Operations Research Models Applied for Allocation of Public Resources Under the Efficiency-Effectiveness-Equity (3E) Perspective

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Operations Research Models Applied for Allocation of Public Resources under the Efficiency-Effectiveness-Equity (3E) Perspective

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Melissa Pizarro Aguilar

Graduate Program in Industrial and Systems Engineering

The Ohio State University

2012

Master's Examination Committee:

Ramteen Sioshansi, Advisor

Jerald Brevick

Melissa Pizarro Aguilar

2012

Abstract

The main difference among operation research models for the private sector and the public sector is the inclusion of the equity criteria. In this sense, one of the objectives of this project was identifying proposed models to solve allocation problems in the public sector, under the efficiency, effectiveness and equity (3E) principles as the providers of public services need to guarantee non-discriminatory access to the services to all of the population, and at the same time make the best use of the limited resources. We identified various models that include the equity perspective, but we focused on the data envelopment analysis (DEA) resources allocation model developed by Goaz Golany and

Eran Tamir, as it integrates the 3E. This integration is important as the tradeoffs among certain decisions at each dimension could affect the performance in other dimension.

The second objective of this thesis is validating a systematic budget allocation methodology for the primary health care sector in Costa Rica. The institution evaluated is the area of health Jiménez Núñez (Goicoechea 2) which is composed of 10 Basic Teams for Comprehensive Care in Health (EBAIS). The EBAIS were selected as the decision making units for the validation. We applied the model under study progressively, as the first evaluation done was the DEA to obtain the efficiency scores per EBAIS: four

EBAIS out of ten were found efficient. Then, to demonstrate how the DEA allocation model improves the efficiency of the DMUs under study, we applied the model for the

ii multi-input and multi-output scenario. As a result of the proposed allocation, now eight

EBAIS were found efficient. Finally, we include the equity perspective into the analysis.

The DEA proved to be a useful management tool as it performs the efficiency assessment from a comparison between DMUs through data and among data by generating the efficiency frontier. To run this operations research model, various analytical choices must be made. When these choices depend heavily on the analysts, the appropriateness of the model depends on the consistency between the analytical choices and the judgment of experienced decision makers. There may exist generally accepted standards in the efficiency and equity literature, but the mathematical model developed will always have to address different factors depending on the object of study.

The DEA model has been widely used in health institutions and many other public sector organizations in the world, but this is the first application at the primary health system at

Costa Rica and additionally it is including the equity perspective, as most of the literature shows DEA case studies for efficiency assessment only. We can also think of standardizing and systematizing the decision making at the health areas by disseminating the use of the DEA-RAM with equity model and then applying the extensions along the model to be broadened to incorporate resource allocation at the national level as it would be valuable to develop this analysis for the 103 health areas at Costa Rica as DMUs.

iii

Dedication

This thesis is dedicated to my parents, my inspiration.

Acknowledgments

I would like to express my deepest gratitude to my advisor, Dr. Ramteen Sioshansi for his interest, guidance and support through the development of this project. I thank also the director of the area of health Jiménez Nuñez, Dr. Pedro González and the chief of the

EBAIS at this area of health, Esteban Avendaño for their interest in this thesis. Special thanks to Dr. Brevick, member the supervisory committee.

Vita

2001...... Methodist High School, Costa Rica

2007...... B.S. Industrial Engineering, University of

Costa Rica

2008 to 2011 ...... Faculty, Department of Industrial

Engineering, University of Costa Rica

2011...... Fulbright Faculty Development Program

Grant Award

Fields of Study

Major Field: Industrial and Systems Engineering

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... vi

List of Tables ...... ix

List of Figures ...... xii

Chapter 1: Introduction ...... 1

Chapter 2: Literature Review ...... 4

The 3E Perspective in the Public Sector ...... 5

Operation Research Models for the Allocation of Public Resources ...... 6

The Data Envelopment Analysis (DEA) ...... 13

Equity Assessment in Health Care ...... 20

Chapter 3: The Allocation Model ...... 24

Chapter 4: Case Study ...... 30

The National Health System of Costa Rica ...... 30

Health Area Jiménez Núñez (Goicochea 2) ...... 33

vii

DEA-RAM Equity Model for the Multi Output Scenario ...... 36

Chapter 5: Conclusions and Future Work ...... 50

References ...... 52

Appendix A: Input Data ...... 55

Appendix B: DEA Weight Results ...... 59

Appendix C: DEA RAM Results ...... 60

Appendix D: Calculating the Gini Measure ...... 63

Appendix E: DEA RAM with Equity Results ...... 66

viii

List of Tables

Table 1.Number of users at each EBAIS ...... 34

Table 2. Inputs for each EBAIS, year 2011, area of health Goicoechea 2 ...... 38

Table 3. Outputs for each EBAIS, year 2011, area of health Goicoechea 2 ...... 39

Table 4. Districts served at area of health Goicoechea 2 ...... 40

Table 5. District assignment per EBAIS at area of health Goicoechea 2 ...... 41

Table 6. Summary of the NBI incidences per district and grouping...... 43

Table 7. Efficiency scores for the EBAIS obtained by the DEA methodology...... 44

Table 8. Comparison of the results of the DEA-RAM model between the previous period’s budget and the current budget to allocate for the next period ...... 45

Table 9. Equity constraints for each EBAIS, year 2011, area of health Goicoechea 2 .... 46

Table 10. Gini measure per equity unit ...... 47

Table 11. Optimal solutions per scenario, DEA-RAM with equity ...... 48

Table 12. Annual costs in colones for each of the EBAIS at area of health Jimenez

Nunez, 2011 ...... 55

Table 13. Annual costs in colones for each of the EBAIS in area of health Jimenez

Nunez, 2011 ...... 56

Table 14. Annual costs in dollars for each of the EBAIS at area of health Jimenez Nunez,

2011...... 57

Table 15. Total time in hours per month programmed and used for medical appointments at area of health Jimenez Nunez, 2011 ...... 58

Table 16. Total time in hours per year programmed and used for medical appointments at area of health Jimenez Nunez, 2011 ...... 58

Table 17. DEA weights for the inefficient EBAIS at Goicoechea 2 ...... 59

Table 18. DEA-RAM weights for the inefficient EBAIS at Goicoechea 2, with previous period’s budget...... 60

Table 19. DEA-RAM weights for the inefficient EBAIS at Goicoechea 2, with budget to allocate ...... 61

Table 20. DEA-RAM input allocation for the EBAIS at Goicoechea 2 ...... 61

Table 21. DEA-RAM output allocation for the EBAIS at Goicoechea 2 ...... 62

Table 22. Gini measure for the budget allocation in the year 2011, using the users with hypertension as the equity unit...... 64

Table 23. Gini measure for the budget allocation in the year 2011, using the users with diabetes as the equity unit...... 64

Table 24. Gini measure for the budget allocation in the year 2011, using the users over 65 years with diabetes as the equity unit...... 65

Table 25. Input and output allocation, E1, with previous period’s budget ...... 67

Table 26. Input and output allocation, E1, with current budget to allocate ...... 67

Table 27. Input and output allocation, E2, with last period’s budget ...... 68

Table 28.Input and output allocation, E2, with current budget to allocate ...... 68

Table 29. Input and output allocation, E3, with previous period’s budget ...... 69

Table 30. Input and output allocation, E3, with current budget to allocate ...... 70

Table 31. Weights, E1, with previous period’s budget ...... 71

Table 32. Weights, E1, with current budget to allocate...... 71

Table 33. Weights, E2, with previous period’s budget ...... 72

Table 34. Weights, E2, with current budget to allocate ...... 72

Table 35. Weights, E3, with previous period’s budget ...... 73

Table 36.Weights, E3, with current budget to allocate ...... 73

List of Figures

Figure 1. Illustration of a Lorentz curve (Mandell, 1991) ...... 11

Figure 2. Example to illustrate the concept of a reference set...... 19

xii

Chapter 1: Introduction

Today, there is not much available literature on the equity, efficiency and effectiveness tradeoffs and their application in the public sector, from the operations research perspective. This is an important need as the managers of public services require reliable tools that can provide a clear idea of what would happen if they make certain choices while allocating public services and/or resources. The decision makers in the public sector may be under a great pressure when managing, most of the time, very limited resources, as the stakeholders in this case are all the tax payers and even further, the society. In an effort to find which models have been used to allocate resources in the public sector, the existing literature was surveyed. From this first inquiry, the conclusion is that the difference among resource allocation models between the private and the public sector is the incorporation of the equity perspective in the latter. Also as a result of the research done, we centered our attention in three specific works that use three interesting types of models. The first, a linear integer goal programming model formulated to support a state-level resource allocation process with geographic equity, developed by Tingley and Liebman. The second is Marvin Mandell’s model, which examines the tradeoff between effectiveness and equality using the Gini measure of inequality, under the structure of an absolute goal program. Finally, Golany and Tamir propose a model based on data envelopment analysis (DEA) which is formulated as a linear program. The appealing characteristic about these three models is that one author 1 builds from what the previous author has done, improving the model by eliminating its deficiencies.

Golany’s mathematical program with equity was found to be the most appropriate model for the allocation of resources in the public sector, as it considers the three perspectives, efficiency, effectiveness and equity, and can be used in a multi-input, multi-output scenario. In our thesis we explain in detail the DEA-based resource allocation model

(DEA-RAM), and then we clarify how it should be modified to include the equity constraints (based on those proposed by Mandell), to finish with the description of the case when various outputs are analyzed. We also validated this model by using it in a case study at the primary health care services of Costa Rica. The reason for our interest in the health sector is better explained by Jacobs et al. (2006): “The international explosion of interest in measuring the inputs, activities and outcomes of health systems can be attributed to heightened concerns with the costs of health care, increased demands for public accountability and improved capabilities for measuring performance”.

The institution chosen to validate the model is the area of health Jiménez Núñez

(Goicoechea 2). Health areas were defined to provide comprehensive health services to the population located in a defined territorial space, and they are responsible for the primary care level. The primary care at Costa Rica includes basic health services that perform actions of health promotion, disease prevention, and curing and rehabilitation of lower complexity diseases. These actions are carried out by the members of the support teams and the Basic Teams for Comprehensive Care in Health (EBAIS). The area of health Jiménez Núñez is composed of 10 EBAIS. For the application of the DEA-RAM

2 equity model at the health area Goicoechea 2 we choose the main components of the model by using references in the literature but also considering the most experienced criterion of the decision makers at the area of health. The EBAIS where chosen as the decision making units of the model as they capture the entire production process of interest. We applied the model under study progressively, as the first evaluation done was the data envelopment analysis (DEA) to obtain the efficiency scores per EBAIS. Then, to demonstrate how the DEA allocation model improves the efficiency of the DMUs under study by calculating the appropriate amounts of inputs to be used and the outputs obtained from this assignment, we applied the model for the multi-input and multi-output scenario. Finally, we include the equity perspective into the analysis.

This thesis is organized into five chapters. Chapter 2 includes the literature review done to develop the thesis. This will help the reader to understand the concepts of efficiency, effectiveness, and equity, which are the focus of the models that will be reviewed. A summarized explanation of how the models of Kim Tingley and Judith Liebman, Marvin

Mandell, and Boaz Golany and Eran Tamir operate is also included, and finally to complete the section a small survey on how the concepts of efficiency and equity are assessed in health care is presented. Chapter 3 explains in depth the methodology to be followed for the application of the Efficiency-Effectiveness-Equity (3E) allocation model. Chapter 4 includes the case study of primary health care in Costa Rica as an application and its results, Chapter 5 concludes the paper.

Chapter 2: Literature Review

One of the objectives of this thesis is to adapt operations research methodologies for the public sector. Through a bibliographical review, we came across various applications related to the allocation of resources in the public sector, and specifically those who seek to link the concepts of efficiency, effectiveness and equity in their execution. The first section of this chapter will explain the very basic concepts that must be understood as they are going to be used throughout this document. These are the concepts of public service, efficiency, effectiveness and equity. On the second section, we are going to describe the three operations research models chosen to illustrate the allocation of resources in the public sector under the 3E (efficiency, effectiveness, and equity) perspective. As the main component of one of these models is data development analysis

(DEA), we focus more on explaining its use in the third section of this chapter. In the fourth section, we describe how the concept of equity has been assessed by different authors, as the most important difference among the allocation models for the private sector and the public sector is the inclusion of the equity criteria. In this last section, the reader will notice that the focus is on the application of equity of health care allocation.

This is because, as we explained in the introduction, the case study developed in this thesis is in the health sector.

The 3E Perspective in the Public Sector

A public service refers to any of the common, everyday services provided by federal, state, and local governments (Savas, 1978). Examples of these services include health care, education, water supply, wastewater collection and treatment, among others. The majority of public services are used by citizens simultaneously and users cannot be excluded. Another important aspect that the provider of these services needs to consider is how to guarantee non-discriminatory access to the services to all of the population.

Therefore, market mechanisms that are adequate to provide private goods and services are inadequate for supplying public goods and services (Savas, 1978).

Continuing with the characterization of public services, they are either provided at facilities that are geographically distributed or delivered throughout an area by resources allocated to that area. Consequently, the performance of public services is determined to a large extent by the spatial distribution of resources that provide the service (Savas,

1978) and the allocation of public resources should be guided by the maximization of social welfare (Athanassopoulos, 1998). To assess this performance three measures are identified as the key indices for public services: efficiency, effectiveness, and equity (the

3E). Efficiency and effectiveness, as they have being used widely in the private sector, are insufficient performance measures for public services. For these kinds of services equity is of identical importance, and the three measures interact.

It is important to have a clear notion of the measures mentioned, as stated by Savas and

Golany. Efficiency measures the ratio of service outputs to service inputs; it seeks to achieve “more for less” (Golany & Tamir, 1995). Unfortunately in the public sector, in

5 the majority of cases inputs are easier to define and measure than outputs. On the other hand, effectiveness measures how well the need for the service is satisfied. In simple words, effectiveness measures the difference between observed outputs and the desired goals (Golany et al., 1995). It is a measure of the adequacy of service relative to need, and incorporates the notion of service quality. Once again, although it is difficult to measure effectiveness in public services it is not impossible. Also, a service can be efficient but ineffective and vice versa. Finally, equity refers to the fairness, impartiality, or equality of service. It measures the degree of fairness in the allocation of resources or the distribution of outputs among the units that are evaluated. A service can be efficient and effective but it could be perceived as inequitable if it fails to reach or treat all segments of the population similarly. Considering this, we can notice that there exist tradeoffs among the equity, effectiveness, and efficiency of a service.

According to Savas, different equitable formulae can be used for the allocation of public services. They are based on four broad principles: equal payments, equal outputs, equal inputs, and equal satisfaction of demand. Each of the corresponding formulae are clearly equitable in a certain aspect, but inequitable in terms of other competing principles or even specific aspects. Considering this phenomenon, it is said that equity is a matter of values and each analyst or decision maker will have different approaches to the same problem.

Operation Research Models for the Allocation of Public Resources

In the search for operation research models applied in the public sector, we came across three allocation models. The interesting thing about these three models is that they are

6 related, in the sense that one author took the model of the previous one and improved it.

The first one is a linear integer goal programming model formulated to support a state- level resource allocation process with geographic equity, developed by Tingley and

Liebman. The second is Marvin Mandell’s model which examines the tradeoff between effectiveness and equality using the Gini measure of inequality, under the structure of an absolute goal program. Finally, a model based on Data envelopment analysis(DEA) proposed by Golany and Tamir, which is formulated as a linear program.

The first allocation model for public services we considered was developed in 1984 by

Kim Tingley and Judith Liebman. They develop a linear integer goal programming model to support a state-level resource allocation process with geographic equity in the United

States Department of Agriculture Special Supplement Food Program for Women, Infants, and Children (WIC). WIC was authorized in 1972 in the United States with the goal of reducing infant mortality and promoting proper physical and mental development of children through better nutrition (Tingley & Liebman, 1984). Three problems were identified by Tingley and Liebman and solved through the mentioned mathematical program: the lack of a systematic approach to allocating funds to local agencies, the exclusion of total numbers of potentially eligible participants in the decision process, and the need to consider the priority subgroups (the federal regulations specify six subgroups within the target population of women, infants and children, that are ranked in order of priority for WIC services) when allocating funds.

A special characteristic of their approach was incorporating the subjective attitudes of state-level WIC administrators, the experts, who have a strong familiarity with the WIC

7 program in their states. This was achieved by allowing the administrators, as the future users of the model, to choose the relative importance of each goal as weights at the objective function. This peculiarity is important as then the model can change as the goals change in time. This also allows evaluating different weights for each goal and considering how the final allocation varies. The model proposed is useful in all public sector programs characterized by multiple objectives and hierarchical decision making

(Tingley et al.,1984). The authors defined extensions along the model to be broadened to incorporate resource allocation at the federal-aggregate level, and to be used in the case of allocating budget cuts.

The model created by Tingley and Liebman was developed to allocate funds for expanding local WIC agencies and starting up new local agencies through an integer goal programming formulation. Through this model the service level of each priority group across the state is seen as a separate goal, with specified target value and individually assigned weights that serve as penalties for deviating from that target (Tingley et al.,1984). To do so, the model requires several inputs such as the estimation of target values (desired number of additional participants to be served in each priority group across the entire state) for each priority group, the weights to be assigned to each priority group, and the estimation of the cost of serving the proposed number of additional participants in each priority group at each local agency (Tingley et al.,1984).

The allocation process is modeled as a series of decisions to fund or not fund each priority group (binary variables) at each existing WIC agency and to fund or not fund each proposed new WIC agency (Tingley et al., 1984). These decisions are subject to a

8 limitation on the state budget for expanding the WIC coverage. The equity dimension is considered as geographic equity is incorporated into the model by dividing the state into regions and setting lower bounds on the number of agencies receiving additional funds within each region. This will prevent a disproportionate amount of funds from flowing into a large city at the expense of neglecting smaller cities and rural areas or vice versa

(Tingley et al.,1984).

Seven years later, in 1991, Mandell developed a model that can be employed to examine the tradeoff between effectiveness and equality, the latter defined in terms of the Gini measure, which we will describe later. For Mandell, public sector’s management science models have frequently ignored equity considerations entirely, and the most significant flaw found in those approaches that try to incorporate equity into the mentioned models is the violation of the principle of transfers. The principle of transfers requires that a transfer of service units from a subgroup to any relatively worse-off subgroup result in an improvement in the measure (Mandell, 1991). Mandell summarizes in three categories the commonly used approaches to incorporate equity which violate the principle of transfers. The first category is specifying equity in terms of the minimum and/or maximum levels of service that can be provided to any population group. This is where the author mentions the model proposed by Tingley and Liebman as an example of this flaw. In this sense, the geographical equity defined in the model for the WIC violates the principle of transfers. The second category is defining equity as the range between the maximum and minimum levels of service, and the third is calculating equity in terms of the sum of absolute deviations from the mean level of service. In conclusion, although

Tingley’s model has special characteristics as incorporating the expertise of the users, defining priority groups and the possibility of aggregation to be applied at other decision levels, the approach to incorporate equity is not the best and we should look to incorporate this dimension with an approach that fulfills the principle of transfers.

Mandell then proposes two related bicriteria mathematical programming models to identify the tradeoffs between effectiveness and equity that result from alternative allocations of service resources among different service delivery sites. Mandell uses an objective function for each the overall output and equity, and expresses equity in terms of the Gini coefficient. The Gini measure can address inequality in inputs as well as inequality in the outputs, as a result of resource allocation. For understanding the Gini coefficient, using a Lorenz curve (see Figure 1) is the clearest approach. A given point on a Lorenz curve, (x, y), indicates the cumulative proportion of service received by the most disfavored percentage of the population (in terms of the service). The diagonal line connecting the points (0, 0) and (1, 1) represents the Lorenz curve that would be obtained if services were distributed perfectly equitably, this means each group with the same level of services received per equity unit (Mandell, 1991). The Gini coefficient is defined as the ratio of the area between the Lorenz curve and the diagonal line (the shaded area in

Figure 1) to the total area below the diagonal line (Mandell, 1991).

Figure 1. Illustration of a Lorentz curve (Mandell, 1991)

Mandell uses an absolute goal programming structure to solve the model. The target function of inequality is transformed into a constraint that ensures that its level does not exceed an arbitrary small parameter. The largest value this parameter can have is calculated by solving the problem without the equity constraints. Running the model with different parameter values creates a set of possible optimal combinations of output and 11 inequality levels that constitute a curve or frontier from which a suitable combination is to be selected by the decision makers (Mandel, 1991).

In 1995, Golany and Tamir developed a resource allocation model based on data envelopment analysis(DEA) to evaluate the relative efficiency of decision making units

(DMUs) in the public sector. The model extends the original DEA methodology from measuring efficiency to include the evaluation of effectiveness and equality measures as well. Golany and Tamir include the Gini coefficient as an important part of their model to incorporate the equity measure, but they identify some drawbacks that needed to be corrected from Mandell’s proposal. We summarize these downsides in three aspects, as stated by the authors. First, Mandell’s model basically ignores the efficiency criterion by assuming all units are operating at full efficiency. Second, he defines as an important input of the model a certain production function to describe the behavior of the units studied; all units are then assumed to be IID (independent and identically distributed).

Finally, Mandell's model is limited to single output scenarios. DEA can include multiple inputs as well as multiple outputs. The model will choose a set of weights that achieves the highest efficiency rating for each DMU, while assuring that these weights do not cause any other DMU to have an efficiency rating higher than 1 (Golany et al., 1995).

This model will be described extensively in Chapter 3, as we chose to apply this model to the case study. The DEA approach will be explained in the next section.

The Data Envelopment Analysis (DEA)

According to Jacobs, Smith & Street, there exist two analytic efficiency measurement techniques: the stochastic frontier analysis (SFA) and the Data envelopment analysis

(DEA). As the author describes, the SFA is parametric method, similar to the conventional regression analysis, but decomposes the unexplained error in the estimated function into inefficiency and a two-sided random error. The SFA defines the efficient behavior by specifying a stochastic (or probabilistic) model of output and maximizing the probability of the observed outputs given the model. The DEA analysis on the other hand, is a non-parametric method that uses linear programming methods to infer a piecewise linear production possibility frontier, seeking those efficient observations that dominate (or envelop) the others. DEA is a data-driven approach as the location and shape of the mentioned efficiency frontier is determined by the data, using the simple notion that an organization that employs less output than another to produce the same amount of output can be considered more efficient (Jacobs et al., 2006).

Emmanuel Thanassoulis prefers to classify the modeling methods of comparative performance measurement in two categories: parametric and non parametric. Among the parametric he describes two approaches: modeling with no allowance for any inefficiency in production using a regression method and modeling with the allowance for inefficiency using the stochastic frontier methods. The stochastic frontier methods estimate average rather than efficient levels of input for given outputs, and they attribute all differences between estimated and observed levels of input to inefficiency. From the non parametric perspective, the main method is DEA, where there is no need to

13 hypothesize a functional form linking input to outputs; instead a production possibility set from the observed input-output correspondences is used.

To support the validity of DEA approaches for the case study elaborated in the present thesis, we found two major surveys on the topic of efficiency assessment in health care that have been developed. Jacobs et al. mention a literature survey by Hollingsworth

(2003). In this survey, Hollingsworth identified 189 relevant studies in terms of efficiency assessment in health and health care. Of these, about 50% are in the hospital sector, reflecting its central policy importance and the ready availability of data (Jacobs et al., 2006). Other efficiency studies were applied in physicians, pharmacies, primary care organizations, nursing homes and purchasers. Hollingsworth finds that DEA is the dominant approach to efficiency measurement in health care and in many other sectors of the economy. Also, a study of the United States prepared by the Southern California

Evidence-based Practice Center by McGlynn in 2008 examined 158 articles describing measures of health care efficiency in the United States. Of these 158 articles surveyed, 93 articles (59%) measured the efficiency of hospitals, followed by studies of physician efficiency as the second most common (21%). In this more recent review, the two most frequent approaches used to measure health care efficiency were DEA and SFA. The great majority of studies have used DEA and its variants, which demonstrates the credibility of the method.

Data envelopment analysis, in its most fundamental form, is a method to assess the comparative efficiency of homogeneous operating units. The basic DEA model defines efficiency as the ratio of a weighted sum of outputs and a weighted sum of inputs.

Efficiency analysis is centrally concerned with measuring the competence with which a set of inputs are converted into a set of valued outputs (Jacobs et al., 2006). To measure performance of a unit, we need to estimate the input and output levels at which a unit could be operated if efficient. Mathematically, and using the nomenclature presented by

Jacobs et al., if an organization 0 consumes a vector of M inputs and produces a vector of S outputs , it’s overall efficiency ( ) is measured by applying weight vectors U and V (weights U and V indicate the relative importance of an additional unit of input or output) to yield

∑ (1)

∑

Where is the amount of the sth output produced by organization 0, is the weight

th given to the sth output, is the amount of the m output consumed by organization 0

th and is the weight given to the m input (Jacobs et al., 2006).

To construct a DEA model, the components need to be well defined. First, the appropriate unit of analysis must be chosen. According to Jacobs et al., three criteria must be evaluated to make this choice: the unit of analysis should capture the entire production process of interest, they should be decision making units (DMU) the function of which is to convert inputs into outputs, and finally, the units comprising the analytical sample should be comparable (for example, they produce the same set of outputs). Second the outputs and inputs must be identified, and this depends entirely on the DMU under analysis. For example, in the health care area, they are categorized diversely depending on the author. Jacobs et al. uses health outcomes (additional health conferred to the

15 patient and patient satisfaction) and health care activities (for example patients treated) as groupings for the outputs, and for the inputs, labor inputs (hours of labor or costs of labor) and capital inputs (investment). Third, the analyst should evaluate if there exist significant environmental constraints that are faced by any of the DMUs studied. An example of an environmental constraint is the case of mortality rates that are heavily dependent on the demographic structure of the population under consideration (Jacobs et al.,2006). If they are found, Jacobs et al. proposes three ways in which environmental factors can be taken into account in the efficiency analysis. The evaluator may restrict comparison only to organizations within a similarly constrained environment (by clustering, comparing DMUs with similar exogenous influences). Another way is modeling the constraints explicitly, treating them as inputs, and finally the analyst can adjust the organizational outputs for differences in circumstances before they are deployed in an efficiency model.

Having defined the components, the DEA formulation can be applied1. Suppose there exist n DMUs to be analyzed, each of which uses m inputs to produce s outputs. Let

be the amount of input i used by DMU j, and the amount of output r produced by DMU j. The decision variables for the problem are the weights that correspond to each of the outputs and inputs, in order to maximize the efficiency of the specific DMU k. The variable is a positive weight placed on input i by DMU k and

is a positive weight attached to output r, by DMU k. A constraint is included so that

1 For this description we are using the nomenclature proposed by Thomas R. Sexton, included in the publication edited by Richard Silkman, Measuring Efficiency: An Assessment of Data Envelopment Approach, 1986. 16

DMU k chooses weights so that no other DMU would have efficiency greater than one if it used the same set of weights. Also, the selected weights cannot be negative. The DEA computes the technical efficiency by solving for each DMU k the following mathematical program:

∑ ( ) (2) ∑

Subject to:

∑

∑ (3)

(4)

(5)

Now, the non linear problem is transformed to a linear program as follows:

∑ (6)

Subject to:

(7) ∑ ∑

(8) ∑

(9)

(10)

The dual of this linear program is also preferred among the analysts as the value of the objective function obtained will be the efficiency score for the evaluated DMU, and we also obtain the coefficients of the linear combination of the efficient DMUs to create a third hypothetical efficient DMU. In other words, in case we obtain an inefficient score from a specific DMU from DEA, we can obtain the desired output level of a hypothetical efficient DMU. Next, the dual of the linear program, using Thomas Sexton’s nomenclature:

(11)

Subject to:

(12) ∑

(13) ∑

(14)

By linear programming duality theory, the optimal value of the variable equals the

value. Also, if the DMU is efficient, then it will be the only DMU in its reference set

(frontier), and the corresponding dual variable will be equal to one (Sexton, 1986). If

DMU k has an efficiency score less than one, it is inefficient. In other words, for those inefficient DMUs the values of the weights will indicate their efficient reference set.

As in the primal program, the dual linear program must be solved separately for each

DMU in the sample. For a better understanding, let’s take a look at the example2 in

Figure 2. This is a single input, multi-output case where a regional health authority manages 6 hospitals, the decision making units. The number of patients is scaled, and the axis in the graphic represents the quantity of patients per $1000 operating expenditure treated. The efficient DMUs A, B, C and D compose the reference set. For inefficient

DMU E, E’ is that reference point that can be calculated through a linear combination of points B and C.

Figure 2. Example to illustrate the concept of a reference set.

Finally is important to discuss that although DEA is widely used, as evaluators it is important to have in consideration the shortfalls of this methodology that can drive the study into incorrect results (Jacobs et al., 2006). As DEA is deterministic and based on outlier observations, it assumes that all variables are measured accurately. In this sense,

2 Thanassoulis, 2001. 19 data that is feed into the model has to be reliable. The decision maker has to be careful interpreting the results, as they are sensitive to small samples and outlier observations as well. Another challenge is choosing which inputs and outputs to include in the model, as the inclusion or exclusion of certain variables can bias efficiency estimates. A good approach to test this is preparing different models, applying the DEA and comparing the efficiency results to see if they change depending on the choices of the inputs and outputs. Another important thing to consider is that the larger the number of input and output variables used in relation to the number of DMUs in the model, the more DMUs will be assigned as fully efficient. So the last recommendation of testing different models, in terms of quantities of inputs and outputs included, is also applicable in this case.

Equity Assessment in Health Care

As mentioned before, the difference among an allocation model for the private sector and a model for the public sector is the addition of the equity perspective in the latest. On the other hand, the case study to be developed in this thesis will be applied in the health care area of Costa Rica, specifically in primary health care attention. Having this in mind it is important to know how equity has been included in the analysis of health care systems.

Most of the surveyed literature on the measurement of equity of health care and health is more oriented towards creating monitoring systems. Although this is not the objective of our research, it gives us insights on which indices and strategies are commonly used to assess equity.

Some of the more helpful publications on this matter are from Paula Braven, who proposes eight steps in policy-oriented monitoring of equity in health and its determinants

20 on the article Monitoring Equity in Health and Healthcare: A Conceptual Framework

(2003). In another publication for the World Health Organization (1998), she provides practical suggestions regarding data sources and indicators for monitoring health equity.

She considers as central the inclusion of indicators of the determinants of health status apart from health care and also states that the first step to make the system work is the identification of the social groups of a priori concern.

The article by Anand, Diderichsen, Evans, Shkolnikov, and Wirth included in the publication Challenging Inequities in Health: From Ethics to Action, summarizes more theoretical concepts in terms of the existent measures of health equity. They divide these measures into two families, intergroup differentials and interindividual differentials. This last group includes the Gini coefficient. Anand et al. describe that there exist four uses of the measures of health equity, namely, describing differences between groups and between individuals, calculating the public health impact, attributing causality, and assessing interventions. The authors also define the various issues that must be addressed when constructing a measure of health equity. These include the measure of health status, the population grouping across which health inequalities are assessed, identifying the reference group or norm against which differences are measured, and the tradeoffs between absolute versus relative measures.

Yukiko Asada, in his article included in the compilation Tackling Health Inequities through Public Health Practice proposes a three-step framework for measuring health inequity. The first is defining when a health distribution becomes inequitable; in this matter the author highlights the importance of the determinants of health. The second is

21 deciding on measurement strategies to operationalise a chosen concept of equity, this decision may need the analyst to answer questions such as why does health distribution cause moral concern and within what time period should health equity be sought, to then choose between an individual or group approach. The third step is quantifying health inequity information, and this means choosing between measures such as the range measures, the concentration index, and the Gini coefficient. In this sense, the author recommends taking into consideration the basis of the comparison, if we are going to look at differences absolutely or relatively, how should the differences be aggregated, if the assessment of health inequity will be sensitive to the population’s mean health and population size, and subgroup considerations. When a comparison is made, the range measures compare the worst off with the best off. Other measures compare everyone to a norm or to a mean, whereas the Gini coefficient compares everyone with everyone.

As a result of this review, we recognize the importance of analyzing the population that will be addressed to determine if they are significant differences within it in terms of the determinants of health. For this matter, we recall the Strategic and Conceptual Model from the Ministry of Health of Costa Rica, the institution that has the steering role in terms of health in the country. On the mentioned model, updated in 2011, the determinants of health (adapted from Lalonde, 1974) include the biological determinants

(all those elements, both physical and mental, that develop within the human body as a result of the biological and organic basic aspects of the individual), the environmental determinants (environment in general and the human habitat, for example the water quality, natural events, and working conditions), socioeconomic and cultural

22 determinants (for example income and equity in its distribution, education, employment, and political participation), and the determinants of health-related services (access, coverage, quantity, quality, nature, timing, use, relationship with users, and availability of resources). These determinants are considered on our further analysis.

Chapter 3: The Allocation Model

The main objective of this thesis is to determine the most appropriate model for the allocation of resources in the public sector. When this model is identified, it will be validated by applying it in the primary health services at Costa Rica. As mentioned before, for a model to be applied in the public sector it must include the equity dimension. We also found that there are recommended characteristics that the equity measures should satisfy, for example fulfilling the principle of transfers, as stated by

Mandell. Taking this into consideration, Golany extends the use of the data envelopment analysis by creating a resource allocation model that that can be used to analyze tradeoffs among efficiency, effectiveness, and equity measures. This last model satisfies our main objective and in this chapter, we are going to describe it as it was developed by Boaz

Golany and Eran Tamir. It is important to stress that this improved resource allocation model assesses the needs from Mandell’s model described in the literature review. We are going to start explaining the new DEA-based resource allocation model (DEA-RAM), and then we will clarify how it should be modified to include the equity constraints, to finish with the description of the case when various outputs are analyzed.

The new DEA-based resource allocation model (DEA-RAM3) can be applied at any organization with n decision making units (DMUs), each using m inputs (resources) to produce a single output. The analyst then has to define two matrices to represent the past performance of the DMU’s in a particular period: the matrix of inputs and the vector of outputs . Also, the analyst has to consider the fact that there are probably limited amounts, , of resources available to all the DMUs in each i є C, where C represents the set of controllable resources. The purpose of the model is maximizing the overall effectiveness of the organization (objective function). This will be measured by the sum of the potential outputs across all DMUs (j=1,…, n) that can be achieved with the allocation of resources , (i=1,...,m). The model will choose the set of weights that achieves the highest efficiency rating for each DMU, while assuring that these weights do not cause any other DMU to have an efficiency rating higher than 1 (Golany et al. 1995).

The allocation has to take into account the empirical production function (this is the data- based efficiency frontier as observed in the chosen period) as well as the limited amounts of resources. The DEA-based allocation model stated by Golany and Tamir is then:

∑ (15)

Subject to:

∑ (16)

3 For this description we are using the nomenclature proposed by Boaz Golany and Eran Tamir, published in their article “Evaluating Efficiency-Effectiveness-Equality Trade-Offs: A Data Envelopment Analysis Approach” in 1995. 25

∑ (17)

∑ (18)

∑ (19)

(20)

In the primal DEA mathematical program, the objective is to maximize the efficiency score. In the DEA-RAM case, the objective function assesses the effectiveness criterion.

Constraints (16), (17) and (18) are the same as in the DEA model, or in other words, these constraints are enveloping each DMU. The combination of the objective function with output constraint (16) ensures efficient output targets. Constraints (17) and (19) guarantee that for any given output level, a minimal feasible resource allocation is identified (Golany et al, 1995). Other differences from the DEA model are considering the resource limitations in the equation (19) and having the outputs and inputs as decision variables and no longer only parameters. The non-negativity of the decision variables is enforced by constraint (20).

The equity measure has not yet been described within the DEA-RAM model. To assess inequality in the model, Golany and Tamir include two new constraints, based on those proposed by Mandell. The new constraints (21) and (22), assume that the equity constraint is imposed on a particular input dimension, i*, and requires the Gini coefficient to be no greater than . This is considered by adding variables and which represent

26 the positive and negative absolute differences respectively, between the allocations of the input at the DMUs under study.

(21) ∑ ∑ ∑

=0, j=1,...,n-1 , k (22) > j

In other words, the analysts may choose which of the m inputs has to be allocated with equity. An example could be choosing the investment per period on each of the DMUs.

Now the allocation of inputs will consider constraints (17), (19), (21) and (22). It is also important to specify what  mean, in order to understand what these new constraints do.

We begin by explaining how the Gini coefficient, G, is calculated. Let the number of units of input i* units allocated in DMU j, where j=1,..,n. The variable is the proportion of equity units contained in DMU j. The equity units will be selected by the analyst as the factor over which equity is assessed. For example, the priority of a health care program could be focusing on the population over 65 years. Then, the total number of persons over 65 years which receive services at each DMU is the number of equity units. As Mandell describes, the Gini coefficient will give an average “perceived net envy level” associated with the allocation of resources by calculating the following:

∑ ∑ | | (23)

∑

In this equation, the service level received by each DMU is compared to every other

DMU. If there exists no inequity among the DMUs, then G=0. So,  , and G as an upper limit can be calculated by solving the DEA-RAM without the equity constraints

27 in equations (21) and (22). Equation (22) is the result of a simple transformation which linearizes equation (23).

Some other changes must be done to the maximization problem presented to include the equity constraints. The non-negativity constraint is modified to include the new variables, equation (26). Then, trade-offs between the effectiveness and equality criteria are examined by decreasing the value of  in equation (21). Also as the equity constraint is tightened, a new trade-off arises as maintaining feasibility of equations (21), (22), (17) and (19), is not always possible (Golany et al., 1995). To address this situation, a new set of variables is defined, allowing deviations from the observed efficient performance.

These new variables are included as shown in constraints (24), (25) and (26). In addition,

M is defined as a large penalty term. Because of M, these deviations will be used only to avoid potential infeasibility caused by the inclusion of the equity constraints.

(24) ∑ ∑ ∑

Subject to (2), (4), (5), (7), (8) and

(25) ∑

(26)

As a final point, to make the extension to the multioutput scenario we must change the objective function. The effectiveness is measured by the sum of the outputs, so if various are analyzed, subjective weights must be applied on the different output dimensions

(r=1,..,s) in order to allow their aggregation in the objective function (Golany et al, 1995).

DEA-RAM is modified by repeating constraint (16) for every output and modifying objective function (24) as following:

(27) ∑ ∑ ∑ ∑

As we can see, the model can be employed for resource allocation purposes without requiring a priori assumptions on the form of the underlying production function, in contrast to Mandell’s approach. To feed the single output DEA-RAM model the analyst will need to define the decision making units under study, the inputs, the output and if there exist limited amounts of inputs (in the case that they can be controlled). For the

DEA-RAM model including the equity constraints the equity units, equity proportion and the  value will be the new parameters to add to the analysis. To run the model in the multioutput case, all of the above mentioned have to defined, plus the subjective weights.

Chapter 4: Case Study

After finding an allocation model that can be applied to the public sector, we wanted to validate it by using it in a case study. For this matter, we chose the primary health care services of Costa Rica. The reason for this is better explained by Jacobs et al.: the international explosion of interest in measuring the inputs, activities and outcomes of health systems can be attributed to heightened concerns with the costs of health care, increased demands for public accountability and improved capabilities for measuring performance. The first section of this chapter is intended to describe the structure of the health system in Costa Rica. In section two, the organization chosen for the application of the model, the Health Area Goicochea 2, is characterized. Section three then develops the

DEA-RAM equity model for the multi output case. Finally, at section four we present a discussion of the results obtained.

The National Health System of Costa Rica4

There are two primary institutions in the National Health System of Costa Rica, the

Ministry of Health and the Caja Costarricense de Seguro Social (CCSS). They execute their roles all over the country. Thus to have a better understanding of their operation, in this section we are going to describe their basic functions and how they are organized to perform them.

4 These information was extracted various documents corresponding to the authorship of the Ministry of Health of Costa Rica, the Caja Costarricense de Seguro Social and CENDEISS. 30

The Ministry of Health exercises the steering role over the actors involved in the social production of health by encouraging their active participation and by guiding their actions towards the development and constant improvement of the health levels of the population. Managerially, the Ministry has three levels of management. The central level is the political-strategic level of the institution. The regional level is the political-tactical level and the link between the central and local level. Finally, the local level is the political and operational level of the institution for the implementation of the lead roles and provision of health services.

The Caja Costarricense de Seguro Social (CCSS) is the social security institution responsible for the comprehensive care of people. The function of the CCSS is to provide health services to all people according to the social security principles: solidarity, universality, unity, equality and equity. As the CCSS has powers and responsibilities throughout the national territory, it is organized into three administrative levels in order to facilitate the coordination and implementation of its activities. The central or national level is eminently political, regulatory, and financial, and it is driven by the higher authorities. The reference point it takes for its functioning is the National Health Policy determined by the Ministry of Health. The regional level’s function is to operationalize and organize in their geographical area of influence the strategies, plans, programs and budgets defined by the central level. It is also responsible for coordinating, supervising and training the local human resources and managing the physical resources and funds allocated to the region. At the local level, the staff is responsible for programming, implementing and monitoring the health activities operationalized through plans and

31 programs defined by the central and regional level. This level is comprised of all the institutions in which perform activities of health promotion, prevention and treatment of diseases, and rehabilitation, or in other words, all health services. These institutions include the national specialized and general hospitals, regional hospitals, peripheral hospitals, health areas and the health sectors with their teams, the Basic Teams for

Comprehensive Care in Health (Equipos Básicos de Atención Integral en Salud, EBAIS).

The institutions at the local level of the CCSS attend care needs and health problems of varying complexity, ranging from low to very specialized. Consequently, the local level is also organized into three different levels of care. The first level of attention, the primary care, includes basic health services that perform actions of health promotion, disease prevention, and curing and rehabilitation of lower complexity diseases. These actions are carried out by the members of the support teams and the EBAIS. The second level of attention provides support to the first level and offers ambulatory and hospitalized interventions for basic specialties such as internal medicine, pediatrics, gynecology and obstetrics, psychiatry and general surgery. The third level of attention provides inpatient and outpatient services in complex specialties and all subspecialties. It serves hospitalized users, high complexity pathologies, and other emergencies requiring hospitalization and specialized surgical procedures. Additionally, this level provides support services and diagnostics and therapeutics requiring high technology and specialization. The institutions of this level of care are regional, national general, and specialized hospitals.

As the CCSS covers the vast majority of the population in Costa Rica, and the case study for this project is developed for the primary care level of this institution, we describe the first level structure. Costa Rica, for purposes of the CCSS, is divided into seven health regions. In each of these regions the CCSS established the health areas to provide comprehensive health services to the population located in a defined territorial space, as responsible for the primary care level. The health areas serve populations between 15000 and 40000 in rural areas and between 30000 and 60000 inhabitants in urban areas. Also, the health areas are considered the basic administrative and geographical unit of the

National Health System (management systems and institutional financing). They are under the command of a director advised by a technical and administrative team called the support team. Also, each of the health areas is subdivided into two or more health sectors, which are geographical divisions in which between 4,000 and 4,500 people live, on average. The organization of the health areas must ensure the timely delivery of services to the population, according to two basic elements: the number of people assigned and the dispersion and/or concentration of population. Each of the health sectors is in charge of a team called Basic Team for Comprehensive Care in Health (EBAIS).

Each EBAIS is composed of at least one general doctor, one nursing assistant, one assistant coach of primary health care, and a Technical Assistant in Primary Care

(Asistente Técnico de Atención Primaria, ATAP).

Health Area Jiménez Núñez (Goicochea 2)

The institution chosen to validate the model explained in the previous chapter is the area of health Jiménez Núñez (Goicoechea 2), founded in 1966. The basic reason we decided

33 to select this health area is that various projects have been developed between this entity and the Department of Industrial Engineering at the University of Costa Rica. In this sense, the senior officers of Goicoechea 2 have a clearer vision of how an academic project is structured and a clearer sense of which are the health area’s needs, as a result of previous analysis conducted. In this section, we describe the basic characteristics of this area of health as well as the needs we are seeking to address with the allocation model.

In terms of geographical distribution, this area of health belongs to the North Central regional division, but from the administrative level, it is responsibility of the Central

South. Classified as a Type II health area, it provides health services for first and second level of care (general medicine, pediatrics, psychology, internal medicine, family medicine, psychiatry, clinical laboratory, pharmacy, diagnostic imaging, electrocardiography, dentistry and emergency). The area of health Jiménez Núñez is composed of 10 EBAIS, each one serving between 4000 and 7500 people. In Table 1, the

EBAIS and their corresponding number of users are presented.

Name of the EBAIS Number of Users Las Lomas 7473 Barrio Pilar 6284 Barrio Fátima 5153 Centeno Guell 4927 Divino Pastor 4875 Santa Eduviges 4647 Calle Blancos 1 4528 El Encanto 4311 Santa Cecilia 4284 Calle Blancos 2 3293 TOTAL 49775 Table 1.Number of users at each EBAIS

As it is stated in the Organizational Manual for the Health Areas developed by the CCSS, each health area “should be provided with financial resources in accordance with the objectives and targets set, to promote equity in the distribution and solve real needs, taking into account the following aspects: population assigned, human development index, implementation of special processes, epidemiological indicators, among others”.

But, the allocation of these resources has been done according to historical estimate (the spending in the past). The absence of other criteria, such as enrolled population, productivity levels, or efficiency, represents a suboptimality in the budget allocation process.

Within the area of health under study, the budgeting process from the central level to the area of health was described by its Director Pedro González as follows. The budget management department at the central level of the CCSS determines a maximum amount to be allocated to each area of health, according to revenue projections and the historical behavior of the spending unit. Then, each area of health prepares a detailed budget by budget account (Goicoechea 2 handles between 60 and 70 budget accounts). If any differences are found between the total amount budgeted for the clinic and proposed by the central level, it is negotiated. Continuing with the topic of the assigned budget for the health area Goicoechea 2, as explained also by the director himself, the EBAIS under this health area do not handle their own budget, because they have no administrative structure to manage it. In turn, the chief of the first level (EBAIS), in collaboration with the support team, performs a needs assessment that is integrated into the overall budget of the area of health.

In conclusion, the budget allocation for the health areas, as well as for the EBAIS, is not systematic as it lacks a clear, non empirical methodology to follow. It also fails to consider the impact of the health areas’ activities over the target population and the performance of the operative units. In this sense, we are going to validate the DEA-RAM equity model developed by Golany and Tamir as a suitable systematic approach to help the allocation decision making at the health area level.

DEA-RAM Equity Model for the Multi Output Scenario

To begin with the application of the DEA-RAM Equity Model at the health area

Goicoechea 2 we need to start by identifying and choosing the main components of the model: the decision making units, the inputs and the outputs, and we also need to determine if there exist environmental factors that will influence the performance of the

DMUs. To do so, we ask for the more experienced criterion at the health area by working with the supervision of the director of the health area, Pedro González, and the chief of the EBAIS, Esteban Avendaño.

The same structure of the first level of attention in health care of the National Health

System at Costa Rica, made the choice of the DMUs easy. The health areas are divided into sectors, and each of the health sectors is in charge of an EBAIS. The EBAIS team is in charge of developing the substantial processes of the health services provided at the first level. In this sense, the EBAIS captures the entire production process of interest, they convert inputs into outputs, and they are comparable as they produce the same set of outputs.

Although the health system in Costa Rica has several data sources, not all of them are systematized in an electronic format. For example, patient files typically paper-based.

This was an important limitation faced in the development of the model as we must settle with information that could be easily obtained electronically. As discussed with the decision makers in Costa Rica, this is a first approach to show the viability of applying a

DEA allocation model in their system. In the future, without the space and time constraints we face, they might be able to improve the model by testing and including more variables when the physical information is processed and available electronically.

Having clarified this, we describe the inputs and the outputs chosen.

Three variables are used as inputs: the annual budget, time contracted (programmed) for medical appointments in hours per year, and the actual time used for medical appointments in hours per year. The annual budget is used as it is the focus of the allocation we want to develop and a need for the health area, as discussed in the previous section. The medical consultation is the process that best describes the functioning of an

EBAIS team currently. This is why the hours planned and used for medical consultations are satisfactory inputs for the allocation model in terms of representing the work done by the EBAIS. When the physical data are processed into electronic data and become available to the managers at the EBAIS, other inputs, such as the labor hours of each of the other professionals in the team, can be included. In Appendix A, the description of these variables and the procedures used to calculate them are broadly described. The following table shows the information that will be included in the model.

Name of the EBAIS Total Annual Time contracted for Time used for Budget appointments (in hours appointments (in hours 37

(dollars) per year) per year) Barrio Fatima 1,241,119.09 1656 1569.12 Barrio Pilar Jiménez 948,110.87 1752 1396.56 Calle Blancos 1 842,353.79 1752 1329 Calle Blancos 2 873,531.49 1656 1245.6 Centeno Guell 624,064.84 1752 1329 Divino Pastor 1,333,918.33 1752 1684.32 El Encanto 603,752.20 1752 1245.6 Las Lomas 859,450.98 1752 1684.32 Santa Cecilia 1,894,102.13 1752 1684.32 Santa Eduviges 1,504,078.00 1752 1684.32 Total 10,724,481.71 17328 14852.16 Table 2. Inputs for each EBAIS, year 2011, area of health Goicoechea 2

The outputs that are going to be considered for the analysis are the annual number of medical consultations and the annual number of home visits done by the ATAPS. These two outputs characterize both the results that best represent the functions of the doctor and the ATAP at an EBAIS team. But, as a downside, these measures cannot reflect the quality of the service offered. As mentioned by Jacobs et al. the measure of a health outcome should indicate the value added to the health as a result of the contact with the health system. In this sense, better outputs should measure the additional health conferred to the patient or even the patient’s overall satisfaction. Other authors mention the difficulty on measuring the real effectiveness of a public health care system as it is subject to a vast heterogeneity of users. From the cost benefit perspective, it may also be too expensive to obtain these measures. In this sense, we are facing the same issues as other analysts have encountered when trying to assess the efficiency of health care systems. Therefore, it is important that the decision makers consider formulating careful interpretations of the results given in this case study. We recommend including in the 38 future other measures that are being analyzed for the ASIS (Análisis de Situación en

Salud, Health Situation Analysis) of the health area, but they are not yet available for each of the EBAIS, for example: the degree of satisfaction of users served by EBAIS, the percentage of complaints resolved by EBAIS, the number of successful projects developed by EBAIS, total queries resolved by EBAIS, quantity of days a user has to wait for an appointment at an EBAIS, among others. The outputs used are detailed in the next table.

Name of the EBAIS Medical Consultations Home Visits by ATAPS (annual) (annual) Barrio Fatima 21,483 763 Barrio Pilar Jimenez 18,785 688 Calle Blancos 1 17,020 810 Calle Blancos 2 15,797 771 Centeno Guell 12,439 675 Divino Pastor 25,355 872 El Encanto 12,936 601 Las Lomas 20,924 983 Santa Cecilia 24,040 684 Santa Eduviges 21,148 765 Total 189,927 7,612 Table 3. Outputs for each EBAIS, year 2011, area of health Goicoechea 2

Also, we needed to determine if there exist significant environmental constraints that affect the DMUs studied. In other words, we were looking to evaluate the determinants of health at the health sectors that correspond to each of the EBAIS. We also faced some limitations to find the appropriate information. In Costa Rica, there exist seven provinces, which are divided into 81 cantons, and each of these cantons is divided into districts. The

EBAIS and the health areas do not obey the same political division over their areas of influence. The area of health Goicoechea 2 includes 5 different districts, but only two of them completely, as shown in the following table.

Percentage of Assignment to District the Area of Health (%) Guadalupe 100 San Francisco 100 Calle Blancos 84 Mata de 30.8 Plátano Purral 11.6 Table 4. Districts served at area of health Goicoechea 2

Costa Rican institutions arrange and analyze most of the education, housing, and income indices by cantons. So, it is a challenge to find information by districts, considering also that each of the EBAIS under study serves only a percentage of the five mentioned districts5, as shown in the following table.

5 Source: Caja Costarricense de Seguro Social. (2011) Inventario de Áreas de Salud, Sectores, EBAIS, Sedes y Puestos de Visita Periódica en el Ámbito Nacional con Corte al 31 de Diciembre del 2010. 40

Name of the Districts assigned EBAIS Divino Pastor Guadalupe Fátima Guadalupe Santa Eduviges Guadalupe Santa Cecilia Guadalupe Guadalupe Las Lomas Mata de Plátano Purral Barrio Pilar Guadalupe Calle Blancos Centeno Güell Guadalupe San Francisco Calle Blancos 1 Calle Blancos Calle Blancos 2 San Francisco Calle Blancos El Encanto Calle Blancos Table 5. District assignment per EBAIS at area of health Goicoechea 2

One indicator that is disaggregated to the district level is the unsatisfied basic needs

(NBI, necesidades básicas insatisfechas) methodology. The NBI was proposed by the

Economic Commission for Latin America (CEPAL) in the seventies. The main objective of this indicator is to identify households and individuals that fail to satisfy a set of requirements deemed necessary according to welfare standards accepted as universal, using census information available (INEC,2000). The NBI used for this thesis has as a data source the national census developed by the INEC6 in the year 2000. Four

6 Entity with the technical lead and steering role of the National Statistics System at Costa Rica. It coordinates the country's statistical production in order to meet the needs of information requirements at a national level. 41 dimensions were defined by the experts at the INEC for the calculation of the critical gaps indicator of the NBI, and each of them has different components:

 Access to shelter: includes three components that express different degrees of

privation, these components are the quality of housing (slum), the quality of the

housing materials, if there exist overcrowding, and if the house lacks electricity.

 Access to healthy living: evaluates the sanitary infrastructure in terms of

drinkable water availability and the existence of a waste disposal system.

 Access to knowledge: considers school attendance and schooling lag for the

population between 7 and 17 years. It is considered absent for the household if

there is at least a member between 7 and 17 years that is not attending school or if

he/she attends but with more than two years’ lag.

 Access to goods and services: measures the economic capacity, it is considered

absent when the head of the household was aged 50 or more and completed

primary school or less.

Every household in Costa Rica is analyzed for each of the four dimensions, and using the critical gaps indicator, the households are classified as having one, two, three or four critical gaps. For a household to have a gap in some dimension, it has to meet at least one of the criteria defined for each component. It is important to mention that the four dimensions are equally weighted. To appreciate gaps at the district level, the INEC made a grouping of districts by percentage of critical gaps. A clustering technique is applied according to the percentage of incidence (percentage of households with one or more critical deficiencies by district), resulting in five groups of districts. The results for the

42 five districts served at the area of health Goicoechea 2 is almost the same, with four of the districts clustered in group 5. Only the Purral district, is classified within a different group (group 4). Table 6 summarizes the classifications on a scale of 1 through five, 1 represents the population with biggest needs and 5 the population with best quality of life. It is important to remember, however that only a 11.6% of the population of the

Purral district is served by the area of health studied.

Table 6. Summary of the NBI incidences per district and grouping.

This means all the districts served by Goicoechea 2 are classified as having higher levels of quality of life (in). Based on these findings, we assume that there are no significant differences among the EBAIS studied due to environmental factors.

With the DMUs, inputs, and outputs defined and the environmental constraints analysis done, the first evaluation to be applied at the area of health Goicoechea 2 is the data envelopment analysis (DEA)7 to obtain the efficiency scores per EBAIS. We find that only four out of the ten EBAIS at Goicoechea 2 are efficient based on the inputs and outputs defined, these efficient DMUs are: Calle Blancos 1, Calle Blancos 2, Divino

7 For the calculations we use the program described by equations 11 through 14. 43

Pastor, and Las Lomas. The efficiency scores generated are shown in the next table and the weights are detailed in Appendix B.

Name of the Efficiency Score EBAIS Barrio Fatima 0.924434 Barrio Pilar 0.960945 Jimenez Calle Blancos 1 1 Calle Blancos 2 1 Centeno Guell 0.945674 Divino Pastor 1 El Encanto 0.880071 Las Lomas 1 Santa Cecilia 0.948136 Santa Eduviges 0.85908 Table 7. Efficiency scores for the EBAIS obtained by the DEA methodology.

With the actual allocation of resources, only 4 EBAIS are efficient. To demonstrate how the DEA allocation model improves the efficiency of the DMUs under study by calculating the appropriate amounts of inputs to be used and the outputs obtained from this assignment, we apply the model for the multi-input and multi-output scenario. We apply the model under two settings: one uses the budget of the previous period (year

2011) and the budget8 to allocate as the resource constraints. For the other inputs (time contracted, and time used for the appointments) the sum of resources used in year 2011 define the resource constraint. As this is a multi-output case, the formulation requires a weight for each of the outputs analyzed, as they need to be aggregated in the objective

8 The estimation of the budget for the next period is 13,941,826.23 dollars according to the managers of the area of health Goicoechea 2. This includes the growth and also the inflation; together they represent approximately a 30% more of the previous period’s expenditure. 44 function. Following the recommendation of the decision makers at the health area

Goicoechea 2, the same weights are assigned to each output (0.50 -0.50).

As shown in table 8, when using the 2011 budget constraint the allocation of inputs given by the DEA-RAM model doubles, the number of efficient EBAIS from 4 to 8. With the current budget to allocate, this number rises to 9 efficient DMUs. In both cases the two outputs considered (total medical consultations and the home visits by the ATAPS) show an improvement. It is important to clarify that there is no specified target of outputs per

EBAIS or for the health area as a whole. This is the reason we have similar improvements despite the increased budget in the second case. The inclusion of such constraints may result in a decrease in the number of efficient DMUs, but could be more realistic in terms of meeting the decision maker’s expectations for each EBAIS. The weights, input allocation, and output results per EBAIS are detailed in Appendix C.

Results for previous Results for current period's budget budget to allocate (10,724,481.71 dollars) (13,941,826.23 dollars) Optimal Solution 107,619.6 109,217.3 Total medical 206,879.5 (16.95% 210,172.9 (20.25% consultations improvement) improvement) (annual) Total home visits by 8,359.5 (9.82% 8,261.6 (8.53% ATAPS (annual) improvement) improvement) Efficient EBAIS 8 9 Table 8. Comparison of the results of the DEA-RAM model between the previous period’s budget and the current budget to allocate for the next period

After applying the DEA model and the DEA resource allocation model and identifying the advantages of these methodologies, we include the equity perspective into the analysis. As discussed in Chapter 3, the decision makers need to define the equity unit, the factor used by the model to assess equity. Taking into consideration the expertise of the managers of the health area, we discussed which factors are prioritized in terms of the service at the primary level. As a result, we include three different equity units (E) for the analysis: the number of users with hypertension, the number of users with diabetes, and the number of users over 65 years of age with diabetes. We justify this selection as these users may require more specialized care, control and treatment than the rest of the users and this reflects on the resources used by each of the EBAIS. The quantities per DMU for each of the three equity units9 are specified in the next table.

Name of the Users with Users with Users over 65 years EBAIS hypertension diabetes with diabetes Barrio Fatima 651 304 147 Barrio Pilar 554 193 108 Jimenez Calle Blancos 1 471 182 95 Calle Blancos 2 446 139 55 Centeno Guell 361 145 79 Divino Pastor 699 243 114 El Encanto 363 136 36 Las Lomas 640 256 98 Santa Cecilia 709 8 7 Santa Eduviges 558 303 168 Total general 5452 264 144 Table 9. Equity constraints for each EBAIS, year 2011, area of health Goicoechea 2

9 It is important to clarify that the DEA-RAM-equity model, considers only one equity unit per analysis, having three different equity units means the program has to be run for each of the three scenarios. 46

Having the equity units defined and quantified the next step is calculating the Gini coefficient (G). To do so, we choose the previous period’s budget allocation to determine the maximum value of , the upper limit for the value of G in the model. This means that we want to improve the equity level by having the previous period’s Gini measure as our upper limit. The calculations are specified in Appendix D and the Gini measure values obtained for each of the three different scenarios are summarized in the next table.

Gini Equity unit (E) measure Users with Hypertension 0.1155505 Users with Diabetes 0.2029391 Users over 65 years with 0.2189966 diabetes Table 10. Gini measure per equity unit

We have all the necessary parameters to run the DEA-RAM model with equity constraints. We test three different values of  for each of the equity units, and we also consider two different budget constraints: the previous period’s budget (10,724,481.71 dollars) and the current budget to allocate (13,941,826.23 dollars). The optimal solutions of the runs are presented in the next table, and the weights and input and output allocations are detailed in Appendix E.

Results: Total Weighted Outputs δ= Users with hypertension δ= 0,0555 δ= 0,1155 0,01155 Previous period's budget 107,076.61 107,619.56 107,619.56 Current budget to allocate 109,217.31 109,217.31 109,217.31

Users with diabetes δ= 0,06 δ= 0,08 δ= 0,2029

Previous period's budget 103,983.06 105,134.66 107,619.56 Current budget to allocate 109,217.31 109,217.31 109,217.31 Users over 65 years with δ= 0,07 δ= 0,1095 δ= 0,2189 diabetes Previous period's budget 102,043.91 104,413.76 107,619.56 Current budget to allocate 108,039.36 109,217.31 109,217.31

Table 11. Optimal solutions per scenario, DEA-RAM with equity

The basic idea behind the model as a managerial tool is giving the decision makers an insight of how the equity, efficiency and the effectiveness of the allocation interconnect.

In this sense, the analyst may expect to find a tradeoff among effectiveness and equity: as we look to minimize the inequity by decreasing the value of , the optimal solution decreases. We see this behavior very clearly in the cases of users with diabetes and the users over 65 years with diabetes when considering the previous period´s budget. But, unpredictably in most of the cases where the current budget to allocate (13,941,826.23 dollars) is considered, the  value can decrease without affecting the optimal solution. In other words, the system analyzed can be more equitable and still obtain the same outputs.

Of course, the decision makers have to remember that these results depend on the parameters, inputs, outputs, and equity units chosen. One reason for this behavior can be

48 the absence of targets for the outputs, as the budget to be allocated is approximately 30% more than the period of reference. In this sense, for further analysis the area of health may define these target quantities so that they can be added as lower limit constraints for the allocation of the output at each EBAIS.

Chapter 5: Conclusions and Future Work

DEA itself is a useful management tool as it performs the efficiency assessment from a comparison between DMUs through data and among data by generating the efficiency frontier. We find that this model can include more features, and the perspectives of effectiveness, efficiency, and equity all be simultaneously analyzed. This integration is important as the tradeoffs among certain decisions in each dimension could affect the performance in other dimension.

To run this operations research model, various analytical choices must be made: the unit of study, the inputs and outputs to be considered, the weights for the aggregation of the outputs in the objective function, the environmental constraints and when equity is incorporated, the units among which services should be distributed evenly (the equity units). When these choices depend heavily on the analysts, the appropriateness of the model depends on the consistency between the analytical choices and the judgment of experienced decision makers. In this sense, a recommended approach (that in this case study could not be applied due to time and space restrictions) is to develop various models to compare results. By various models we mean changing and combining the mix of inputs, outputs, equity units, and environmental constraints before making a definite allocation decision. This just means that there exist certain generally accepted standards in the efficiency and equity literature, but the mathematical model developed will always have to address different factors depending on the object of study. Every DEA resource 50 allocation model with equity will be different depending on the DMUs analyzed, and for each case, several models could be used as well.

The DEA model has been widely used in health institutions and many other public sector organizations in the world (especially in the United States and Europe), but this is the first application to the primary health system of Costa Rica. We learned that more information should be made electronically accessible in order to strengthen the model that considers the EBAIS as DMUs. Actually, most of the information is available (health evaluations, census information) at the health area level, which means it would be valuable to develop this analysis for the 103 health areas in Costa Rica as DMUs. This would also be more interesting as environmental factors may play a more important role, because health areas comprises cantons with different human development indices, they can also be classified as rural or urban, introducing other environmental factors.

Basically, as happened with Tingley and Liebman’s model, we can think of standardizing and systematizing the decision making at the health areas by disseminating the use of the

DEA-RAM with equity model and then applying the extensions along the model to be broadened to incorporate resource allocation at the national level.

Operation research models applied to public services is still scarce. The development of models analogous to those described in this paper that could incorporate equity indices that satisfy the principle of transfers and other standard criteria for measures of equity is a need, as we all know that the public resources are the majority of time limited and slight changes in their allocation may cause great gains or losses to society.

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Appendix A: Input Data

The annual budget, the time contracted for medical appointments in hours per year, and the actual time used for medical appointments in hours per year are the three inputs that are included in the application of the allocation model for the area of health Goicoechea

2. This area of heath does not count with an aggregate annual budget per EBAIS. Instead of this they determine a cost for their most important expenses: the cost per medical consultation, the cost per home visit made by the ATAPS and the monthly cost of drugs.

The cost of the consultation and the visits already include entries such as salary of the personnel in charge, materials, administrative support, and nursing assistants support. In the following table, these costs are given in the Costa Rican currency (colones).

Cost per Medical Cost per Home Cost of Drugs Name of the EBAIS Consultation Visit by ATAPS (by month, in (colones) (colones) colones) Barrio Fatima 28,130.36 13,193.38 1,660,005.99 Barrio Pilar Jimenez 23,277.62 18,657.87 2,871,149.68 Calle Blancos 1 23,067.70 12,405.79 2,320,769.19 Calle Blancos 2 26,558.58 13,040.74 1,403,681.35 Centeno Guell 22,918.80 21,151.80 1,631,886.69 Divino Pastor 25,334.75 16,515.17 2,081,263.59 El Encanto 21,771.98 33,759.75 552,810.92 Las Lomas 16,045.03 27,879.46 6,343,040.70 Santa Cecilia 38,765.38 22,957.54 1,701,251.98 Santa Eduviges 33,559.64 21,114.91 3,569,334.36 Total 259,429.84 200,676.41 24,135,194.45 Table 12. Annual costs in colones for each of the EBAIS at area of health Jimenez Nunez, 2011

For the costs per medical consultation and home visits, we make an annual approximation using the number of medical consultations and visits of the ATAPS in the year 2011. It is important to mention that these are also the outputs used in the allocation analysis and they are included in Appendix B. Discussing with the managers of Goicoechea 2, the cost of medications does not vary significantly within the year. Their recommendation is to approximate the total annual budget by multiplying the monthly budget by the 12 months of work. The next table shows the results of the annual budgets by item and the summation of these three for the total annual budget of the year 2011.

Total Annual Total Annual Expenditure for Total Annual Expenditure for Cost of Drugs EBAIS Medical Budget (2011 Home Visit by (colones) Consultation period) ATAPS (colones) (colones) Barrio Fatima 604,324,523.88 10,066,548.94 19,920,071.88 634,311,144.70 Barrio Pilar Jimenez 437,270,091.70 12,836,614.56 34,453,796.16 484,560,502.42 Calle Blancos 1 392,612,254.00 10,048,689.90 27,849,230.28 430,510,174.18 Calle Blancos 2 419,545,888.26 10,054,410.54 16,844,176.20 446,444,475.00 Centeno Guell 285,086,953.20 14,277,465.00 19,582,640.28 318,947,058.48 Divino Pastor 642,362,586.25 14,401,228.24 24,975,163.08 681,738,977.57 El Encanto 281,642,333.28 20,289,609.75 6,633,731.04 308,565,674.07 Las Lomas 335,726,207.72 27,405,509.18 76,116,488.40 439,248,205.30 Santa Cecilia 931,919,735.20 15,702,957.36 20,415,023.76 968,037,716.32 Santa Eduviges 709,719,266.72 16,152,906.15 42,832,012.32 768,704,185.19 Total 5,040,209,840.21 151,235,939.62 289,622,333.40 5,481,068,113.23 Table 13. Annual costs in colones for each of the EBAIS in area of health Jimenez Nunez, 2011

To obtain the cost in dollars we use the data base of the Central Bank of Costa Rica, with the exchange rates of the year 2011 to obtain an average exchange rate. The annual costs and the annual budget in dollars are presented in the next table.

Total Annual Total Annual Expenditure for Cost of Drugs Total Annual Expenditure for EBAIS Medical (by month, in Budget (2011 Home Visit by Consultation dollars) period, in dollars) ATAPS (dollars) (dollars) Barrio Fatima 1,182,446.04 19,696.62 38,976.43 1,241,119.09 Barrio Pilar Jimenez 855,580.52 25,116.64 67,413.70 948,110.87 Calle Blancos 1 768,201.17 19,661.68 54,490.94 842,353.79 Calle Blancos 2 820,900.62 19,672.87 32,958.00 873,531.49 Centeno Guell 557,812.78 27,935.87 38,316.19 624,064.84 Divino Pastor 1,256,872.87 28,178.03 48,867.42 1,333,918.33 El Encanto 551,072.89 39,699.48 12,979.83 603,752.20 Las Lomas 656,895.61 53,622.74 148,932.63 859,450.98 Santa Cecilia 1,823,432.21 30,725.05 39,944.87 1,894,102.13 Santa Eduviges 1,388,665.70 31,605.44 83,806.86 1,504,078.00 Total 9,861,880.41 295,914.42 566,686.89 10,724,481.71 Table 14. Annual costs in dollars for each of the EBAIS at area of health Jimenez Nunez, 2011

Finally, it is important to mention that as with the cost of medications, the inputs of time programmed and time used for medical appointments are managed by the EBAIS on a monthly basis. Again, the managers at the area of health Goicoechea 2 determined that there is no significant difference among the times throughout the year and recommended to approximate the total annual time by multiplying the monthly hours by the 12 months of work. The monthly and annual data are detailed in following tables.

Time programmed for Time used for medical Name of the EBAIS medical appointments appointments (contracted) Barrio Fatima 138 130.76 Barrio Pilar Jiménez 146 116.38 Calle Blancos 1 146 110.75 Calle Blancos 2 138 103.8 Centeno Guell 146 110.75 Divino Pastor 146 140.36 El Encanto 146 103.8 Las Lomas 146 140.36 Santa Cecilia 146 140.36 Santa Eduviges 146 140.36 Total 1,444.00 1,237.68 Table 15. Total time in hours per month programmed and used for medical appointments at area of health Jimenez Nunez, 2011

Time programmed Time used for for appointments Name of the EBAIS appointments (in (in hours per year, hours per year) contracted) Barrio Fatima 1656 1569.12 Barrio Pilar Jiménez 1752 1396.56 Calle Blancos 1 1752 1329 Calle Blancos 2 1656 1245.6 Centeno Guell 1752 1329 Divino Pastor 1752 1684.32 El Encanto 1752 1245.6 Las Lomas 1752 1684.32 Santa Cecilia 1752 1684.32 Santa Eduviges 1752 1684.32 Total 17,328.00 14,852.16 Table 16. Total time in hours per year programmed and used for medical appointments at area of health Jimenez Nunez, 2011

Appendix B: DEA Weight Results

By definition, the weights obtained for the efficient DMUs are equal to one. On the other hand, for inefficient DMUs the values of the weights represent the efficient reference set.

Consider as an example the inefficient EBAIS Santa Eduviges. This EBAIS has Divino

Pastor and Las Lomas as its reference for efficiency. As shown in Table 17, Santa

Eduviges needs to combine 0.716001 of the performance of Divino Pastor and 0.14308 of the performance of Las Lomas to reach the efficiency frontier. The EBAIS not listed are efficient.

Efficiency Frontier Inneficient Reference Set EBAIS Reference Weight Calle Blancos 1 0.0611 1 Barrio Fatima Divino Pastor 0.7771 Las Lomas 0.0388 Barrio Pilar Divino Pastor 0.4769 2 Jimenez Las Lomas 0.3198 3 Centeno Guell Las Lomas 0.6866 4 El Encanto Las Lomas 0.6182 5 Santa Cecilia Divino Pastor 0.9481 Divino Pastor 0.7160 6 Santa Eduviges Las Lomas 0.1431 Table 17. DEA weights for the inefficient EBAIS at Goicoechea 2

Appendix C: DEA RAM Results

The DEA-RAM for the multi-input and single output case is described in Chapter 2

(equations 15 through 20). For the multi-input, multi-output case we need to change the objective function, adding subjective weights for the different output dimensions as in

(28) and we also repeat constraint (16) for every output, as shown in (29).

∑ ∑ (28)

∑ (29)

In the next tables, the model results for the weights, input allocation and output allocation are displayed for both the previous period’s budget (10,724,481.71 dollars) and the current budget to allocate (13,941,826.23 dollars).

Inneficient Efficiency Frontier EBAIS Reference Weight Calle Blancos 1 0.1341 Barrio Pilar 1 Calle Blancos 2 0.5427 Jimenez Las Lomas 0.3231 Calle Blancos 2 0.4572 2 Divino Pastor Divino Pastor 0.5428 Table 18. DEA-RAM weights for the inefficient EBAIS at Goicoechea 2, with previous period’s budget

Inneficient Efficiency Frontier EBAIS Reference Weight Calle Blancos 2 0.5383 Centeno Guell Divino Pastor 0.4617 Table 19. DEA-RAM weights for the inefficient EBAIS at Goicoechea 2, with budget to allocate

Results for last period's budget (13941826.23 dollars) Results for budget to allocate (13941826.23 dollars) Time programmed Time used for Time programmed Time used for Total Annual Total Annual Name of the EBAIS for appointments appointments for appointments appointments Budget (dollars) Budget (dollars) (hours per year) (hours per year) (hours per year) (hours per year) Calle Blancos 1 842353.79 1752 1329 873531.49 1656 1245.6 Calle Blancos 2 842353.79 1752 1329 873531.49 1656 1245.6 Santa Cecilia 1333918.33 1752 1684.32 1333918.33 1752 1684.32 Centeno Guell 842353.79 1752 1329 1086095.217 1700.323851 1448.16 Divino Pastor 1123414.437 1708.105666 1483.722894 1333918.33 1752 1684.32 Santa Eduviges 1333918.33 1752 1684.32 1333918.33 1752 1684.32 El Encanto 1333918.33 1752 1684.32 1333918.33 1752 1684.32 Barrio Fatima 873531.49 1656 1245.6 3565544.893 1899.676149 1245.6 Las Lomas 1333918.33 1752 1684.32 1333918.33 1752 1684.32 Barrio Pilar Jimenez 864801.0928 1699.894334 1398.557106 873531.49 1656 1245.6 Table 20. DEA-RAM input allocation for the EBAIS at Goicoechea 2

Results for last period's budget Results for budget to allocate (13941826.23 dollars) (13941826.23 dollars) Medical Medical Home Visit by Home Visit by Name of the EBAIS Consultations Consultations ATAPS (annual) ATAPS (annual) (annual) (annual) Calle Blancos 1 17020 810 15797 771 Calle Blancos 2 17020 810 15797 771 Santa Cecilia 25355 872 25355 872 Centeno Guell 17020 810 20209.99344 817.6323851 Divino Pastor 20984.77038 825.8195028 25355 872 Santa Eduviges 25355 872 25355 872 El Encanto 25355 872 25355 872 Barrio Fatima 15797 771 15797 771 Las Lomas 25355 872 25355 872 Barrio Pilar Jimenez 17617.7978 844.7381165 15797 771 Total 206879.5682 8359.557619 210172.9934 8261.632385 Table 21. DEA-RAM output allocation for the EBAIS at Goicoechea 2

Appendix D: Calculating the Gini Measure

Tables 22 through 24 summarize the values obtained for the Gini measure for each of the three equity units evaluated, using formula (23).

∑ ∑ | | (23)

∑

Is important to clarify also that the allocated budget in dollars for each of the EBAIS in the year 2011 is and the proportion of equity units q is calculated as follows:

(30)

∑

Absolute differences Barrio Barrio Calle Calle Centeno Divino Santa Santa DMU i Ei qi Xij El Encanto Las Lomas Fatima Pilar Blancos 1 Blancos 2 Guell Pastor Cecilia Eduviges 1 Barrio Fatima 651 0.11941 1,241,119.09 0 0 0 0 0 0 0 0 0 0 2 Barrio Pilar Jimenez 554 0.10161 948,110.87 12,905.32 0 0 0 0 0 0 0 0 0 3 Calle Blancos 1 471 0.08639 842,353.79 6,638.81 3,687.41 0 0 0 0 0 0 0 0 4 Calle Blancos 2 446 0.08180 873,531.49 2,775.11 11,203.04 6,556.04 0 0 0 0 0 0 0 5 Centeno Guell 361 0.06621 624,064.84 7,662.84 635.34 1,862.65 6,788.69 0 0 0 0 0 0 6 Divino Pastor 699 0.12821 1,333,918.33 153.81 13,987.76 7,239.59 2,874.35 8,313.13 0 0 0 0 0 7 El Encanto 363 0.06658 603,752.20 10,543.57 1,776.51 3,926.47 8,770.81 1,573.92 11,406.74 0 0 0 0 8 Las Lomas 640 0.11739 859,450.98 43,069.26 23,964.62 24,634.08 32,234.96 16,349.91 46,396.09 13,650.17 0 0 0 9 Santa Cecilia 709 0.13004 1,894,102.13 64,766.52 69,171.31 54,089.01 41,349.18 44,260.62 69,374.41 47,596.99 110,578.62 0 0 10 Santa Eduviges 558 0.10235 1,504,078.00 52,569.76 55,798.49 43,724.75 33,636.87 35,719.73 56,314.03 38,350.44 88,598.00 1,739.24 0 GINI MEASURE TOTAL 5,452 1 10,724,481.71 201,084.99 180,224.49 142,032.59 125,654.86 106,217.31 183,491.28 99,597.59 199,176.61 1,739.24 0.00 0.115550475 Table 22. Gini measure for the budget allocation in the year 2011, using the users with hypertension as the equity unit.

Absolute differences Barrio Barrio Calle Calle Centeno Divino Santa Santa El Encanto Las Lomas DMU i Ei qi Xij Fatima Pilar Blancos 1 Blancos 2 Guell Pastor Cecilia Eduviges 1 Barrio Fatima 304 0.15925 1,241,119.09 0 0 0 0 0 0 0 0 0 0 2 Barrio Pilar Jimenez 193 0.10110 948,110.87 12,267.34 0 0 0 0 0 0 0 0 0 3 Calle Blancos 1 182 0.09534 842,353.79 17,743.79 4,795.86 0 0 0 0 0 0 0 0 4 Calle Blancos 2 139 0.07281 873,531.49 13,935.07 19,728.32 14,130.36 0 0 0 0 0 0 0 5 Centeno Guell 145 0.07596 624,064.84 19,753.53 8,600.93 10,068.66 15,298.43 0 0 0 0 0 0 6 Divino Pastor 243 0.12729 1,333,918.33 1,293.23 14,858.18 8,012.92 2,072.40 8,886.06 0 0 0 0 0 7 El Encanto 136 0.07124 603,752.20 16,327.70 6,195.10 7,852.19 12,841.83 4,482.32 17,623.36 0 0 0 0 8 Las Lomas 256 0.13410 859,450.98 63,812.72 39,810.88 38,712.77 46,834.74 26,780.22 68,690.55 23,740.98 0 0 0 9 Santa Cecilia 8 0.00419 1,894,102.13 220,965.51 188,494.23 160,102.05 151,286.04 122,801.27 237,252.50 123,581.22 218,743.40 0 0 10 Santa Eduviges 303 0.15872 1,504,078.00 17,397.19 2,349.61 3,762.17 15,607.67 538.65 18,884.39 4,314.46 40,147.24 105,039.03 0 GINI MEASURE TOTAL 1,909 1 10,724,481.71 383,496.07 284,833.11 242,641.13 243,941.10 163,488.51 342,450.79 151,636.66 258,890.63 105,039.03 0.00 0.202939135 Table 23. Gini measure for the budget allocation in the year 2011, using the users with diabetes as the equity unit.

Absolute differences Barrio Barrio Calle Calle Centeno Divino Santa Santa El Encanto Las Lomas DMU i Ei qi Xij Fatima Pilar Blancos 1 Blancos 2 Guell Pastor Cecilia Eduviges 1 Barrio Fatima 147 0.16207 1,241,119.09 0 0 0 0 0 0 0 0 0 0 2 Barrio Pilar Jimenez 108 0.11907 948,110.87 34,574.99 0 0 0 0 0 0 0 0 0 3 Calle Blancos 1 95 0.10474 842,353.79 29,414.07 13,710.98 0 0 0 0 0 0 0 0 4 Calle Blancos 2 55 0.06064 873,531.49 29,043.85 31,270.16 24,384.77 0 0 0 0 0 0 0 5 Centeno Guell 79 0.08710 624,064.84 33,584.97 19,166.99 19,456.14 25,033.36 0 0 0 0 0 0 6 Divino Pastor 114 0.12569 1,333,918.33 3,282.36 16,377.70 9,362.95 672.40 9,886.24 0 0 0 0 0 7 El Encanto 36 0.03969 603,752.20 22,829.85 23,717.98 18,724.23 14,718.26 15,207.05 24,462.03 0 0 0 0 8 Las Lomas 98 0.10805 859,450.98 31,477.71 15,109.64 16,766.83 24,076.53 10,521.39 33,937.82 8,011.36 0 0 0 9 Santa Cecilia 7 0.00772 1,894,102.13 216,587.99 185,150.17 157,131.00 148,205.03 120,600.14 232,547.67 121,451.74 215,712.05 0 0 10 Santa Eduviges 168 0.18523 1,504,078.00 50,292.03 22,779.29 26,088.07 38,759.90 16,001.67 54,238.80 11,687.49 17,368.20 155,240.65 0 GINI MEASURE TOTAL 907 1 10,724,481.71 451,087.82 327,282.93 271,913.99 251,465.46 172,216.50 345,186.31 141,150.59 233,080.25 155,240.65 0.00 0.218996551 Table 24. Gini measure for the budget allocation in the year 2011, using the users over 65 years with diabetes as the equity unit.

Appendix E: DEA RAM with Equity Results

We consider:

 Input 1: Total Annual Budget (dollars)

 Input 2: Time programmed for appointments (hours per year)

 Input 3: Time used for appointments (hours per year)

 Output 1: Medical Consultations (annual)

 Ouput 2: Visit by ATAPS (annual)

 E1: environmental constraint considered: users with hypertension.

 E2: environmental constraint considered: users over 65 years and with

diabetes.

 E3: environmental constraint considered: users with diabetes.

Tables 25 through 36 display the input and output allocation per EBAIS and per δ value used.

δ= 0.011552 δ= 0.02 Name of the EBAIS Input 1 Input 2 Input 3 Output 1 Output 2 Input 1 Input 2 Input 3 Output 1 Output 2 Barrio Fatima 1291817.7 1743.2212 1644.2008 24481 863 1267860.3 1738.2256 1621.3708 23984 858 Barrio Pilar Jimenez 1099251.3 1752 1514.6945 21376 842 1078865.1 1752 1499.9586 21030 840 Calle Blancos 1 934596.22 1668.7332 1303.7909 17065 784 917263.64 1665.119 1287.274 16705 781 Calle Blancos 2 884940.05 1712.6447 1346.5932 17343 813 868528.37 1730.4475 1399.9833 17870 841 Centeno Guell 732362.75 1752 1290.5541 15137 714 793279.89 1752 1311.8469 16180 767 Divino Pastor 1333918.3 1752 1684.32 25355 872 1333918.3 1752 1684.32 25355 872 El Encanto 736455.4 1752 1291.9846 15207 717 797712.96 1752 1313.3964 16256 771 Las Lomas 1269964.7 1738.6644 1623.3762 24027 858 1246412.5 1733.7533 1600.9324 23538 853 Santa Cecilia 1333918.3 1752 1684.32 25355 872 1333918.3 1752 1684.32 25355 872 Santa Eduviges 1107256.9 1704.7365 1468.3258 20649 822 1086722.2 1700.4546 1448.7575 20223 818 δ= 0.0555 δ= 0.1155 Barrio Fatima 1151754.1 1734.8991 1533.7744 21954 841 873531 1656 1245.6 15797 771 Barrio Pilar Jimenez 1164448.7 1752 1561.8214 22481 851 1301640 1745.27 1653.56 24685 865 Calle Blancos 1 990027.75 1752 1546.5741 20692 884 1106670 1752 1520.06 21502 843 Calle Blancos 2 937426.43 1669.3234 1306.4879 17124 785 1047870 1752 1588.39 21673 891 Centeno Guell 842353.79 1752 1329 17020 810 848162 1734.11 1313.46 16792 803 Divino Pastor 1236633.4 1752 1613.999 23705 860 1154510 1714.59 1513.35 21630 833 El Encanto 842353.79 1752 1329 17020 810 852902 1752 1336.62 17199 811 Las Lomas 1132270.4 1709.9523 1492.1621 21169 828 1057080 1752 1484.21 20661 837 Santa Cecilia 1254284.4 1735.3947 1608.4338 23702 855 1170990 1718.03 1529.06 21972 836 Santa Eduviges 1172929 1718.4305 1530.9072 22013 837 1311120 1752 1667.84 24969 869

Table 25. Input and output allocation, E1, with previous period’s budget

δ= 0.011552 δ= 0.02 Name of the EBAIS Input 1 Input 2 Input 3 Output 1 Output 2 Input 1 Input 2 Input 3 Output 1 Output 2 Barrio Fatima 1686231.35 1899.67615 1245.6 15797 771 1575417.54 1995.67615 1684.32 25355 872 Barrio Pilar Jimenez 1434871.18 1679.54824 1353.21545 18142 796 1340575.97 1752 1684.32 25355 872 Calle Blancos 1 1219944.11 1728.23406 1575.70967 22989 847 1139773.23 1711.51681 1499.3118 21324 829 Calle Blancos 2 1155127.08 1714.7184 1513.94307 21643 833 1079215.77 1698.88935 1441.60431 20067 816 Centeno Guell 934975.11 1656 1245.6 15797 771 873531.49 1656 1245.6 15797 771 Divino Pastor 1810499.3 1752 1684.32 25355 872 1691518.99 1752 1684.32 25355 872 El Encanto 940200.012 1656 1245.6 15797 771 878413.028 1656 1245.6 15797 771 Las Lomas 1657706.21 1752 1684.32 25355 872 1548766.98 1697.9177 1437.16389 19970 815 Santa Cecilia 1836341.39 1752 1684.32 25355 872 1715662.81 1656 1245.6 15797 771 Santa Eduviges 1265930.48 1737.82315 1619.53181 23944 857 1350339.04 1752 1684.32 25355 872 δ= 0.0555 δ= 0.1155 Barrio Fatima 1519608.98 1899.67615 1245.6 15797 771 877445.93 1899.67615 1245.6 15797 771 Barrio Pilar Jimenez 1640669.81 1656 1245.6 15797 771 1790099.14 1656 1245.6 15797 771 Calle Blancos 1 1394916.49 1752 1684.32 25355 872 1521963.04 1656 1245.6 15797 771 Calle Blancos 2 1320802.98 1700.32385 1448.16 20210 818 1441099.39 1752 1684.32 25355 872 Centeno Guell 1069075.37 1656 1245.6 15797 771 1166444.88 1700.32385 1448.16 20210 818 Divino Pastor 1631597.58 1752 1684.32 25355 872 1682118.84 1752 1684.32 25355 872 El Encanto 873531.49 1656 1245.6 15797 771 873531.49 1656 1245.6 15797 771 Las Lomas 1493902.51 1752 1684.32 25355 872 1540160.13 1752 1684.32 25355 872 Santa Cecilia 1654886.12 1752 1684.32 25355 872 1706128.49 1752 1684.32 25355 872 Santa Eduviges 1342834.91 1752 1684.32 25355 872 1342834.91 1752 1684.32 25355 872

Table 26. Input and output allocation, E1, with current budget to allocate

δ= 0.07 δ= 0.109498 Name of the EBAIS Input 1 Input 2 Input 3 Output 1 Output 2 Input 1 Input 2 Input 3 Output 1 Output 2 Barrio Fatima 1613040 1752 1684.32 25355 872 1417480 1752 1684.32 25355 872 Barrio Pilar Jimenez 1185090 1720.97 1542.5 22265 839 1258710 1736.32 1612.66 23794 856 Calle Blancos 1 1042440 1691.22 1406.56 19304 808 1107200 1704.73 1468.27 20648 822 Calle Blancos 2 639778 1752 1307.41 14062 655 722074 1750.2 1439.93 16528 773 Centeno Guell 866871 1701.41 1453.12 18222 871 920726 1665.84 1290.57 16777 781 Divino Pastor 1250930 1710.24 1634.2 23273 835 1328640 1750.9 1679.29 25246 871 El Encanto 603752 1752 1245.6 12936 601 603752 1752 1245.6 12936 601 Las Lomas 1075360 1744.17 1648.53 22511 915 1142170 1712.02 1501.59 21374 830 Santa Cecilia 603752 1752 1245.6 12936 601 603752 1752 1245.6 12936 601 Santa Eduviges 1843470 1752 1684.32 25355 872 1619970 1752 1684.32 25355 872 δ= 0.218997 Barrio Fatima 1613038.62 1752 1684.32 25355 872 Barrio Pilar Jimenez 1185089.6 1720.96619 1542.49548 22265 839 Calle Blancos 1 1042439.92 1691.22084 1406.55922 19304 808 Calle Blancos 2 639778.365 1752 1307.41257 14061 655 Centeno Guell 866871.098 1701.41012 1453.12425 18222 871 Divino Pastor 1250927.91 1710.23518 1634.20222 23272 835 El Encanto 603752.2 1752 1245.6 12936 601 Las Lomas 1075359.08 1744.16767 1648.52625 22511 915 Santa Cecilia 603752.2 1752 1245.6 12936 601 Santa Eduviges 1843472.71 1752 1684.32 25355 872 Table 27. Input and output allocation, E2, with last period’s budget

δ= 0.07 δ= 0.1094 Name of the EBAIS Input 1 Input 2 Input 3 Output 1 Output 2 Input 1 Input 2 Input 3 Output 1 Output 2 Barrio Fatima 2095236 1869.382 1448.16 20210 818 1996365 1995.676 1684.32 25355 872 Barrio Pilar Jimenez 1539357 1752 1684.32 25355 872 1466717 1752 1684.32 25355 872 Calle Blancos 1 1354064 1752 1684.32 25355 872 1290168 1742.877 1642.629 24447 862 Calle Blancos 2 873531.5 1656 1245.6 15797 771 1207964 1725.736 1564.293 22740 844 Centeno Guell 1126011 1656 1245.6 15797 771 1072877 1697.567 1435.563 19936 815 Divino Pastor 1624877 1752 1684.32 25355 872 1548202 1694.143 1419.915 19595 811 El Encanto 873531.5 1656 1245.6 15797 771 873531.5 1656 1245.6 15797 771 Las Lomas 1396824 1752 1684.32 25355 872 1330910 1656 1245.6 15797 771 Santa Cecilia 663839.4 1730.618 1245.6 13573 639 873531.5 1656 1245.6 15797 771 Santa Eduviges 2394555 1752 1684.32 25355 872 2281560 1752 1684.32 25355 872 δ= 0.2189 Barrio Fatima 873531.5 1899.676 1245.6 15797 771 Barrio Pilar Jimenez 1704459 1718.494 1531.197 22019 837 Calle Blancos 1 1499292 1752 1684.32 25355 872 Calle Blancos 2 873531.5 1656 1245.6 15797 771 Centeno Guell 1246780 1733.83 1601.283 23546 853 Divino Pastor 1799151 1752 1684.32 25355 872 El Encanto 873531.5 1656 1245.6 15797 771 Las Lomas 1546638 1752 1684.32 25355 872 Santa Cecilia 873531.5 1656 1245.6 15797 771 Santa Eduviges 2651380 1752 1684.32 25355 872

Table 28.Input and output allocation, E2, with current budget to allocate

δ= 0.06 δ= 0.08 Name of the EBAIS Input 1 Input 2 Input 3 Output 1 Output 2 Input 1 Input 2 Input 3 Output 1 Output 2 Barrio Fatima 1588517.3 1752 1684.32 25355 872 1499707.8 1752 1684.32 25355 872 Barrio Pilar Jimenez 1043319.6 1691.4043 1407.3975 19322 808 1059449.5 1694.7677 1422.7683 19657 812 Calle Blancos 1 983855.81 1679.0049 1350.7322 18087 795 999066.4 1682.1766 1365.227 18403 799 Calle Blancos 2 751406.36 1752 1498.9404 17549 822 794250.79 1748.744 1511.5149 18231 857 Centeno Guell 783841.17 1697.8256 1255.3339 15027 721 828535 1752 1324.1698 16783 798 Divino Pastor 1313609.7 1747.7652 1664.9671 24933 868 1333918.3 1752 1684.32 25355 872 El Encanto 735188.96 1752 1376.2288 16061 754 777108.69 1690.3117 1245.6 14774 710 Las Lomas 1337698.8 1752 1684.32 25355 872 1333918.3 1752 1684.32 25355 872 Santa Cecilia 603752.2 1752 1245.6 12936 601 603752.2 1752 1245.6 12936 601 Santa Eduviges 1583291.9 1752 1684.32 25355 872 1494774.6 1752 1684.32 25355 872 δ= 0.16 δ= 0.2029 Barrio Fatima 1281846.6 1752 1646.6808 24472 865 883772.79 1658.1355 1255.3593 16010 773 Barrio Pilar Jimenez 1205470.2 1725.216 1561.9169 22688 844 1261901.1 1746.5941 1626.298 24035 860 Calle Blancos 1 1136764.6 1710.8895 1496.4448 21262 829 1189979.3 1752 1580.2758 22914 854 Calle Blancos 2 868188.37 1672.4521 1259.8928 16007 778 908830.34 1752 1377.0516 18147 818 Centeno Guell 905664.13 1752 1374.7629 18093 818 948060.43 1752 1405.4084 18812 823 Divino Pastor 1277663.6 1752 1684.32 24830 885 1333918.3 1752 1684.32 25355 872 El Encanto 849450.5 1752 1334.1297 17140 811 889215.31 1659.2704 1260.5457 16123 774 Las Lomas 1079449.8 1719.1797 1534.3313 21181 860 1127006.9 1752 1534.7572 21847 846 Santa Cecilia 842353.79 1752 1329 17020 810 847878.85 1752 1443.8239 18282 866 Santa Eduviges 1277630 1740.2627 1630.6808 24186 860 1333918.3 1752 1684.32 25355 872

Table 29. Input and output allocation, E3, with previous period’s budget

δ= 0.06 δ= 0.08 Name of the EBAIS Input 1 Input 2 Input 3 Output 1 Output 2 Input 1 Input 2 Input 3 Output 1 Output 2 Barrio Fatima 2086404 1904.549 1267.869 16282 776 2041814 1899.676 1245.6 15797 771 Barrio Pilar Jimenez 1324592 1750.055 1675.433 25161 870 1296283 1744.152 1648.456 24574 864 Calle Blancos 1 1249097 1734.313 1603.491 23594 853 1222402 1728.747 1578.052 23040 848 Calle Blancos 2 953981 1672.775 1322.263 17467 789 933592.6 1668.524 1302.835 17044 784 Centeno Guell 995160 1681.362 1361.504 18322 798 973891.6 1656 1245.6 15797 771 Divino Pastor 1667751 1752 1684.32 25355 872 1632108 1752 1684.32 25355 872 El Encanto 933391.5 1668.482 1302.643 17040 784 913443.1 1664.322 1283.633 16626 780 Las Lomas 1756972 1752 1684.32 25355 872 1719422 1752 1684.32 25355 872 Santa Cecilia 894935.3 1660.463 1265.996 16241 776 1173772 1710.579 1495.024 21231 828 Santa Eduviges 2079541 1752 1684.32 25355 872 2035098 1752 1684.32 25355 δ= 0.16 δ= 0.2029 Barrio Fatima 1024084 1899.676 1245.6 15797 771 873531.5 1899.676 1245.6 15797 771 Barrio Pilar Jimenez 1399924 1656 1245.6 15797 771 1418118 1656 1245.6 15797 771 Calle Blancos 1 1320135 1749.126 1671.186 25068.85 868.9763 1337293 1752 1684.32 25355 872 Calle Blancos 2 1008235 1679.647 1353.667 18151.35 795.8786 1021339 1686.821 1386.451 18865.6016 803.4261 Centeno Guell 1051756 1656 1245.6 15797 771 1065426 1656 1245.6 15797 771 Divino Pastor 1762598 1752 1684.32 25355 872 1785506 1752 1684.32 25355 872 El Encanto 986474.7 1679.551 1353.228 18141.79 795.7776 999295.7 1669.503 1307.309 17141.3918 785.2063 Las Lomas 1856894 1752 1684.32 25355 872 1881027 1752 1684.32 25355 872 Santa Cecilia 1333918 1752 1684.32 25355 872 1333918 1752 1684.32 25355 872 Santa Eduviges 2197808 1752 1684.32 25355 872 2226372 1752 1684.32 25355 872 δ= 0.22 Barrio Fatima 873531.5 1899.676 1245.6 15797 771 Barrio Pilar Jimenez 1418118 1656 1245.6 15797 771 Calle Blancos 1 1337293 1752 1684.32 25355 872 Calle Blancos 2 1021339 1686.821 1386.451 18865.6 803.4261 Centeno Guell 1065426 1656 1245.6 15797 771 Divino Pastor 1785506 1752 1684.32 25355 872 El Encanto 999295.7 1669.503 1307.309 17141.39 785.2063 Las Lomas 1881027 1752 1684.32 25355 872 Santa Cecilia 1333918 1752 1684.32 25355 872 Santa Eduviges 2226372 1752 1684.32 25355 872

Table 30. Input and output allocation, E3, with current budget to allocate

As the program also gives the corresponding efficiency weights, we include in this appendix the matrices of weights for the three equity units evaluated at the maximum δ value desired (this is the value of the Gini measure calculated in Appendix D). Is important to notice that with the current budget to allocate, there exist significantly less inefficient units after the allocation. 70

Inneficient Efficiency Frontier Reference Set EBAIS Reference Weight

Barrio Pilar Calle Blancos 2 0.0701049 Jimenez Divino Pastor 0.929895 Calle Blancos 1 0.462292 Calle Blancos 1 Divino Pastor 0.537708 Calle Blancos 1 0.269991 Calle Blancos 2 Divino Pastor 0.406853 Las Lomas 0.323156 Calle Blancos 1 0.813694 Centeno Guell Calle Blancos 2 0.186306 Calle Blancos 2 0.389691 Divino Pastor Divino Pastor 0.610309 Calle Blancos 1 0.978541 El Encanto Divino Pastor 0.0214587 Calle Blancos 1 0.563184 Las Lomas Divino Pastor 0.436816 Calle Blancos 2 0.353898 Santa Cecilia Divino Pastor 0.646102 Calle Blancos 1 0.0463741 Santa Eduviges Divino Pastor 0.953626 Table 31. Weights, E1, with previous period’s budget

Inneficient Efficiency Frontier Reference Set EBAIS Reference Weight

Centeno Calle Blancos 2 0.538293 Guell Divino Pastor 0.461707 Table 32. Weights, E1, with current budget to allocate.

Efficiency Frontier Reference Set Inneficient EBAIS

Reference Weight Calle Blancos 2 0.0349435 Barrio Fátima Divino Pastor 0.6419 Las Lomas 0.323156 Calle Blancos 2 0.401666 Barrio Pilar Jiménez Divino Pastor 0.598334 Calle Blancos 2 0.702077 Calle Blancos 1 Divino Pastor 0.297923 Calle Blancos 2 0.102064 Calle Blancos 2 Divino Pastor 0.897936 Calle Blancos 2 0.263015 Divino Pastor Divino Pastor 0.736985 Calle Blancos 1 0.134076 Las Lomas Calle Blancos 2 0.489595 Divino Pastor 0.376329 Calle Blancos 1 0.00664006 Santa Eduviges Divino Pastor 0.99336 Table 33. Weights, E2, with previous period’s budget

Inneficient Efficiency Frontier Reference Set EBAIS Reference Weight Barrio Pilar Calle Blancos 2 0.349021 Jiménez Divino Pastor 0.650979 Calle Blancos 2 0.189272 Centeno Guell Divino Pastor 0.810728 Table 34. Weights, E2, with current budget to allocate

Inneficient Efficiency Frontier Reference Set EBAIS Reference Weight Calle Blancos 2 0.977755 Barrio Fátima Divino Pastor 0.022245 Calle Blancos 1 0.0937661 Barrio Pilar Calle Blancos 2 0.0563116 Jiménez Divino Pastor 0.849922 Calle Blancos 1 0.292818 Calle Blancos 1 Divino Pastor 0.707182 Calle Blancos 1 0.864765 Calle Blancos 2 Divino Pastor 0.135235 Calle Blancos 1 0.784959 Centeno Guell Divino Pastor 0.215041 Calle Blancos 2 0.965933 El Encanto Divino Pastor 0.0340666 Calle Blancos 1 0.420924 Las Lomas Divino Pastor 0.579076 Calle Blancos 1 0.676844 Santa Cecilia Las Lomas 0.323156 Table 35. Weights, E3, with previous period’s budget

Efficiency Frontier Reference Inneficient Set EBAIS Reference Weight Calle Blancos 2 0.678949 Calle Blancos 2 Divino Pastor 0.321051 Calle Blancos 2 0.859344 El Encanto Divino Pastor 0.140656 Table 36.Weights, E3, with current budget to allocate