Almost every OR/MS professional working in the field of health care at some point will be hear the following remark: "Patients aren't widgets in a factory — OR/MS won't work in this field." The remark does provide some hints as to the challenges that health care presents, however, there are numerous other challenges that are equally important for consideration. For example:

Uncertainty in human decision-making. Health care operations are remarkably challenging from a variability and uncertainty perspective. It is well understood that each patient is different in terms of overall health level, presence of risk factors, reactions to medications and therapies, tolerance to pain, ability to communicate and so on. These factors play a large role in care delivery. Although there has been much progress in the development and use of clinical care pathways and protocols, the process of clinical care largely involves human decision-making. Individual care providers make clinical and operational decisions to the best of their abilities based on their training, experience, intuition and understanding of the capabilities of other care providers. But, each care provider varies considerably in each of these areas. The logic that drives patient flow through health systems goes beyond typical process flow charts seen in industrial settings.

Flexible capacity. To further complicate the issue from a modeling perspective, health care providers are extremely resourceful. When faced with surges in demand for services, health care providers work faster and handle higher caseloads of patients in order to provide the best care possible. The level of flexibility is another human decision-making process often involving multiple parties. In this sense the capacity and speed of the system can be considerably difficult to model accurately.

Engagement and buy-in. In the Canadian health care system there are many stakeholders that wield significant power and influence. Health authorities and hospital administrators are responsible for managing hospital operational budgets. These budgets cover direct care costs such as staffing (nurses, technicians, care aides, porters/orderly), health care supplies and diagnostics, but also indirect costs such as plant services, information systems, finance and hospital administration. In addition, specialized services such as cardiac surgery, cancer care, specialized neonatal care and transplant services can also be funded separately even though the services draw on shared hospital resources.

In many hospitals the physicians operate on a fee for service basis, where they are compensated directly from the government for the clinical services they provide. While health authorities and hospital administrators are responsible for balancing budgets, they have limited influence on demand for services, inpatient lengths of stay in the hospital, admission rates from the Emergency Department and the proportion of surgical cases performed on a "day care" basis. With the exception of demand for services, these factors are primarily driven by clinical decisions that physicians make as part of routine care delivery. Unfortunately, it is not uncommon for physicians to interpret lack of beds as a "hospital problem" or a "health system" problem. Physicians with admitting privileges are generally not responsible for balancing hospital budgets and are more chiefly concerned with providing the best possible care to the patients that present to them, being compensated appropriately and managing their medical risk. Physicians play a pivotal role in patient flow; however, they are not "incentivized" accordingly.

Almost every provider and program in the Canadian health care system — from porters to radiologists to physicians, in rural care, community care and tertiary/quaternary care settings — feels that they are faced with a higher volume of patients that are more complex than ever, with lower funding and manpower than ever. Almost every health program perceives they are overtaxed and under resourced to a greater degree than any other program. This situation creates an environment of mistrust, where stakeholders of the system are often suspicious of solutions they did not have a hand in developing.

Many health care systems consist of multiple departments that are locally optimized [2]. The areas where OR/MS can have a material impact on efficiency and effectiveness are on processes that cross these boundaries. Successful OR/MS solutions involve engagement of all relevant stakeholders in both understanding the problem and developing solutions. For reasons described above, engagement of stakeholders in the health care system is even more crucial and hard to achieve.

Data quality: medical standards versus operational standards. Clinicians, particularly specialist clinicians, often hold high standards for data quality that is learned from clinical research projects involving controlled experiments and publications fraught with p-values and confidence intervals. While the Canadian health care system collects standardized, relatively high-quality data in all hospitals based on national standards, the data is primarily designed for administrative and operational purposes. Data is captured at the level of detail of the patient episode, but typically the data is grouped at a case mix level that is sometimes confusing to clinicians. For example, a frail elderly patient who undergoes hip replacement surgery, recovers post-operatively but then develops unrelated medical complications is considered both a "surgical" and a "medical" patient. It is relatively easy for clinicians to claim that an analysis or model is flawed when the underlying data does not meet their expectations.

Measuring positive outcomes. One of the largest challenges in the Canadian health care system is the lack of health outcomes data. The available outcomes data is mostly focused on clinical trials and highly specialized patient populations. For example, for heart health, it is very difficult to compare the outcome of proactive disease management, to the outcome of a surgical cardiac intervention, to the outcome of doing nothing. Health outcomes are typically described in terms of life expectancy, potential years of life lost, reduction in pain symptoms, recurrence of disease, degrees of independence (ability to live and function independently) and employment status.

It is even more challenging to compare the net outcome of interventions on different body systems. For example, how does the net outcome of a cataract surgery compare to the net outcome of a hernia repair? How does the outcome of a new, expensive cancer treatment program compare to the outcome of multiple patients accessing a less expensive older treatment program? Such questions pose unique challenges for OR/MS modeling in health care systems.

Limited understanding of actual costs and cost trade-offs. One of the largest challenges in the Canadian health care system is the limited understanding of systems costs. Activity-based costing is performed in various hospitals; however, few people understand the assumptions involved in assigning the costs from shared departments and services. As a result, the information is infrequently used for operational decision-making. More importantly, the health care system does not know the cost of not taking an action.

Many administrative decision-makers in the health care system focus on the cost savings of service reductions (closing beds, reduced operating room time, reduced support services, reduced clerical support, etc) but are unable to assess how these reductions may result in cost increases in other areas (increases in use of overtime, Emergency Department overflow, increased medical risk, etc). The health care system is extremely complex and inter-related, and this presents a challenge when attempting to build validated and manageable OR/MS tools involving cost considerations.

The above challenges will be present for many years to come, however, the following are some approaches to overcome these barriers to applying OR/MS in health care:

• Make sure you understand the current state of the system to be modeled, including process flow, current performance levels, service standards, patient populations, staff attitudes, political factors, organization and reporting structures and funding sources.
  
  
• Communicate what you are doing to all potential stakeholders so there is clear understanding of the overall project objectives and the project approach. Communications should be done through multiple channels (e-mail, posters, memos, presentations) in order to accurately convey these messages.
  
  
• Be as transparent as possible in any analysis and modeling. Some clinicians are extremely detail-oriented. Highlight any assumptions and limitations and be prepared to review the details of your work with interested parties.
  
  
• Be as resourceful as possible with imperfect data. More often than not you will need to work with what is available, and it will contain missing and inaccurate information. Leverage the knowledge of the experts in the system when analyzing and interpreting the information.
  
  
• Engage all key stakeholders in the development of solution ideas, so they can develop truly actionable approaches and take ownership after the project is finished.
  
  
• Focus on simple, measurable improvement and not complex optimization. Very few health systems are sufficiently well-defined and have good enough data to be in a position to use sophisticated OR/MS models.

Simulation modeling of emergency departments. Emergency Department (ED) overcrowding is an issue that has grown in severity in the past decade. The key negative outcome of the problem is excessive waiting times for patients to enter the ED and be assessed by a physician.

We worked with a Canadian regional health authority to investigate these issues on their four largest EDs and to develop actionable solutions to improve ED patient flow. Each hospital ED involved a separate project of approximately six months in length. Our general approach involved process observation, process mapping, interviews with all stakeholders including front-line staff, extensive data analysis and data quality improvement, development of opportunities for improvement and simulation modeling to evaluate the potential improvement associated with the top ranked improvement strategies. The process was transparent where all opinions, perspectives and ideas were noted and invited from ED staff and programs that interact with the ED. Wherever possible, data analysis was conducted to gauge the relative magnitude of each contributor to congestion. By undertaking a transparent, inclusive and evidence-based approach, the hospitals were able to focus their efforts more productively on areas with high potential impact.

Discrete-event simulation models were developed to evaluate the impact of various strategies for decongestion, such as the use of pre-admission units, medical observation units, expedited triaging and parallelization of clinical assessments. As always, a key challenge in the simulation modeling work was developing a verified and validated baseline model. The process flow was limited to the major stages of patient flow: arrival, triage, registration, entry to the ED, primary nurse assessment in the ED, primary physician assessment in the ED, decision to admit (for those patients to be admitted), delay for inpatient bed, total length of stay in the ED and departure from the ED.

Initial attempts to model the departments based on their staffed stretcher capacity yielded queueing and wait times that far exceeded actual values. A more detailed analysis of the data revealed that the EDs often operated above their staffed capacity, and in fact, in times of peak patient volumes, tasks were performed more quickly than under ordinary circumstances. This meets with intuition. For example, triage nurses often conduct faster assessments and seek help from other nurses when multiple patients present to the ED at the same time. They do this in order to minimize delays for the initial triage assessment and to best manage patient safety. Modeling the flexing of capacity and the relationship of patient volume to speed of service durations was extremely challenging, as these are human decision-making processes. Figure 1 shows: 1. the modeled wait times to enter an ED based on the model operating under a fixed capacity and fixed service durations, 2. the modeled wait times based on a flexible capacity and variable durations, and 3. the actual wait times of the actual ED. Clearly the system relies heavily on flexible capacity and variable service durations to avoid significant congestion.

Figure 1: Wait times to enter the Emergency Department.

Scenario analysis was also conducted to evaluate the impact of redirecting the volume of lower acuity patients on overall ED congestion. These model results were instrumental in conveying to administrators that these strategies would have remarkably little impact on decongesting the EDs. The scenario analyses of the pre-admission unit, medical observation units and expedited triaging strategies identified promising potential in decongesting the EDs. At the two largest sites in this health authority these strategies are currently being implemented and are starting to yield positive results.

Dynamic smoothing of inpatient surgical beds. A popular topic in health operations improvement involves smoothing surgical bed utilization [3]. The typical pattern of bed utilization on a surgical ward is characterized by increasing utilization throughout the days of the week, with remarkable decreases in admissions and discharges on the weekends. This pattern is driven primarily by the scheduled elective patients. Comparatively, the average bed utilization of emergent patients is much more consistent throughout the days of the week. This practice of operation presents an opportunity to increase the average level of bed utilization by decreasing the controllable variability in the system.

The concept appears to be a relatively easy opportunity for improvement. One can develop a model of the surgical system that includes inpatient beds, and then evaluate the impact of rescheduling specific scheduled work to different days of the week and different times of day to minimize the overall variation in bed utilization.

Figure 2: The surgical bed smoothing concept.

Unfortunately, in practice, the delivery of surgical care involves numerous uncertainties. The health condition of the patient, nature of the surgical operation to be performed and individual skills of the surgeon each introduce significant variability. We developed a simulation model of a surgical suite in a tertiary-level hospital to evaluate these scenarios. Early in the data modeling and distribution fitting stages it was clear that within each "homogeneous group" (i.e. same surgical intervention, same patient age group and same surgeon) the variations in durations were frequently as large as the average durations. Despite the considerable variability, some modest opportunities were identified to smooth the average inpatient bed utilization across the days of the week, but these improvements were outweighed by the inherent variability in the system.

Based on these findings the team determined that the smoothing bed utilization concept needed to be performed on an operational basis in order to have an impact. We worked again with the hospital's surgical team to develop a tool that would connect to the hospital's information systems to extract the current state of the system, and then used historical patterns and a purpose-built simulation engine to project the next two week's worth of surgical activity. Key inputs include the planned surgical slate (typically it is populated with schedules two weeks into the future) and the current inpatient bed census levels on the surgical nursing units. The surgical slate contains information on the surgeon, procedure type and case type (inpatient versus day care).

Each combination of factors has associated distributions for the surgical procedure duration, post-anesthesia recovery duration, pre-operative durations, probability of requiring intensive care and inpatient length of stay duration. The model samples from these distributions on a case basis, simulates the individual episodes of care and summarizes over the key resources (operating room, post-anesthesia recovery room, inpatient beds). In addition, the model simulates the discharge patterns for patients currently in the system. By leveraging the known information from the system, the model is able to provide up-to-date, short-term projections of inpatient bed census levels (Figure 3) that are considerably more useful than general schedule patterns developed by the more traditional simulation approach.

Figure 3: Block diagram of dynamic smoothing application.

The managers use the information from the model to identify peaks and valleys in inpatient bed utilization in the upcoming two weeks and take proactive action to avoid either extreme. They are able to engage in productive discussions with surgeons on their cases currently in the system awaiting discharge and their upcoming scheduled inpatient cases. Previously these discussions would occur the day before a given surgeon's scheduled operating room day, in a frantic and reactive manner. With the tool in use, these discussions now take place many days in advance of a given surgeon's scheduled operating room day, in a proactive manner.

The model also identifies the estimated patterns of utilization in the pre-operative area and the post-anesthesia recovery room, which changes significantly depending on the mix of surgical cases scheduled on a given day. These estimates can be used to identify staffing requirements and the need for overtime on specific days.

This tool has been in use for six months and the managers report a notable difference in the number of disputes and complaints raised by surgeons during this period. Analysis is currently underway to assess the impact of this tool on variation in bed utilization, increased throughput and increased lead time on operating room schedule revisions.

Methodologies for the allocation of health care resources. Health care systems involve considerable resources such as human resources, medical/surgical supplies and most importantly, inpatient beds and surgical operating room time. As described in the first sections of this article, there are many important stakeholders in the health care system. Historically, the allocation of precious resources such as inpatient beds would be based on political considerations, the ability of the division's lead to present a convincing case for bed increases and personal relationships within the organization. The allocation of operating room time has historically been slightly better with considerations of the size of the associated wait list and the division's ability to utilize their current allocation of operating room time. Unfortunately in the past these decisions rarely considered the perspectives of all stakeholders that would be impacted by the decision.

We worked with Canadian regional health authorities in developing and implementing allocation methodologies for inpatient beds and surgical operating room time. These were separate projects with separate clients, each involving large multidisciplinary project steering teams and each taking over a year to implement. At the root of each of these methodologies was the desire of the organization to develop fair, transparent, data-driven approaches for allocating scarce resources. These engagements involved extensive analysis of input factors, performance targets and relative performance of different services. The core concepts of the methodologies involved basic queueing and risk management concepts. Various adjustment factors and design options were presented to the project teams for consideration in the methodologies, along with their associated strengths and weaknesses.

Each of these engagements concluded with the successful implementation of operational methodologies for allocating hundreds of millions of dollars worth of scarce health resources. The methodologies are still in use after two years of operation.

Conclusion


OR/MS practitioners working inside the Canadian health care system often comment that the system has a long way to go in terms of using data and models to support decision-making, planning better and achieving measurable improvements. The use of operations research, management science, and industrial engineering in health care is gradually gaining popularity, and with any hope this trend will continue. While the immediate OR/MS opportunities are very fundamental and basic in nature, this is the necessary groundwork the Canadian health care system needs in order to pursue the more sophisticated technologies that OR/MS has to offer in the future.



Jason Goto (jgoto@analysisworks.net) is the president of AnalysisWorks Inc., a Vancouver, B.C.-based consultancy that combines practical management consulting with advanced analytical tools to help organizations achieve measurable improvements. He has worked with a wide range of industries including airlines, distribution, logistics, electrical utilities, research, telecommunications, digital media and health care. He holds an engineering degree from the University of Waterloo and a Master's of Science in management science from the University of British Columbia, and he has taught graduate level courses in simulation methods, statistics and consulting practices.

References

1. Carter, M., 2002, "Diagnosis: Mismanagement of Resources," OR/MS Today, Vol. 29, No. 2, pp. 26-32.
2. Ronen, B., Pliskin, J. S., 2006, "Focused Operations Management for Health Services Organizations," Wiley.
3. Institute for Healthcare Improvement, 2003, "Optimizing Patient Flow Moving Patients Smoothly Through Acute Care Settings," Innovation Series.

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