Perioperative process improvement using discrete event simulation

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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

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Perioperative process improvement using discrete event simulation

Masters of Applied Science, 2010

Solmaz Azari-Rad

Graduate 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 Gengen-eral 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) sequencschedul-ing 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.

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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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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

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post-surgical units on the number of post-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.

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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 departdepart-ments, operating rooms and out-patient departdepart-ments, 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.

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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.

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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.

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an operating team and minimizing the inefficiencies. By observing and studying their as-signed tasks and workflow patterns, a re-deas-signed 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.

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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

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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.

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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.

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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

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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 papa-tient 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

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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

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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.

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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

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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 difdif-ferent 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

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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.

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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.

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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

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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.

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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.

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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

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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.

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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

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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.

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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,

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Patient ID 1

Status 2

Show 1

Case Number 444580

Case Description Whipple Procedure

Age/Gender 61/F

Surgeon ID 7

OR Number 1

Booked length of case 460 Actual length of case 520

PACU 0 PACU LOS 0 MSICU 1 MSICU LOS 2880 SDU 0 SDU LOS 0 Ward 1 Ward LOS 5760 MDU 0

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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

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Figure 1: Sim ulation Mo del Screenshot

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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.

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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

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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

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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.

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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 reasonavail-able, 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.

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• 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.

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Figure 2: Calculating the w arm-up p erio d

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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.

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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.

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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 in the 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

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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 number in 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

Perioperative process improvement using discrete event simulation