CHAPTER 4

Health Services Configuration and Capacity Design

This chapter presents cases in which the Business Design of the previous chapter is converted into a process architecture that makes it operational, performing what we defined as a Level ii design in Chapter 2. Also a case which does not have a previous Business Design is presented, illustrating what we defined as a local case.

Service Innovation in a Private Hospital

Taking as a starting point the Business Design of the previous chapter in Figure 3.1 and the requirements derived from it, a process architecture is designed. Mapping the Business Pattern (BP) in Figure 3.1 to the processes needed is straightforward, by rules given in section “Design Methodology” of Chapter 2. They are clearly included in the general macroprocesses defined in Figure 2.7: “New Capabilities Development” (Macro2) and “Hospital Planning” (Macro3) interacting with Macro1 to collect performance and use data and change hospital services as designed. Here the idea implies recursively generating a Capability that is able to generate new Capabilities when it is routinely executed. The mapping is done by specializing these macros to this case, resulting in Figure 4.1, where the two macroprocesses, “Strategic Planning” and “New Capabilities Development,” to be designed are included. A detailed design was performed, including a formal strategic planning procedure that provides guidelines for the generation of innovation project proposals that results in the flow “Investment budget, Objectives, and metrics” and “Accepted projects.” In addition “New Capabilities Development” was created, which, based on aforementioned guidelines, produces the “Projects implemented” and interacts with “Strategic Planning” by means of the flow “New projects proposal” and “Progress and results new projects.” Both of these macroprocesses interact with the other processes in the architecture through “New Capability performance” and “Needs and ideas.” What we have then is a sequence, which is implicit in Figure 4.1, because it is a nonsynchronous representation, where first “Strategic Planning” will issue guidelines; based on this and “Ideas and results” arising from other processes, “New Capabilities Development” generates new projects ideas that will be submitted back to “Strategic Planning,” which will then define the projects to be implemented. Later, projects will be designed and constructed by “New Capabilities Development” and implemented on the other processes. Finally, during all the preceding sequences and after the project is implemented, a monitoring of the progress and result of such projects will be performed. This sequence is formalized and made explicit in the more detailed levels of design presented next.

Figure 4.1 Architecture design for the private hospital case

To illustrate the following level of design, we use “New Capabilities Development” for which a general pattern for a macroprocess of this type is used.¹ Such pattern is instantiated for this case, resulting in Figure 4.2, where the first process is “Generation of new projects proposals” that, based on guidelines arising from “Strategic Planning,” does a formal definition and evaluation of projects, interacting with the “Other macroprocesses” and acquiring market information; this interaction means an active participation of the Heads of the medical and other services operating units in generating new project ideas. Now this hospital has a strategic alliance with the medical school of a private university for training their medical school students; then such school may participate in the generation of medical innovations that can be considered in the project generation. The first result of its effort is “New Capabilities ideas” to be considered by “Strategic Planning,” where the projects to be implemented are decided. For such projects, the process “Manage design and construction of new capability” is executed, which generates “Design and construction plans” to be executed by “Design and construction of new Capability.” The business logic to be executed by these two processes is essentially good project management practices as proposed by the Project Management Body of Knowledge (PMBOK).² All these processes have feedback flows that allow monitoring and correcting actions, such as “Plan feasibility and resources needs.” To provide the adequate system support there is the process “State updating,” where all the information about projects in their various states, plans, and resources are maintained up to date.

Figure 4.2 “New Capabilities Development” design for the private hospital case

“Design and construction of new capabilites”in Figure 4.2 is where the detail design of the service itself and its production is performed as defined in Chapter 2 in “Design Levels for Health Services.”

There are several levels of design details, as will be exemplified in later cases, which define the operation of the processes and the business logic that is executed, but are not included for this case.

The project reported earlier was developed during approximately 18 months, where formal processes of planning and management of strategic projects were designed and implemented, which did not exist before this effort, with a custom-made information system support. Moreover, a formal effort was implemented that took care of the factors of change management within the organization. Such effort made a difference in this case, since it is difficult to change management practices in a radical way in a medical environment, where doctors emphasize mainly their discipline. In making the innovations feasible, the support from the Board of Directors and the active participation of the medical unit heads were the key factors. As a result of this design, the visibility of plans and projects’ execution was considerably increased; also the communication between the Directors and the section heads improved. Finally, the results motivated the creation of a Project Management Office that supervises and leads the innovation initiatives. It is convenient to emphasize the enormous cultural change that this project produced in the executives of the organization, including its board and all the medical unit heads, which had to change their practices of planning and management of projects in a fundamental way, a great merit in a medical atmosphere, where they tend to subvalue the improvement in the management practices.

This case proves again that a profound and good Business Design involves integrated and systemic changes in the structure of the organization, the process architecture, and IT support; that is, true Enterprise Architecture.

Innovation Resource Assignment in the Public Sector

Based on the BP presented for this case in the previous chapter we propose an architecture based on the general health multilevel architecture of Figure 2.12, which should exist at the top of the public health system to guide its development with an emphasis on resource assignment for innovation projects on existent hospitals. Hence, we overlook features such as ordinary annual budgeting, investment in new facilities, health campaigns, and many other activities that are necessary in a centralized country health management, which are summarized in the “Other processes” component of the architecture. We also do not consider the level of subnetwork in Figure 2.12, which are groups of hospitals managed by a centralized authority, since they do not play a significant role on resource assignment.

Our selection of innovation resource assignment is based on the execution of many projects with hospitals, where the implementation of well-selected projects, which change in a radical way the medical and management practices of services in hospitals, has generated significant social value.³ Thus, our key idea is to generalize and extend our experience to the public hospitals system.

In the architecture in Figure 4.3, which is an instantiation of the general pattern in Figure 2.12, the main idea is that, besides “Regular planning and budgeting” oriented to continuing operation, Macro3 of the central level includes a new process of “Innovation planning and budgeting.” Such process executes a logic, which will be explained later, to determine the innovation projects that are to be executed in selected hospitals in trying to maximize the value associated with the objectives stated earlier. This innovation relates to new Capabilities to be developed for hospitals in a similar way to the previous case of the private hospital; the difference in this case is that we are dealing with all the hospitals in the Chilean health system in a centralized planning approach for this type of innovation. Then the projects are defined in detail by “Innovation projects organization and monitoring,” which determines the budget and the possible external services suppliers that can execute them. Next, the projects are communicated, by means of the flow “Project definition and budget” to the selected hospitals, determined as explained in the following, to be defined in detail by them with the collaboration of the “Suppliers Processes,” which are academic or consulting services specialized in the types of projects to be defined. The idea behind this proposal is that hospitals do not have health innovation and project management specialists, so the projects should be executed by means of externalized services, as it has been the case in many historical projects dealing with IT support or process design. In implementing this approach, hospitals need, as shown in Figure 4.3, three new processes: (a) “Strategy definition” that, besides doing the current budgetary planning, which includes resources and other medical factors, will perform the overall planning to execute the projects assigned to the hospital, (b) “New Capability project planning” that requests proposals for executing projects from external suppliers, evaluates them, and decides which consulting group will actually develop the project; and (c) “New Capability Implementation” that will coordinate with suppliers and the people from “Management and production of health services,” who will execute the new Capability, and put the project into practice. Similar examples of such Capabilities will be presented when the logic that defines which new Capabilities are to be implemented is specified. Besides, the processes just explained for “Health System Planning” in Figure 4.3, the design includes “Define Mission and Objectives” that provides a frame of reference for the rest of the processes and “State updating” that carries out its usual task of keeping up to date and reporting the status of the all the processes in the design; in particular, the situation and results of each innovation project.

Figure 4.3 Design for resource assignment in the Public Sector

Notice that this architecture is centralized on decision of funds assignments to innovations projects that maximize efficiency improvements on hospitals and its justified by agency theory that says that principal (government) interests are better taken care of with this option.⁴ But execution of projects is decentralized, since the same theory says that this is better because operators (agents) know more about these implementations issues and if principal tries to manage them he would incur in severe opportunity costs due to lack of information.

The key business logic that makes possible the implementation of the aforementioned architecture is the one that, in “Innovation planning and budgeting,” measures efficiency of the hospitals and determines which projects to develop in the less efficient ones to make them improve. Such logic was developed by measuring the efficiency, based on the Data Envelopment Analysis (DEA) analysis, for 40 hospitals and it is detailed as follows.

As stated in Chapter 2, we pursue three objectives: quality, efficiency, and fairness in designing health services. This is a multicriteria problem for which it is impossible to find a solution that optimizes all the objectives simultaneously; thus, a possibility is to prioritize the optimization of an objective and then take into consideration the others. Hence, the logic proposed for the design of new Capabilities for innovation projects generation, in “Innovation planning and budgeting” of Figure 4.3, is founded on the idea that it is possible to measure and compare the efficiency of the hospitals by using the economic theory of efficiency frontier as presented by Farrell,⁵ which takes into account such variable. Subsequently, based on efficiency comparisons, take into consideration the fairness and quality variables as we explain later. Next, we briefly summarize the economic theory used for the efficiency measurement and comparison.⁶

According to economic theory, a unit is efficient when it is able to produce, relatively to comparable group, a greater amount of product for given resources, or to use a smaller amount of resources for a given production. One formal approach to measure efficiency is the one of Farrell, which is based on the empirical results of the units and not on the possible ideal or optimal results. For this reason, the levels of efficiency of the units are defined in relative terms, given the information available. Thus, the most efficient units are those that define the productive frontier. According to Farrell, three types of efficiency can be distinguished: technical, allocative, and scale. The technical efficiency is obtained when a unit obtains the maximum results with its resources. The allocative efficiency is obtained when a unit uses its resources in the optimal proportions and maximizes results. Finally, the scale efficiency occurs when both types of efficiency are obtained.

In 1978, Charnes et al.⁷ generalized the proposal of Farrell with a mathematical nonparametric model, called DEA. This model constructs the technical efficiency frontier on the basis of the provided data (inputs and outputs) that can be of constant returns to scale (CRS) and variables (VRS), which is an extension of Banker, Charnes, and Cooper.⁸ In calculating the technical efficiency frontier, inputs can be minimized or outputs can be maximized. The first calculation looks for the breach between the evaluated unit with respect to the amount of resources established by the efficient frontier, given a production level and the second looks for the optimal production amount, given the level of resources.

Some advantages that distinguish DEA from other methodologies of efficiency calculation, like the Stochastic Production Frontier,⁹ are: (a) it does not assume a form of the production function on the basis of the resources, (b) it is possible to use different measurement units for the inputs and outputs amounts and multiple inputs, and (c) outputs can be integrated.¹⁰ The limitations are that the DEA is very sensible to the sample; it does not allow identifying the theoretical maximum efficiency, interprets any deviation from the frontier as inefficiency, and it is complex to perform sensitivity analyses.¹¹

A graphical interpretation of an efficiency frontier, in the simple case of just one input and output, is shown in Figure 4.4, where the curve that envelopes the pairs of inputs and outputs that define the data points is the frontier. Data points on the frontier are efficient and those under the frontier are inefficient.

The efficiency frontier can be calculated by solving the following optimization problem:

subject to:

Where there are n decision units that generate similar products and the evaluated unit is the kth; each unit consumes diverse amounts of m different resources to produce s different products; x_ij is the amount of the resource i that uses the jth unit; y_ij is the amount of product r of the jth unit; and v_i and u_r are the weights associated with resource i and product r, respectively.

Figure 4.4 Input, output, and the efficiency frontier

The model evaluates the n units, one at a time, and, in each iteration, it looks for the set of weights that maximizes the efficiency level for each evaluated unit k. Such levels are in fact the values of efficiency for each unit. According to Dyson et al.,¹² the flexibility in the election of the weights is a weakness and simultaneously the strength of this approach. It is a weakness because the model can arbitrarily consider that a unit is not related to the value of some resource or product, allowing it to appear as efficient, which is possible to correct. It also shows strength, since if a unit, in spite of getting the most favorable weights, turns out to be inefficient and implies a breach between that unit and the more efficient ones. Thus, DEA can be used in those cases where the different resources and products from the units are valued accurately and also when there is a high degree of uncertainty or disagreement on the values of some resources or products.

The DEA methodology has been extensively used internationally to compare the efficiency of hospitals; thus Hollingsworth¹³ makes a revision of 317 international studies where 75 percent of them use DEA to measure efficiency in health units.

The AP model, named after Andersen and Petersen proposal, is an extension to the original formulation of DEA¹⁴ because it allows discriminating in a more effective way the possible errors of the data.¹⁵ In this model, when the evaluated unit is the same as the compared unit, the weights may take values greater than one, which are then known as super-efficiency levels. The AP model is criticized because the units that emphasize a single resource and a product in the results, also known as “mavericks,” tend to obtain higher efficiency values, as found by O’Neill and Dexter.¹⁶ Thus, O’Neill and Dexter proposed an indicator of robustness based on an adaptation to the model AP,¹⁷ which indicates if the hospital is a maverick.

To apply the DEA model, appropriate software to manage the data and solve the optimization problem is necessary. Of the many alternatives available, General Algebraic Modeling System (GAMS)¹⁸ was used, because it is easy to use and more convenient than other programs.

In applying the DEA analysis to Chilean hospitals, it is necessary to measure their output. For this, and in order to standardize the production of multiple different outputs, a weighted measure has been proposed, which is called Diagnosis-Related Group (DRG). In the literature, the use of DRG as an adjustment of hospital’s production is common,¹⁹ since it has been empirically observed that the relative weights of the DRG are correlated with the real cost of a hospital.²⁰ The creators of this methodology at the University of Yale were Fetter and Thompson.²¹ They managed to generate 465 DRG using the historical data of patients by classifying them into groups with similar patterns in the use of resources and with clinical coherence.²² The groupings were obtained based on the time of hospitalization of the patients and validating those groups by means of their cost. Also, to generate these groups, they produced an indicator that identifies the Potential relative consumption of the resources for a DRG, which is estimated with the expected cost of the DRG based on the average cost of the hospitalized patients.²³ Currently, Chilean hospitals use an international version of the DRG developed by the 3M Company, called International Refined DRG (IR-DRG), that defines 1,077 different types from groups of related diagnoses differentiated by severity levels, discounting the cases with ambulatory medical services.²⁴ The DRGs are being used in the great majority of the hospitals of high complexity.

Now, given that we have the basis to measure hospital production or output using DRG, we define the data to apply the DEA analysis. The variables used to make the DEA analysis of Chilean hospitals is summarized in the Table 4.1 and in Table 4.2, where the descriptive statistics of such variables are given.

Then using the data just presented, the obtained efficiencies, calculated with the DEA method, are shown in Table 4.3 and Figure 4.5.

With these results we now come to the key question: Which variables explain such results and what actions can be taken over such variables to increase efficiency? At the same time quality and fairness issues too are to be considered. In answering the preceding question, 240 variables associated with the hospitals that may affect efficiency were considered; for example:

1. Social-delinquency vulnerability index of the population attended by the hospital, which may decrease efficiency because the health of the population is poor.

2. Percent of child births, because it is a complex medical procedure that may also affect efficiency.

3. Patients without social security—also an adverse factor to efficiency.

4. Percent of programmed patients, which means that medical procedures are planned in advance, as opposed to urgency patients, which favor efficiency.

5. Children hospital.

6. Patients coming from emergency services.

Table 4.1 Variables definition for the DEA model

Variable	Definition
DMUs or decision units	Self-managed hospitals with sufficient data during the period October, 2011 to September, 2012. Altogether, 40 hospitals.
Input	Number of doctors who discharge hospitalized patients from the hospital. Number of registered beds.
Output	Amount of discharged patients adjusted by clinical complexity (DRG), differentiated by: Simple interventions (DRG weight less than 1). Medium complexity interventions. Complex interventions (DRG weight greater than 4).
Type of orientation	orientation to the input, because the hospitals accept demand for health services, which is an exogenous variable; however, the resources are handled by the hospital.
Type of returns	CRS, since, a priori, the level where the (des) economies of scale happen is not known, but explanatory variables related to the size of the hospital are considered.

Table 4.2 Variables’ statistics

	Inputs		Outputs DRG weighted discharges
	Doctors	Beds	Simple	Medium Complexity	Complex
Minimum	65	130	1,388	1,362	5
Maximum	566	870	20,118	14,018	4,742
Average	198	384	8,014	4,848	1,535
Standard deviation	107.49	183.32	3,806.83	3,103.49	1,213.55

Table 4.3 Efficiency results with constant returns to scale

	Efficiency (CRS) calculated with DEA model (CCR25)	Efficiency (CRS) calculated with AP model
Minimum	0,634	0,661
Maximum	1	1,511
Average	0,8212	0,913
Standard Deviation	0,1092	0,191
Hospitals in and over the efficiency frontier	6	7

Figure 4.5 Efficiency results with AP model for hospitals

Further, by using a statistical procedure proposed by O’Neill and Dexter,²⁶ which detects outliers, correlated, and nonsignificant variables, 13 variables were determined as good candidates to explain efficiency and hence possible to be manipulated, if possible, to increase efficiency in a hospital. These variables are shown in Table 4.4.

In selecting hospitals where manipulation of variables in Table 4.4 may provide better results, we come back to the comparative hospital efficiencies to prioritize them for intervention. A simple rule used for intervention is by selecting the hospitals that have an efficiency of less than 0.80, which means that one-third, or 13, of the hospital are prioritized for improvement as shown in Figure 4.5.

To further refine the selection of variables to be considered for intervention, the opinion of health experts was requested, who selected six variables they thought that hospitals could possibly manage to improve efficiency. Then each of these variables was analyzed for its impact on efficiency. For example, in Figure 4.6, the impact on efficiency of the variable “Meeting payment deadlines with suppliers” is shown, where the rhombuses are the values of efficiency for each hospital and the squares are the tendency line of the efficient hospitals; this line represents the value the less efficient hospitals could achieve if properly managed. By constructing the same curves for the six selected variables, it was concluded that only five have possibilities to improve the hospitals efficiency. With this analysis, a Potential for efficiency improvement for each variable and hospital can be calculated with the following expression:

Table 4.4 Main explicative variables

No	Name	Category	Correlation	p-value for significance
1	Social-delinquency vulnerability index	Social factors	–0.40	0.012
2	Percent of programmed patients	Patient management	0.44	0.005
3	Patients coming from a lower level in health network	Network integration	0.35	0.026
4	Meeting payment deadlines with suppliers	Supply and financial management	0.40	0.013
5	Patients coming from an emergency service	Demand behavior	–0.39	0.012
6	Hospital with breast surgery	Hospital structure	–0.36	0.021
7	Hospital with maxilla-facial surgery	Hospital structure	–0.40	0.011
8	Hospital with neurosurgery	Hospital structure	–0.45	0.003
9	Percent of adult patients	Demand behavior	–0.38	0.016
10	Percent of child births	Complex variable	–0.47	0.002
11	Date hospital started with self-management	Complex variable	–0.49	0.002
12	Children hospital	Demand characteristics	0.38	0.015
13	Rotation index	Complex variable	0.34	0.033

Figure 4.6 Relationship between efficiency and the variable “Meeting payment deadlines with suppliers”

Where j is the index of the Potential variable, e_i is the efficiency of the ith hospital, and e′_ij is the value of the efficiency of the tendency line of the hospitals in the efficiency frontier, which the ith hospital could achieve.

The calculation of the Potential for each of the 13 prioritized hospitals for each variable allows constructing Figure 4.7, where it is apparent how by making effective the Potentials for each hospital, its efficiency can be improved from its current value to close to one.

Finally, by selecting the variables with greater improvement impact, projects can be defined to make effective the Potential and improve efficiency, the outcome of which is expected. For example, the variable Programming or “Percent of programmed patients” has a relatively large Potential for low productive hospitals, which implies that if processes incentivizing programming are introduced, efficiency will improve. If, at the same time, formal programming methods are introduced, which these hospitals do not have, the efficiency improvement can be reinforced. We have performed many projects related to programming in several hospitals, some of which will be reported in the next chapters, where we have introduced processes to characterize demand, prioritize, and program it on hospital facilities: ambulatory services, urgency, beads, and operating rooms. In all cases, the result has been a large improvement in use of facilities, thus increasing the efficiency. But, at the same time, better service has been provided by defining explicit medical-based priorities for patient treatment, assuring attention at the right time and reducing waiting times. Therefore, quality and fairness can be improved in parallel with efficiency, as they usually go hand in hand.

Figure 4.7 Efficiency and Potential for each variable and hospital

A more systematic procedure to define projects is to select variables that experts evaluate as more feasible to manipulate to generate increased efficiency. A preliminary list of such variables, discussed with some health authorities and derived from the data in Figure 4.7, is shown in Table 4.5.

Typical projects consistent with the list in Table 4.5 and which have increased efficiency in specific cases are:

Table 4.5 Candidate variables for project definition

No	Categorization	Projects
1	Social factors	- Patient education
2	Patient management	- Train support personnel to schedule patients with medical criteria - Ambulatory patient programming - Bed management
3	Health network integration	- Preventive examinations and treatments - Interconsults and contra reference management - Waiting list management

1. Ambulatory patients’ prioritization managed on a first-come-first-served basis. A case in this same chapter shows this is inefficient and unfair. As a result, there is a huge Potential for efficiency improvement by applying these ideas in hospitals that are low as shown in Figure 4.7.

2. Predictive models for chronic patients to detect critical situations in advance, avoiding crisis and expensive treatments. This has a lot of Potential because chronic diabetes and hypertension patients constitute a significant part of the hospitals’ costs. Besides, this idea was tested for diabetes in a private hospital and proved feasible, as will be shown in Chapter 6. Currently, this idea is being implemented in a children’s hospital for patients with respiratory problems that can be treated at home, as presented in Chapter 3 and will be detailed in Chapter 6, for which predictive models are being developed that, based on line monitoring, will give suggestions to doctors when there is any risk for such patients. The goal is to encourage home treatment for chronic diseases to improve fairness and efficiency.

3. Bed management at the level of the health system, monitoring availability, and assigning patients centrally to the right hospital that has the possibility of attention. This has been used for several years and produced good results.

4. Operating room management, including patients’ prioritization, operation scheduling, and intervention monitoring. We have performed projects of this type in several hospitals that show benefits; we will present a case proving this in Chapter 6.

The approach proposed in this section has as an important by-product the possibility of learning from hospitals that are more effective and efficient, those at the efficiency frontier, and share medical and management solutions that have proved successful for them. This can generate a virtuous circle due to the centralized assignment of innovations resources oriented to improve efficiency, taking into account quality of service, which will move lower-performing hospital to the efficiency frontier. This will generate a powerful learning process that will improve the transference of proven methods to other hospitals in future innovation resource assignments.

Operating Room Capacity and Assignment

We present what we defined as a local case, in “Design Levels for Health Services,” where there is not a Business Design and Configuration Design, since current situation is taken as given. However, the Strategy and Business Model are still relevant to guide the definition of the appropriate capacity and its assignment. Then, the positioning in this case should be best product with an emphasis on operational efficiency, since operating rooms are a very scarce resource, and value to be provided to users is on-time delivery of the surgery, according to maximum waiting time (MWT) associated to the patient illness. The main Capability necessary to accomplish these objectives is being able to design an operating room capacity according to demand, so as to assure meeting of MWT, assigning and using it in the best possible way. So an Intelligent Structure II is needed to provide the required Analytics and the relevant BP is BP6, “Optimun Resource Usage.” This BP maps directly into Macro1 specialized for hospitals as shown in Figure 2.9, where the “Operating Room Service” is defined in the context of hospital’s operation, and its detail design given in Figure 2.11. In this case we concentrate on “Demand Analysis,” which forecast demand for surgery and determines the necessary resources to be able to process such a demand according to the aforementioned objectives, the design of which is given in Figure 4.8. We will design the details of this process to be executed periodically in time to determine adjustments to capacity and its assignment, according to the dynamics of the demand.

Figure 4.8 Design for “Demand Analysis”

“Demand Forecasting and Characterization” in Figure 4.8 is the subprocess that provides a forecast that allows the hospital to allocate OR resources in “OR Capacity Analysis.” In particular, it is determined if current capacity of the hospital is enough to meet the demand or if it is necessary to change it. If more capacity is needed, the possibility of doing so should be studied in the subprocess “Analyze OR capacity increase.” Finally, changes and assignments are implemented in “Implement Capacity Changes.” What we need then is a business logic to perform such subprocesses, which is defined as follows.

There are two ways to perform the assignment of operating rooms to specialties that use them: block assignment, in which fix duration of time on given days are schedules for each specialty, and case scheduling where individual surgical operations are assigned independently. In both cases all capacity would be used up, because there are waiting lists due to lack of enough capacity.

Currently, in the hospital under study, capacity is assigned as shown in Table 4.6, where the different specialties that require OR service are: General Surgery (GS), Urology (Uro), Trauma, Traumatology Cord (TC), and Plastic Surgery (PC).²⁷

This is a typical static block assignment and there is no formal method or criteria to justify it in this hospital, having only a historical justification. So, in particular, there is no way to prove that this assignment contributes to fairness, which is one of the relevant objectives in this case. Therefore, considering the high number of people on the waiting lists for the different specialties, no assurance exists that patients are being operated according to the required MWTs determined by their pathology.

Therefore, what is proposed for this case is a design of OR capacity and its assignment in such a way that patients are operated meeting a required MWT and that different specialties have the same possibilities to operate their patients according to their demands (fairness); also capacity should be used in an efficient way, which relates to one of the other objectives we defined at the beginning of this section.

The process “Demand Forecasting and Characterization” is designed in detail, including the business logic that will be executed, where the services demanded by patients are determined and described according to various attributes, such as of MWT category. This subprocess is modeled with BPMN in Figure 4.9.

Table 4.6 Current OR capacity assignment

	Monday morning	Monday afternoon	Tuesday morning	Tuesday afternoon	Wednesday morning	Wednesday afternoon	Thursday morning	Thursday afternoon	Friday morning
OR 1	GS	Uro	Uro		Uro		Uro		Uro
OR 2	GS	GS	GS	GS	GS	GS	GS	GS	GS
OR 3	Trauma	Trauma	TC	TC	Trauma		Trauma		Trauma
OR 4	PC		PC		PC	PC	PC		PC
OR 5	Trauma		Trauma

In Figure 4.9, historical data is first prepared, where only the useful information to generate forecasts is considered, leaving aside attributes such as name, ID, or the patient’s address. Then the model to be used is selected from a set of alternatives previously developed and its parameters are set to run it and generate a forecast. Finally, the forecast is approved and sent to “OR Capacity Analysis.” The data and models that are used are presented later. Once the prediction and characterization of demand is obtained, the subprocess shown in Figure 4.10 is performed. First the forecast is requested; then the allocation of a percentage of surgical time for each OR is assigned to each specialty to meet the objectives set by the hospital, which is determined through an Integer Linear Programming (ILP) model, which will be explained later. The assignment can be run again with different information and model parameters if the result is not satisfactory in terms of meeting hospital performance objectives. If it is satisfactory, the next question is whether more capacity is needed to reduce the overall excessive waiting time for patients. In the case in which more capacity is necessary, the subprocess “Analyze OR capacity increase” is executed according to the design shown in Figure 4.11. In this subprocess, the main activity is the use of the same ILP model of “OR Capacity Analysis” within a simulation that evaluates possible increases in capacity in “Run model to evaluate Scenario.” Such Scenario defines which forecast will be used, parameters of the ILP model and other parameters, as detailed next.

Next, the details of Analytics that are used in the subprocesses are presented. As in all the cases we have included in this book, this a key component of the design, assuring that the objectives of the process, in this case, fairness for patients and efficiency in the use of resources, are accomplished.

For “Execute Demand Forecast and Characterization Models,” part of the subprocess of Figure 4.9, regression, moving averages, Neural Networks, and Support Vector Regression²⁸ are considered. Given the objectives of the case and also considering the information available, its quality, and finally the volume of demand for the various specialties, the forecast is done on a monthly basis. Historical information regarding the number of patients admitted to waiting lists is available for the different specialties: Plastic Surgery, General Surgery, Traumatology, and Urology.

Figure 4.9 Design of “Demand Forecasting and Characterization”

Figure 4.10 Design of “OR Capacity Analysis”

Figure 4.11 Design of “Analyze OR capacity increase”

Analysis of the information provided by the hospital is presented. This is done through the study of the waiting lists, categorizing each diagnosis presented by the patient according to the four different specialties mentioned earlier. The information is recorded every day, so it is aggregated on a monthly basis and presented graphically, as shown in Figures 4.12 and 4.13 for General Surgery and Urology. Characteristic behavior patterns can be appreciated on a monthly basis as the graphs of 2004 to 2010 show:

Figure 4.12 Admission to General Surgery waiting list

Figure 4.13 Admission to Urology waiting list

1. In all specialties, a decrease in patients admitted to waiting list for the summer months of December to February is observed, showing a considerable drop in the month of February (vacation month in Chile).

2. An increase is observed in all the specialties to waiting lists for the month of March.

3. In general, good quality of data is available without a large amount of outliers, which are eliminated manually to avoid errors in the forecast.

4. Specialties, such as Urology, Traumatology, and General Surgery, are much more stable in contrast to Plastic Surgery, which has more variation.

Forecasting models are developed separately for each specialty, since they independently manage their waiting lists and each of them has characteristic behavior patterns. To develop such models, and based on previous experience with forecasting, several variables are considered as possible determinants of future demand behavior, such as the demand of the previous month or two previous months to the one to be forecasted; the value of the demand for the same month last year or two or three years ago; and the difference between the current and the previous month in the year prior to the month to be forecasted.

Then the different models are estimated with the data, leaving a set of data unused in order to test for models errors. The results for each model in terms of forecasting quality measured by forecasting error mean absolute percentage error (MAPE) of the forecast, as shown in Table 4.7.

Table 4.7 MAPE for the different forecasting models

	Neural Network (percent)	Linear Regression (percent)	Support Vector Regression (percent)	Moving Averages (percent)
General Surgery	38	18	28	23
Plastic Surgery	71	58	46	92
Traumatology	20	11	12	71
Urology	12	22	14	50

The models finally chosen correspond to those having lower MAPE. The high value of this error in Plastic Surgery is explained by the number of patients who enter the waiting list, which is very low; so a little difference in these forecasts can have a big effect on the error.

Given a forecast, we present the business logic (based on Analytics) that allows assigning a percentage of surgical time to each specialty, as required in the subprocess of Figure 4.10, in order to comply with the already stated objectives of the hospital. To perform such assignment, a multicriteria ILP model is used.

First, a set of criteria is defined to assign the OR capacity. They are based on the objectives described at the beginning of this section: fairness in relation to the patient and efficiency in the use of resources for the hospital and, hence, for the public health services. This is detailed in the criteria explained later.

The first criterion relates to the characteristics of the patient, that is, the complexity of the pathology involved, the category of MWT for the surgery that determines the opportunity, and finally the total surgical time. The determination of complexity is done by the DRG—explained in the case “Innovation Resource Assignment in the Public Sector” in this chapter—of the surgical intervention. The opportunity is defined in terms of the characterization of each specialty based on the MWTs for surgery defined for Categories A, B, C, D, and E. These categories are defined in terms of the risk the patient has if he is not operated: A is maximum risk and E is minimum. Of course, MWT allowed before surgery should be low for A and high for E. This time is determined based on medical factors by doctors and also depends on aggravating factors such as age and general health of a patient. The application of this idea in current practice is shown in Figure 4.14, where real waiting times for categories are presented, which show that the idea is present but not fully applied. This work creates conditions for the MWTs of the different categories to be duly followed.

As for the total surgical time for specialty for the patients, statistical analysis shows a great variability, so they must be described by probability distributions. For example, Urology has the surgical time distribution as shown in Figure 4.15. Now what is needed is the distribution for each category: A, B, C, D, and E. On the basis of historical data, such distributions were normal with different parameters for each category.

Figure 4.14 Categorization of patients on waiting list Historical and current in Urology

Figure 4.15 Distribution of surgical time in Urology

Now the different categories have the distributions as shown in Figures 4.16 and 4.17 for Urology. These are approximated to normal with parameters given in Table 4.8.

Figure 4.16 Distribution of surgical time Categories A and B

Figure 4.17 Distribution of surgical time Categories D and E

Table 4.8 Distribution of surgical times by category

Category	Distribution
A	Normal(80.4;46.6)
B	Normal(102.2;39.8)
D	Normal(89;42.8)
E	Normal(91.5;42.5)

The second type of criteria considered is the interests of the hospital and of the health system. On the one hand, the hospital has economic interests because it has a variable income, besides the regular budget, paid by health authorities for specific surgical interventions, including a tariff and a target number, which correspond to central health policies explained in the case “Resource Assignment in the Public Sector” in this chapter. Also the hospital may have some target for the reduction of its surgical waiting lists and the government may also require the reduction or elimination of waiting lists for certain pathologies defined as a priority to treat in the health system.

All the factors in the previous criteria should be considered in the assignment of OR capacity to specialties. This is done by the ILP model with the following variables, parameters, objective function, and constraints.

The model, which is based on Zhang et al.²⁹ aims to ensure the service for patients in the waiting lists, either through compliance with the MWT for the category of his pathology or, if not possible, minimizing the tardiness in operating the patient after MWT has expired. Hence, the first term of the objective function to be minimized models the cost of not satisfying MWT demand as:

where

u_jkm: unfulfilled demand for patients from specialty j, category m that have their MWT expired the day k

θ_Vjm: economic cost of not satisfying the demand of patients having its MWT expired in specialty j and category m

The second term of the objective function that model the cost of not satisfying demand for patients who have not yet got to MWT has a similar form:

where:

v_jkm: unfulfilled demand for patients from specialty j, category m who do not have their MWT expired at day k

θ_NVjm: economic cost of not meeting the demand of patients of specialty j, category m who do not have their MWT expired

The three other terms of the objective function include the cost associated with the postponement of a surgical intervention of patients with MWT expired and not expired and a cost associated with not meeting a desired level of capacity assignment to a given specialty. The cost parameters of this objective function depends on fairness and the economics interests of the hospital, since the costs considered may have a component associated with the patients’ well-being and another with the economic losses a hospital incurs because of the postponement of certain surgical interventions, that is, the ones to which government has given priority.

Besides the variables and parameters in the objective function, other parameters include: number of OR of a given type, number and amount of available OR hours per day per type, demand of patients who have their MWT expired for specialty j, category m in day k measured in hours of OR and demand of patients who do not have their MWT expired for specialty j category m in day k, measured in hours of OR. The main variable is

x_ijk: number of OR of type i assigned to specialty j on day k

where x_ijk must be a nonnegative integer.

Then the constraints model relationships such as:

1. An OR can be assigned to just one specialty on any given day;

2. Relationship among OR assignment, postponed demand for patients with overdue MWT, and for patients not overdue and OR time available per day for each specialty and day; this constraint defines the values of u_jkm and v_jkm, among other variables;

3. Maximum time over MWT that a surgery can have; and

4. A specialty should not be assigned to more than a given number of ORs on a given day.

To have a benchmark to compare the ILP, Table 4.9 shows both the assignment and the average occupancy of the OR. From this, it can be concluded that the final percentages of assignment and use for each specialty are practically the same; this implies that the hospital follows the criteria of maintaining such percentages, since they are considered to be at an adequate level.

Now, the ILP assignment model is applied to the same conditions for which results in Table 4.9 have been obtained for different number of days. The resulting assignment is shown in Figure 4.18.

The figure indicates that the assignment of the model is not too different from what there is today. Therefore, the most important question is the one posed in the activity “Run model to evaluate Scenario” in the subprocess of Figure 4.11, that is, how the behavior of waiting time for patients is affected by an optimal assignment and how more capacity should be assigned to best improve the meeting of MWT and the reduction of waiting time in general? The logic behind the answer to such question is a simulation model, which has as a component the optimal assignment model just presented.

Table 4.9 Average assignment and occupation of OR

	Average percentage of OR assignment (percent)	Average percentage of OR occupation (percent)
General Surgery	31	29
Plastic Surgery	30	30
Urology	19	20
Traumatology	19	20

Figure 4.18 Percentage capacity assignment to each specialty

In the simulation model, which is presented in Figure 4.19, the following modules are considered:

1. Admission of patients to the waiting list; in this case, it is necessary to consider two factors: patients who are currently on waiting lists, which are assigned to each specialty, category, and surgical time; and a forecasting of patients who will enter waiting lists, which will be determined with the forecasting models described at the beginning of this case, also assigning to them a specialty, category, and surgical time.

2. Assignment of priority; in this step, each patient is assigned a priority according to the following factors: category (MWT), MWT expired, and MWT not expired.

3. Assignment of patients to OR; here the patients in the prioritized waiting list for each specialty are assigned to an OR according to the ILP presented earlier.

4. Surgical intervention in the OR; this is characterized by a time that follows a probability distribution, statistically determined for each surgical step.

Figure 4.19 Simulation model for OR capacity evaluation

In the simulation model, ILE TRAU - CP - CG - URO simulates the admission of patients to the waiting list. It uses the forecasting model by specialty and is carried out on a monthly basis; LE represents the current waiting list that the hospital keeps; in the priority assignment and formation of waiting lists, the logic of prioritization of patients according to their category and time on waiting list is used, which is done weekly; LE URO - CP - CG - TRAU represents the weekly ranked waiting list, which means that patients are selected to be treated surgically on OR according to such lists; for comparison, statistics of patients remaining in waiting lists are collected, including those who were not present during the simulation.

The simulation model was built using ProModel³⁰ and several runs of such a model allowed evaluating various scenarios. The main variable manipulated in the model was OR capacity. For example, in Figure 4.20, the average opportunity for patient care is represented according to the current assignment of OR in the hospital. This opportunity is defined as the average percentage of the MWT a patient waits before surgery. The x-axis of the figure shows the capacity represented by the number of OR morning and afternoon shifts the hospital will have during a week. This capacity goes from 6 shifts (according to the minimum allocation of pavilions that can be performed) and a maximum of 50, limited by the number of ORs the hospital has. The ordinate axis shows the average opportunity of attention in percentage as compared to MWT for a category; for example, it can be observed that for a capacity of 18 OR shifts, there is an average opportunity of 250 percent approximately; this implies that the hospital takes 2.5 times more than the maximum time allowed according to the category of prioritization, that is, for a patient of Category A, who has a MWT of 15 days, the hospital takes on average 52 days in taking care of him. Finally, different simulation horizons ranging from 6 months to 10 years are shown.

Figure 4.20 Average patient care opportunity

Next a validation of the simulation of the current situation of the hospital is presented. Currently, the hospital has an OR capacity of 16 to 19 shifts, which implies, according to the simulation model, an average opportunity of patients between 400 and 250 percent approximately. These values are in agreement with the average delay beyond MWT patients have today. While it is observed that from a number of shifts equal to 32, the hospital would be meeting the attention opportunity defined according to the category of prioritization for each patient based on his diagnosis and aggravating factors.

However, the concept of average opportunity attention has the problems of considering on an equal footing the different categories of MWTs; this is not right, since it has been determined that it is more damaging that seriously ill patients requiring immediate attention are served late than those who are not so ill. Therefore, a new indicator that considers the opportunity of caring for patients in a weighted manner, giving more weight to the more risky categories from A to E, is built. Considering this, it can be seen in Figure 4.21 the weighted opportunity as a function of OR capacity. This chart presents the effect that produces the weighting of categories of MWTs. Thus, for a smaller quantity of OR the weighted opportunity is higher than the average opportunity in Figure 4.20; for a greater capacity, the weighted opportunity decreases. The weighted opportunity in this sense is a better indicator, since lower capacity accounts for the fact that only patients of more risky categories (e.g., A and B) are attended to, who have lower MWTs and hence have a higher probability of being overdue. The figure confirms that for more than 32 shifts the opportunity of attention is close to the MWT, and this is the recommended capacity.

Figure 4.21 Weighted patient care opportunity

Another analysis that can be carried out is to see how it changes the weighted opportunity for patients’ attention, given a fixed capacity of OR, for different time periods of evaluation horizons. This situation is shown in Figure 4.22.

Figure 4.22 presents the weighted chance to care for patients for a capacity of between 16 and 28 of OR shifts. Here it can be seen how, for the two-year simulation horizon, the opportunity for each defined capacity is lower than for other evaluation horizons. This behavior will be named as the “Prioritization effect” and represents how, in this evaluation horizon, patients are attended in an orderly manner according to the waiting list prioritization. Then, when the point is reached where all these patients who initially were on waiting list (where the opportunity is minimum) are attended to and, given that the capacity offered is less than the demand even during the period when the patients were still being updated in the waiting list, it can be seen that they begin to accumulate and therefore the weighted opportunity increases.

Figure 4.22 Weighted opportunity of attention for capacity of 16 to 28 OR shifts

Figure 4.23 Weighted opportunity for current allocation compared with proposed allocation

Finally, the difference between the current assignment and assignment proposed by the model is evaluated. This analysis has been made considering a simulation period of five years, because, as shown earlier, a two-year period is necessary for the waiting list to be ordered according to priorities. The behavior of the weighted opportunity for the current and proposed assignments is presented in Figure 4.23.

Figure 4.24 Number of patients operated for a capacity of 23 days of ORs

Since assignments are very similar, it is expected that the opportunity of a patient is maintained in the same value. This can be checked visually by looking at the graph and observing an average improvement of about 2 percent in weighted opportunity patient care. While this value is small, the proposed assignment has not only managed to reduce the average opportunity to care for patients, but also allowed to increase the number of operated patients by 10 percent, which mainly belong to the D and E prioritization categories, as it can be seen in Figure 4.24 for the case in which the OR capacity is 23 shifts.

As already commented in previous cases, this type of design clearly includes organizational design, since by periodically executing the processes presented, with the analytical support, the structure of the OR service, including the determination of the human resources needed, can be dynamically adapted to new conditions, assuring defined levels of service and good use of resources. Moreover, in executing the processes, the roles in the lanes of the BPMN diagrams have been assigned specific tasks in the execution of the process, which also defines organization. Furthermore, IT support is also specified precisely for data processing and, more importantly, as a container for embedded logic that allows optimizing resource assignment, which defines integration with current systems and analytical tools for forecasting and simulation.