SYSTEM ENGINEERING AND MANAGEMENT SCIENCE FOR HEALTHCARE: EXAMPLES AND FUNDAMENTAL PRINCIPLES

Alexander Kolker, Children’s Hospital and Health System, Milwaukee, WI 53226

Abstract Relatively little technical and intellectual resources

have been devoted to process engineering and analysis of overall healthcare delivery as an integrated system that should provide high quality care for many thousands of patients in an economically sustainable way.

A real long-term impact on quality of care and efficiency of healthcare as an integrated system can be achieved only by using fundamental principles of management engineering. Probability theory, optimization, computer simulation are scientific and technical foundations for such an approach.

This paper includes a quantitative analysis of a typical entire hospital system represented as a set of interdependent subsystems. It is demonstrated that local improvement of one subsystem does not necessarily result in improvement of the entire system.

In conclusion, fundamental management science/ engineering principles are summarized. The main take-away is that hospital/clinic managerial operational decisions are most effective if based on objective data analysis and process simulation rather than subjective opinion, intuition and past experience.

Introduction

Modern medicine has achieved great progress in treating individual patients. This progress is based mainly on life science (molecular genetics, biophysics, biochemistry) and development of medical devices and imaging technology.

However, relatively little resources and technical talent have been devoted to the proper functioning of overall health care delivery as an integrated system in which access to efficient care should be delivered to many thousands of patients in an economically sustainable way.

According to the joint report published by Institute of Medicine and National Academy of Engineering, a real impact on quality, efficiency and sustainability of the health care system can be achieved only by using health care delivery engineering (Reid et al., 2005).

A systematic way of developing effective managerial decisions using information technologies and predictive design of the process of delivery and organizational operations is the scope of what is called healthcare systems engineering.

The objective of this paper is to illustrate the predictive and analytical power of management engineering applied to a typical hospital-wide system that consists of a set of interdependent subsystems. Fundamental management engineering principles for effective managerial decision-making in healthcare settings are summarized in the Conclusions.

What is Management?

There are many possible definitions of management. For the purpose of this paper, management is defined as controlling and leveraging available resources (material, financial and human) aimed at achieving a system’s performance objectives.

Traditional healthcare management is based on past experience, feeling, intuition, educated guess and/or static pictures or simple linear projections.

In contrast, management engineering is the discipline of building mathematical models of real systems and their analysis for the purpose of developing justified managerial decisions. Management decisions for leveraging resources that best meet system performance objectives are based on outcomes of valid mathematical models.

The underlying foundation of a management engineering approach is that analysis of a valid mathematical model leads to better justified decisions rather than traditional ‘common sense’ decision making such as educated guesses, past experiences and/or simple linear extrapolations.

A system is defined as a set of interrelated elements (subsystems) that form a complex whole that behaves in ways that these elements acting alone would not. Models of a system enable one to study the impact of alternative ways of running the system, i.e. alternative designs, different configurations and management approaches. System models enable one to experiment with systems in ways that cannot be used with real systems.

Large systems are usually deconstructed into smaller subsystems using natural breaks in the system. The subsystems are modeled and analyzed separately, but they should be reconnected back in a way that recaptures the most important interdependency between them.

Analysis of a complex system is usually incomplete and can be misleading without taking into account subsystems’ interdependencies. Analysis of a mathematical model using analytic or computer algorithmic techniques reveals important hidden and

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critical relationships in the system that allows leveraging them to find out how to influence the system’s behavior into desired direction.

Management engineering decisions are often counterintuitive compared to traditional management decisions. There are two main reasons for this. First, most managerial decisions are being made in an uncertain environment with large variability. It is a general human tendency to avoid the complications of incorporating uncertainty into the decision making by ignoring it or turning it into certainty. For example, average time or average numbers of procedures are typically treated as if they are fixed values ignoring the effect of variability around these averages. This practice often results in erroneous conclusions made by traditional management decision-making (the so-called ‘flaw of averages’).

Second, non-linear scaling effect (size effect) of most healthcare systems makes direct benchmarking difficult. Large capacity systems can function at a much higher utilization level and have lower patient waiting time than smaller capacity systems even if the patient arrival rate relative to their size is the same (Kolker, 2009b). Only mathematical models (computer simulation models) offer a means of incorporating the variability and scaling into the effective decision making.

Hospital System Description

A case study hospital system includes the following interdependent high-level subsystems: (i) subsystem 1 -Emergency Department (ED), capacity 30 beds; (ii) subsystem 2 - Intensive Care Unit (ICU), capacity 51 beds; (iii) subsystem 3 - Operating Rooms (OR), capacity 12 OR; (iv) subsystem 4 - Regular Nursing Units (NU), capacity 380 beds. A high-level flow map (layout) of the entire hospital system is shown on Figure 1. When the ED is full, a diversion status on ambulance is declared. Patients who waited longer than 2 hours to be admitted into the ED leave without being seen. Some patients are

treated, stabilized and released home. ED patients admitted into the hospital (ED output) form an inpatient input flow into ICU, OR and/or NU. Length of stay distribution best fit was identified separately for patients released home and patients admitted to the hospital (Kolker, 2008). About 60% of admitted patients are taken into operating rooms (OR) for emergency surgery, about 30% of admitted patients move into ICU, and about 10% of patients admitted from ED into floor nursing units.

The OR suite has 12 interchangeable operating rooms used both for emergent and scheduled surgeries. There are four daily scheduled OR cases at 6 am, 9 am, 12 pm and 3 pm, Monday to Friday (there are no scheduled surgeries on weekends). Scheduled cases form a separate OR admissions flow, as indicated on Figure 1.

Elective surgery duration depends on surgical service type, such as general surgery, orthopedics, neuro-surgery, etc. For the simplicity of this particular model elective surgery duration was weighted by each service percentage, and the best statistical distribution fit was identified.

About 30% of post surgery patients are admitted from OR into ICU (direct ICU admission) while 70% are admitted into floor NU. However some patients (about 5%) are readmitted from floor NU back to ICU (indirect ICU admission from OR). ICU length of stay (LOS) is assumed to be from 1 day to 3 days with most likely 1.5 days represented by a triangle distribution. Kolker (2009a) developed a detailed ICU simulation model and analysis.

Patient LOS in NU is assumed to range between 2 days to 10 days with the most likely 5 days represented by a triangle distribution. At the simulation start ED, ICU and NU were pre-filled with midnight census 15, 46 and 350 patients, respectively.

Simulation Results

Simulation results are summarized in Table 1. There

are seven performance metrics (95% Confidence Intervals-CI) indicated in column 1.

Figure 1. A high-level typical hospital flow map

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Baseline (current state) results are presented in column 2. Aggressive improvement efforts in ED result in reducing LOS for patients admitted into the hospital to less than 6 hours compared to the current state 20 - 24 hours (from ED registration to ED discharge). However, because of the interdependency of the downstream units, three out of seven metrics became worse (column 4). The ED bottleneck just moved downstream into the OR and ICU because of their inability to handle increased patient volume from ED.

Thus, aggressive process improvement in one subsystem (ED) results in a worsening situation in other interrelated subsystems (OR and ICU). Rather than using an aggressive ED LOS reduction, if a less aggressive improvement is implemented, e.g. LOS not more than 10 hours for patients admitted to the hospital, then none of seven metrics become worse than the current state (columns 5 and 6). While in this case ED performance is not as good as it could locally be, it is still better than it is at the current state level. At the same time, this less aggressive local ED improvement does not, at least, have a negative impact on the ICU, OR and floor NU.

Thus, from the entire hospital system standpoint the primary focus of process improvement should be on the ICU because of its highest percent diversion followed by ED and OR. At the same time, the ED patient target LOS reduction program should not be too aggressive, and it should be closely coordinated with that for OR and ICU.

Table 1. Summary of simulation results

Otherwise, even if the ED reports a significant progress in its patient LOS reduction program, this progress will not translate into improvement of the overall hospital system patient flow (do not ‘over-improve’ locally). Of course, many other scenarios could be analyzed using a simulation model to find out how to improve the entire hospital system patient flow rather than each separate hospital subsystem/department.

Conclusions

Improvement of separate subsystems (local optimization or local improvement) should not be confused with the improvement of the entire system that consists of the interdependent subsystems. A system of local improvements is not the best system; it could be very inefficient. Analysis of an entire complex system is usually incomplete and can be misleading without taking into account subsystems’ interdependency.

There are fundamental management engineering principles that govern behavior of most complex healthcare systems. These principles have been illustrated both by examples presented in this paper and examples published elsewhere (Kolker, 2009b). Knowledge and understanding of these fundamental principles alone would help making right managerial decisions even without building a full blown simulation model.

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Neutral11% – 12%Neutral11% – 12%11% – 12%95% CI for % floor NU diversion

Neutral12% – 13%Worse13% – 15%12% – 13%95% CI for % OR diversion

Neutral28% – 32%Worse30% – 34%28% – 32%95% CI for % ICU diversion

Better6.8% – 7.3%Better0.4% – 0.5%22% – 23%95% CI for % ED diversion

Better0 – 3Better023 – 32

Number of patients left not seen (LNS) after waiting more than 2 hours

Neutral57 – 62Worse64 – 6957 – 6295% CI of the number of patients waiting hospital admissions (ED out)

Better17 – 19Better8 – 1025 – 2795% CI of the number of patients waiting to get to ED (ED in)

Downstream Units: Better or

words than current state?

Less aggressive ED improvement: patients admitted within 10 hours

Downstream Units: Better or worse than current state?

Too aggressive ED improvement: patients admitted within 6 hours

Current State

BaselinePerformance Metrics

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Neutral11% – 12%Neutral11% – 12%11% – 12%95% CI for % floor NU diversion

Neutral12% – 13%Worse13% – 15%12% – 13%95% CI for % OR diversion

Neutral28% – 32%Worse30% – 34%28% – 32%95% CI for % ICU diversion

Better6.8% – 7.3%Better0.4% – 0.5%22% – 23%95% CI for % ED diversion

Better0 – 3Better023 – 32

Number of patients left not seen (LNS) after waiting more than 2 hours

Neutral57 – 62Worse64 – 6957 – 6295% CI of the number of patients waiting hospital admissions (ED out)

Better17 – 19Better8 – 1025 – 2795% CI of the number of patients waiting to get to ED (ED in)

Downstream Units: Better or

words than current state?

Less aggressive ED improvement: patients admitted within 10 hours

Downstream Units: Better or worse than current state?

Too aggressive ED improvement: patients admitted within 6 hours

Current State

BaselinePerformance Metrics

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• Overall, systems behave differently than a combination of independent subsystems.

• All other factors being equal, interchangeable resources are, in most cases, more efficient than specialized (dedicated) resources with the same total capacity.

• Scheduling appointments (jobs) in the order of their increased duration variability (from lower to higher variability) results in a lower overall cycle time.

• Size matters. Large units with the same arrival rate (relative to its size) always have a significantly lower waiting time. Large units can also function at a much higher utilization level than small units with about the same patient waiting time.

• Work load leveling (smoothing) of elective procedures schedule is an effective strategy to reduce waiting time and improve patient flow.

• Because of variability of patient arrivals and service time, a reserved capacity (sometimes up to 30%) is usually needed to avoid regular operational problems due to excessive waiting time and long lines.

• Capacity, staffing and financial projections based on average input values usually result in significant errors (the flaw of averages).

• Generally, the higher utilization levels of the resource (good for the organization) the longer the waiting time to get this resource (bad for patient). Utilization levels higher than 80%-85% result in a significant increase in waiting time for random patient arrivals and 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.

Reid, P., Compton, W, Grossman, J., Fanjiang, G., 2005. Building a better delivery system: A new engineering / Healthcare partnership. Committee on Engineering and the Health Care System, Institute of Medicine and National Academy of Engineering. Washington, DC. National Academy Press.

Biographical Sketch

Alexander Kolker, PhD, ASQ CRE, Six Sigma Black Belt

Alex holds a PhD in applied mathematics. He is both an American Society for Quality Certified Reliability Engineer (CRE) and a certified Six Sigma Black Belt.

Alex has extensive practical expertise in quantitative methods for healthcare management, such as hospital capacity expansion analysis, system-wide patient flow optimization, staffing planning, forecasting trends and market expansion analysis. He widely applies process simulation methodology to analyze different scenarios for allocation of resources that result in the most effective operational solutions.

Alex actively publishes in peer reviewed journals, published book chapters and speaks at national conferences in the area of discrete event simulation and management engineering applications in healthcare settings. He serves on the Review Boards of Healthcare Management Science and Journal of Medical Systems.