84.3

0%B

ed93

.00%

99.9

0%97

.00%

99.9

9%87

.70%

Bed

/M45

.00%

90.4

0%68

.50%

48.9

0%B

ed/B

-SL

69.3

0%99

.90%

60.7

0%B

ed/M

-SL

45.5

0%23

.30%

Bed

/B-L

H11

.80%

Tab

le7:

Con

fiden

cele

vel

atw

hic

hth

esc

enar

ioin

the

colu

mn

isb

ette

rth

anth

esc

enar

ioin

the

row

inte

rms

ofth

enum

ber

ofsu

rgic

alca

nce

llat

ions

ina

one

year

per

iod.

B:

Bas

esc

hed

ule

,M

:M

odifi

edSch

edule

,SL

:Surg

ery

lengt

hsh

ort-

to-l

ong,

LS:

Surg

ery

lengt

hlo

ng-

to-s

hor

t,L

H:

Surg

ery

vari

ance

low

-to-

hig

h,

HL

:Surg

ery

vari

ance

hig

h-t

o-lo

w,

Bed

:M

odel

wit

htw

oex

tra

war

db

eds

48

order of length of surgery and variance of surgery duration reduced the number of surgical

cancellations.

The high number of cancellations because of a shortage of beds in the ward verifies that

ward beds are a bottleneck in this system. We explored the effect of adding two ward beds to

the system and observed that the number of surgical cancellations decreased. Combining the

scheduling rules and adding beds to the ward at the same time further reduced the number

of surgical cancellations.

Hence, TGH can create more efficient weekly schedules by calculating the average ward

LOS for patients of every surgeon, ranking the surgeons based on their patients’ ward LOS

(the longer the ward LOS, the higher the rank) and then scheduling the surgeons from start

to the end of the week in increasing order of their ward LOS rank to reduce the number

of surgical cancellations. The average ward LOS should be updated on a regular basis to

provide accurate results. To further reduce the number of cancellations, surgeons in TGH

can sequence the surgical operations in increasing order of the length of surgeries. TGH can

also calculate the variance of the surgery time for different types of surgical operations on

a regular basis, and rank the surgeries based on their variance. Using this ranking system,

surgeons can sequence their surgeries from lower variance of surgery time to higher variance

of surgery time and reduce the number of surgery cancellations. Adding beds to the surgical

ward is another effective way for reducing the number of surgical cancellations.

Adding beds to the ward along with modifying the weekly schedule and applying effective

sequencing rules will further reduce the number of cancellations. Depending on their budget

and surgeons’ preference, TGH can decide to choose the best alternative to reduce the

number of cancellations. Table 7 can guide the decision makers to realize which alternatives

are preferable to the other ones.

This research explored the use of DES modelling in perioperative process improvement

49

in the general surgery service at TGH, and provided a basis for further model development

and system investigation for other services. Expansion of the model to other services will

provide TGH with an integrated perioperative decision tool to reduce the number of surgical

cancellations for all services. Moreover, some research is in progress attempting to create a

generalized framework that can be used to produce more efficient OR schedules for hospitals.

This model can also be used for the validation purpose of generalized frameworks.

This model did not include the staff availability in different stages of the perioperative

process. In future work, the availability of staff, specifically nurse resources in post-surgical

units can be taken into account to more accurately identify the inefficiencies caused by

absence or delay of the medical staff in the perioperative process.

This model excluded the patients who died in the MSICU or other post-surgical units.

Consideration of these patients in future work may result in more accurate outcomes.

As described in Section 3, some in-patients are discharged to the ALC institutions. Short-

age of beds in ALC institutions may extend the patients’ lengths of stay in the ward, and

consequently other post-surgical units. Future work can acquire data on not medically nec-

essary lengths of stays in different units to have a more accurate prediction of the resource

availabilities in these units.

We can use our model to help understand the effect of new scheduling scenarios on other

measures of OR efficiency and cost. Another area for future work is investigating the lengths

of surgery durations in more detail to identify the root causes of variations in the lengths of

surgeries. Future work should acquire data on the length of anaesthesia induction, surgical

operation, turn-over time and unnecessary length of stay in the OR to identify inefficiencies

that result in high variation of the length of surgeries.

Because our model focused only on surgical cancellations, and did not measure other

aspects of OR efficiency or cost, it is possible that some of the scenarios we describe will

50

decrease the number of cancellations, but might exacerbate other measures of OR efficiency,

such as increase over-utilization or increase costs.

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