ASQ_SHS Conference paper, Atlanta, GA, February 26, 2010

1. SYSTEM ENGINEERING AND MANAGEMENT SCIENCE FOR
HEALTHCARE: EXAMPLES AND FUNDAMENTAL PRINCIPLES
Alexander Kolker, Children’s Hospital and Health System, Milwaukee, WI 53226
Abstract The objective of this paper is to illustrate the
predictive and analytical power of management
Relatively little technical and intellectual resources engineering applied to a typical hospital-wide system that
have been devoted to process engineering and analysis of consists of a set of interdependent subsystems.
overall healthcare delivery as an integrated system that Fundamental management engineering principles for
should provide high quality care for many thousands of effective managerial decision-making in healthcare
patients in an economically sustainable way. settings are summarized in the Conclusions.
A real long-term impact on quality of care and
efficiency of healthcare as an integrated system can be What is Management?
achieved only by using fundamental principles of
management engineering. Probability theory, optimization, There are many possible definitions of management.
computer simulation are scientific and technical For the purpose of this paper, management is defined as
foundations for such an approach. controlling and leveraging available resources (material,
This paper includes a quantitative analysis of a financial and human) aimed at achieving a system’s
typical entire hospital system represented as a set of performance objectives.
interdependent subsystems. It is demonstrated that local Traditional healthcare management is based on past
improvement of one subsystem does not necessarily result experience, feeling, intuition, educated guess and/or static
in improvement of the entire system. pictures or simple linear projections.
In conclusion, fundamental management science/ In contrast, management engineering is the discipline
engineering principles are summarized. The main take- of building mathematical models of real systems and their
away is that hospital/clinic managerial operational analysis for the purpose of developing justified managerial
decisions are most effective if based on objective data decisions. Management decisions for leveraging resources
analysis and process simulation rather than subjective that best meet system performance objectives are based on
opinion, intuition and past experience. outcomes of valid mathematical models.
The underlying foundation of a management
Introduction engineering approach is that analysis of a valid
mathematical model leads to better justified decisions
Modern medicine has achieved great progress in rather than traditional ‘common sense’ decision making
treating individual patients. This progress is based mainly such as educated guesses, past experiences and/or simple
on life science (molecular genetics, biophysics, linear extrapolations.
biochemistry) and development of medical devices and A system is defined as a set of interrelated elements
imaging technology. (subsystems) that form a complex whole that behaves in
However, relatively little resources and technical ways that these elements acting alone would not. Models
talent have been devoted to the proper functioning of of a system enable one to study the impact of alternative
overall health care delivery as an integrated system in ways of running the system, i.e. alternative designs,
which access to efficient care should be delivered to many different configurations and management approaches.
thousands of patients in an economically sustainable way. System models enable one to experiment with systems in
According to the joint report published by Institute of ways that cannot be used with real systems.
Medicine and National Academy of Engineering, a real Large systems are usually deconstructed into smaller
impact on quality, efficiency and sustainability of the subsystems using natural breaks in the system. The
health care system can be achieved only by using health subsystems are modeled and analyzed separately, but they
care delivery engineering (Reid et al., 2005). should be reconnected back in a way that recaptures the
A systematic way of developing effective managerial most important interdependency between them.
decisions using information technologies and predictive Analysis of a complex system is usually incomplete
design of the process of delivery and organizational and can be misleading without taking into account
operations is the scope of what is called healthcare systems subsystems’ interdependencies. Analysis of a
engineering. mathematical model using analytic or computer
algorithmic techniques reveals important hidden and

2. critical relationships in the system that allows leveraging treated, stabilized and released home. ED patients admitted
them to find out how to influence the system’s behavior into the hospital (ED output) form an inpatient input flow
into desired direction. into ICU, OR and/or NU. Length of stay distribution best
Management engineering decisions are often fit was identified separately for patients released home and
counterintuitive compared to traditional management patients admitted to the hospital (Kolker, 2008). About
decisions. There are two main reasons for this. First, most 60% of admitted patients are taken into operating rooms
managerial decisions are being made in an uncertain (OR) for emergency surgery, about 30% of admitted
environment with large variability. It is a general human patients move into ICU, and about 10% of patients
tendency to avoid the complications of incorporating admitted from ED into floor nursing units.
uncertainty into the decision making by ignoring it or The OR suite has 12 interchangeable operating
turning it into certainty. For example, average time or rooms used both for emergent and scheduled surgeries.
average numbers of procedures are typically treated as if There are four daily scheduled OR cases at 6 am, 9 am, 12
they are fixed values ignoring the effect of variability pm and 3 pm, Monday to Friday (there are no scheduled
around these averages. This practice often results in surgeries on weekends). Scheduled cases form a separate
erroneous conclusions made by traditional management OR admissions flow, as indicated on Figure 1.
decision-making (the so-called ‘flaw of averages’). Elective surgery duration depends on surgical service
Second, non-linear scaling effect (size effect) of most type, such as general surgery, orthopedics, neuro-surgery,
healthcare systems makes direct benchmarking difficult. etc. For the simplicity of this particular model elective
Large capacity systems can function at a much higher surgery duration was weighted by each service percentage,
utilization level and have lower patient waiting time than and the best statistical distribution fit was identified.
smaller capacity systems even if the patient arrival rate About 30% of post surgery patients are admitted
relative to their size is the same (Kolker, 2009b). Only from OR into ICU (direct ICU admission) while 70% are
mathematical models (computer simulation models) offer a admitted into floor NU. However some patients (about
means of incorporating the variability and scaling into the 5%) are readmitted from floor NU back to ICU (indirect
effective decision making. ICU admission from OR). ICU length of stay (LOS) is
assumed to be from 1 day to 3 days with most likely 1.5
Hospital System Description days represented by a triangle distribution. Kolker (2009a)
developed a detailed ICU simulation model and analysis.
A case study hospital system includes the following Patient LOS in NU is assumed to range between 2
interdependent high-level subsystems: (i) subsystem 1 - days to 10 days with the most likely 5 days represented by
Emergency Department (ED), capacity 30 beds; (ii) a triangle distribution. At the simulation start ED, ICU and
subsystem 2 - Intensive Care Unit (ICU), capacity 51 beds; NU were pre-filled with midnight census 15, 46 and 350
(iii) subsystem 3 - Operating Rooms (OR), capacity 12 patients, respectively.
OR; (iv) subsystem 4 - Regular Nursing Units (NU),
capacity 380 beds. A high-level flow map (layout) of the Simulation Results
entire hospital system is shown on Figure 1. When the ED
is full, a diversion status on ambulance is declared. Simulation results are summarized in Table 1. There
Patients who waited longer than 2 hours to be admitted are seven performance metrics (95% Confidence Intervals-
into the ED leave without being seen. Some patients are CI) indicated in column 1.
Figure 1. A high-level typical hospital flow map
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3. Baseline (current state) results are presented in Otherwise, even if the ED reports a significant
column 2. Aggressive improvement efforts in ED result in progress in its patient LOS reduction program, this
reducing LOS for patients admitted into the hospital to less progress will not translate into improvement of the overall
than 6 hours compared to the current state 20 - 24 hours hospital system patient flow (do not ‘over-improve’
(from ED registration to ED discharge). However, locally). Of course, many other scenarios could be
because of the interdependency of the downstream units, analyzed using a simulation model to find out how to
three out of seven metrics became worse (column 4). The improve the entire hospital system patient flow rather than
ED bottleneck just moved downstream into the OR and each separate hospital subsystem/department.
ICU because of their inability to handle increased patient
volume from ED. Conclusions
Thus, aggressive process improvement in one
subsystem (ED) results in a worsening situation in other Improvement of separate subsystems (local
interrelated subsystems (OR and ICU). Rather than using optimization or local improvement) should not be confused
an aggressive ED LOS reduction, if a less aggressive with the improvement of the entire system that consists of
improvement is implemented, e.g. LOS not more than 10 the interdependent subsystems. A system of local
hours for patients admitted to the hospital, then none of improvements is not the best system; it could be very
seven metrics become worse than the current state inefficient. Analysis of an entire complex system is usually
(columns 5 and 6). While in this case ED performance is incomplete and can be misleading without taking into
not as good as it could locally be, it is still better than it is account subsystems’ interdependency.
at the current state level. At the same time, this less There are fundamental management engineering
aggressive local ED improvement does not, at least, have a principles that govern behavior of most complex
negative impact on the ICU, OR and floor NU. healthcare systems. These principles have been illustrated
Thus, from the entire hospital system standpoint the both by examples presented in this paper and examples
primary focus of process improvement should be on the published elsewhere (Kolker, 2009b). Knowledge and
ICU because of its highest percent diversion followed by understanding of these fundamental principles alone would
ED and OR. At the same time, the ED patient target LOS help making right managerial decisions even without
reduction program should not be too aggressive, and it building a full blown simulation model.
should be closely coordinated with that for OR and ICU.
Table 1. Summary of simulation results
1 2 3 4 5 6
Too aggressive ED Downstream Less aggressive Downstream
Current
improvement: Units: Better ED improvement: Units: Better or
Performance Metrics State
patients admitted or worse than patients admitted words than current
Baseline
within 6 hours current state? within 10 hours state?
95% CI of the number of
patients waiting to get to 25 – 27 8 – 10 Better 17 – 19 Better
ED (ED in)
95% CI of the number of
patients waiting hospital 57 – 62 64 – 69 Worse 57 – 62 Neutral
admissions (ED out)
Number of patients left
not seen (LNS) after
waiting more than 2 23 – 32 0 Better 0–3 Better
hours
95% CI for % ED
diversion 22% – 23% 0.4% – 0.5% Better 6.8% – 7.3% Better
95% CI for % ICU
diversion 28% – 32% 30% – 34% Worse 28% – 32% Neutral
95% CI for % OR
diversion 12% – 13% 13% – 15% Worse 12% – 13% Neutral
95% CI for % floor NU
diversion 11% – 12% 11% – 12% Neutral 11% – 12% Neutral
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4. • Overall, systems behave differently than a
combination of independent subsystems. Reid, P., Compton, W, Grossman, J., Fanjiang, G., 2005.
• All other factors being equal, interchangeable Building a better delivery system: A new engineering /
resources are, in most cases, more efficient than Healthcare partnership. Committee on Engineering and
specialized (dedicated) resources with the same total the Health Care System, Institute of Medicine and National
capacity. Academy of Engineering. Washington, DC. National
• Scheduling appointments (jobs) in the order of their Academy Press.
increased duration variability (from lower to higher
variability) results in a lower overall cycle time. Biographical Sketch
• Size matters. Large units with the same arrival rate
(relative to its size) always have a significantly lower Alexander Kolker, PhD, ASQ CRE, Six Sigma Black Belt
waiting time. Large units can also function at a much
higher utilization level than small units with about the Alex holds a PhD in applied mathematics. He is both
same patient waiting time. an American Society for Quality Certified Reliability
• Work load leveling (smoothing) of elective procedures Engineer (CRE) and a certified Six Sigma Black Belt.
schedule is an effective strategy to reduce waiting Alex has extensive practical expertise in quantitative
time and improve patient flow. methods for healthcare management, such as hospital
• Because of variability of patient arrivals and service capacity expansion analysis, system-wide patient flow
time, a reserved capacity (sometimes up to 30%) is optimization, staffing planning, forecasting trends and
usually needed to avoid regular operational problems market expansion analysis. He widely applies process
due to excessive waiting time and long lines. simulation methodology to analyze different scenarios for
• Capacity, staffing and financial projections based on allocation of resources that result in the most effective
average input values usually result in significant errors operational solutions.
(the flaw of averages). Alex actively publishes in peer reviewed journals,
• Generally, the higher utilization levels of the resource published book chapters and speaks at national
(good for the organization) the longer the waiting time conferences in the area of discrete event simulation and
to get this resource (bad for patient). Utilization levels management engineering applications in healthcare
higher than 80%-85% result in a significant increase settings. He serves on the Review Boards of Healthcare
in waiting time for random patient arrivals and Management Science and Journal of Medical Systems.
random service time.
• In a series of dependent activities, only a bottleneck
defines the throughput of the entire system. A
bottleneck is a resource (or activity) whose capacity is
less than or equal to demand placed on it.
• Reduction of process variability is the key to patient
flow improvement, increasing throughput and
reducing delays.
References
Kolker, A., 2008. Process Modeling of Emergency
Department Patient Flow: Effect of patient Length of Stay
on ED diversion. Journal of Medical Systems, 32(5), pp.
389-401.
Kolker, A., 2009a. Process Modeling of ICU Patient Flow:
Effect of Daily Load Leveling of Elective Surgeries on ICU
Diversion. Journal of Medical Systems, 33(1), pp.27-40.
Kolker, A., 2009b. Queuing Theory and Discrete Events
Simulation for Health Care: from basic processes to
complex systems with interdependencies. Chapter 20. In:
Handbook of Research on Discrete Event Simulation
Technologies and Applications. Ed: Abu-Taieh, E., El
Sheik, A., IGI-press Global, pp.443-483.
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