Mdb As A Sp Tool June 2006

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Some Applications of Multi-directional Benchmarking as a Tool for Strategic Planning

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Mdb As A Sp Tool June 2006

  1. 1. Multi-directional benchmarking as a strategic planning tool Authors: Fučkan Gudac ðurñica Petrov Tomislav Graduate School of Economics & Business, Croatian Financial Services University of Zagreb, Supervisory Agency, Kennedyev trg 6, Gajeva 5, 10 000 Zagreb, Croatia 10 000 Zagreb, Croatia Tel: +385 1/2383-105 Tel: +385 1/4891-807 Mob: 098/271-084 Mob: 091/5977-058 djurdjica.gudac@efzg.hr tomislav.petrov@hanfa.hr Abstract This paper deals with the methods of analyzing competitive markets. The aim of this paper is to demonstrate how Multi-directional benchmarking can be used as a practical tool for strategic planning, a tool capable of providing managers with detailed information on possible improvements of their performance. The empirical economics theory of competition treats companies within the industry as black boxes, and presumes that companies differ primarily in size and relative efficiency. Managers were all but absent in economic models, with virtually no latitude to affect competitive outcomes. This paper will attempt to establish the framework that will enable managers to mathematically explore the company's relative position within the industry, be it a high-tech, low-tech or service industry. The introduced mathematical treatment of the firm can serve as a starting point to bring economic thinking to bear on practice. We used the world production frontier, Croatian manufacturing industries production frontier, Croatian banking sector production frontier and Croatian construction firm's production
  2. 2. frontier as examples that Pareto-efficient unit of assessment doesn't have to be well chosen benchmark. The examples suggest that efficiency may be induced by undercapitalized labor and that frontier shift may be induced by declining value of labor and capital inputs. The measurement of efficiency with reference to frontier in two different time periods causes biased results on Malmquist TFP indexes. Also, inefficiency may be caused by the analyst's superficial knowledge about the extent of a market. The Farrell index ignores the analyst preferences among inputs and outputs and differences in their utilization, while Multi-directional benchmarking is focused on the analyst's benchmark selection procedure and subjective performance improvement direction. Multi-directional benchmarking reveals sources of inefficiency and allow for the input expansion possibility. We suggest that the analyst should calculate target levels for inefficient units of assessment with any known or unknown procedure. The analyst should recognize the confronting problem and choose the appropriate improvement direction procedure for concrete choice of inputs and outputs. At the end, we explored the alternative ways to measure relative technical efficiency and total factor productivity change. We proposed a new way to generalize one-dimensional productivity. We suggested to ex-ante incorporate the analyst judgments about relative importance of inputs and outputs into analysis using some multiple criteria decision making procedure the analyst consider the most appropriate. The proposed total factor productivity (TFP) measure is dimensionless, with the degree of partial homogeneity 1 in every output and degree of partial homogeneity -1 in every input. These desirable properties make the proposed TFP measure look like an appropriate tool for ranking the units of assessment. Key words: Strategic planning, benchmarking, company's relative position EconLit Classification: C61 (Programming Models) D21 (Firm Behavior) D24 (Total Factor Productivity)
  3. 3. 1. Introduction Competitive strategy, and its core disciplines of industry analysis, competitor analysis, and strategic positioning, is now an accepted part of management practice. Today, managers look for concrete ways to tackle strategic planning's difficult questions quickly. Thus to reveal the important differences among industries, to determine trends of industry evolution, and to determine the company's relative position within the industry are all important components of the strategic planning process. Companies can never stop learning about their industry, their rivals, or ways to improve or modify their competitive position. Of course, we understand the distinction between relative technical efficiency and strategic position of the firm, distinction introduced in (Porter, 1996). In turbulent business times, managers are obliged to keep up to pace with any changes and to use analytical tools that will help them improve the company's performance. One of these trendy tools includes benchmarking models which emerged from microeconomic “learning from the best practice” theory. Benchmarking models have proven to be very effective in helping managers identify better business practices. This is the first step in the process known as benchmarking. The second step is to gather data about business processes inside identified “benchmark companies” and to adapt their business processes to fit into our company. This step is known as technology transfer or catching up the production frontier step. If our company is on the production frontier, we can improve current performance only through new ideas and innovation. Hence, benchmarking is extremely helpful in the strategic planning process. In summation, benchmarking process attempts to find examples of higher performance and endeavors to understand the business processes that ultimately lead to higher performance. This paper is arranged as follows. In section 2 we explained technical efficiency paradox through illustrative examples. Pareto efficient unit of assessment may not be a good benchmark unit due to analyst preferences among inputs and outputs. In section 3 we discuss the importance of preferred performance improvement direction for strategic planning purposes. In section 4 we illustrate our approach with a brief example. The emphasis in our approach is to allow input expansion possibility. In section 5 we deliver a link between the firm’s strategy and multidimensional deterministic frontiers. In section 6 we proposed a new TFP measure based on the analyst’s ex-ante incorporated judgments regarding relative importance of inputs and outputs. In section 7 we present concluding remarks and announce our further research.
  4. 4. 2. Motivation: technical efficiency paradox 2.1. Relative position of countries and industries Macroeconomics deals with aggregate economic entities, like countries and industries. Let's take a look at the world production frontier (Henderson, 2004), (Kumar, 2002). We took the aggregate output and aggregate inputs (capital stock and employment) from Penn World Tables. The frontier is defined relative to the “best practice” of countries in this sample. Of course, the constructed frontier is probably well below the “true” but unobservable frontier. The world production frontier unit output isoquant is presented in Figure 1. The empirically constructed technology is a Farrell polyhedral cone (Farrell, 1957), and isoquants are picewise linear. Croatian benchmarks are Hong Kong and Paraguay. C Luxembourg USA Hong Kong Paraguay Sierra Leone E 0 Figure 1 The world production frontier unit output isoquant What is the interpretation of the peculiar finding that Sierra Leone, one of the poorest countries in the world, is on the frontier? Sierra Leone is poor because it has low labor productivity induced with terribly undercapitalized labor and not because it makes inefficient use of the meager capital inputs that it has. Is it meaningful to measure other countries performance against such benchmark country as Sierra Leone? We argue it is not. Industry structure and specific attributes (McGahan, 1997) are important in explaining the dispersion of value-added, profitability and stock market performance within industries. The same Farrell polyhedral cone we used to find the Croatian manufacturing industries “best practice” and to monitor industries movement during the period. The following papers are testimony to the current importance of this topic: (Al-miman, 2004), (Bernstein, 2004), (Fu, 2004), (Grosskopf, 2005), (Ray, 2004) and (Singh, 2004).
  5. 5. The primary criterion for creating measure of “overall performance” of the industry (or company) is the amount of value-added1 produced by that industry (company). Obviously, larger industries2 (companies) can produce more value-added. Therefore, to compare industries (companies) that are different in size, we use productivity ratios. Productivity is traditionally defined as how much output is produced per unit of input. Labor productivity3 is the most often used and the most important measure of productivity. Improvement in productivity is the key to economic prosperity and to sustainable improvements in living standards. C 1997 year frontier Oil manufacturing Textile manufacturing 2001 year frontier E 0 Figure 2 The Croatian manufacturing industries production frontier unit output isoquant and frontier shift during the time The visualization of the Croatian manufacturing industries Farrell polyhedral cone frontier (Petrov, 2003) when the average number of employees per unit of value-added and the value of equity per unit of value-added define coordinate axes is presented in Figure 2. We can see from Figure 2 that the isoquant is almost horizontal. Thus, manufacturing industries differ by productivity of labor (the concept industry specific productivity of labor is often used) remarkably, while the difference in value-added/equity ratio is hardly noticeable. The Croatian manufacturing industries frontier shift came as a result of reduction in real value of equity. Productivity growth can sometimes occur as a result of reduction in inputs (employment and equity). Obviously, economies want to avoid reductions in employment when possible. The greatest goal therefore, is to achieve an improvement in productivity and an increase in 1 The value-added is a sum of gross wages and gross profit. 2 Sense of a word larger is having more inputs: equity, assets and employees. 3 Labor productivity in this survey is calculated by dividing the value-added by the average number of employees, based on working hours.
  6. 6. employment simultaneously. Other observations about Croatian manufacturing industries are very similar with observations described in papers (Al-miman, 2004) and (Bernstein, 2004). As we can see again, efficient industry is not necessarily good industry (textile manufacturing) and treatment of industries as “black boxes” fails to explain their performance. 2.2. Company's relative position within industries and markets Microeconomics deals with the behavior of individual economic units. Such individual economic units may be business firms. The theory of business firms describes the trade-offs that the firms face in terms of the kinds of products that they can produce, and the resources available to produce them. It explains how they play a role in the functioning of our economy and how they interact with other entities to form larger units - markets and industries. In the further text we will focus on the supply side of the markets. For each assessed firm we must first determine the extent of a market - its boundaries, both geographically and in terms of the range of products to be included in it. In other words, for each assessed firm we must determine the firms assessed firm compete against. To explain the former sentence with an example, we ask the following questions: Where construction of road overpasses or railways maintenance differs from construction of buildings, houses and apartments? Which attributes describe the construction industry “competitive subindustries”? Let’s take a look at the Croatian construction industry frontier and the apartment construction company’s frontier, presented in Figure 3. As we see, the important aspect of inefficiency causation may be according to the competitive subindustry assessed company belongs to. C Construction of buildings Road construction Railways Apartments maintenance maintenance E 0 Figure 3 The Company's relative position within the industry and market: Croatian construction industry and apartment construction companies
  7. 7. 3. Imposed versus preferred performance improvement direction of the company The lion's share of economic efficiency theory and most analytical methods for the analysis of competitive markets emerged from public policy standpoint. Public policy analysts usually imposed the improvement direction for the competitive firms in previous industry analysis. We argue that only managers can connect a company's relative position in the marketplace with a company's available resources and other elements that will allow the firm to perform at its best. In our approach, the challenging question regarding the future strategic improvement direction of the firm is best left to the business managers to answer. 3.1. Radial relative technical efficiency analysis The standard version of Data Envelopment Analysis (DEA) uses radial Farrell index of relative technical efficiency (Charnes, 1978). As we have seen, Farrell efficiency index performs badly when the technology is characterized by limited substitution possibilities. In that case, the lion's share of the sample of assessed units will be measured against dominated benchmark units and the efficiency value is practically without economic interpretation and void of managerial information. An extreme example of such a case is the Leontief isoquant when only one assessed unit is undominated and hence determines the frontier. Also, the Farrell index forces the relative improvement potentials to be identical for all inputs (or outputs), ignoring the differences in the utilization of the various inputs (or outputs). In other words, analysts can't draw specific conclusions with respect to possible managerial and policy implications from Farrell index. 3.2. Multi-directional benchmarking analysis Benchmarking models provide the means for mutual comparison of companies within an industry, as well as for mutual comparison of industries. During the last decade, many multifactor based gap analysis methods have been developed. Those methods are fundamental for performance evaluation and benchmarking. Benchmarking is a process of defining valid measures of performance comparison among peer firms, using them to determine the relative positions of the peer firms and ultimately, establishing a standard of excellence. Multi-directional benchmarking analysis differs from DEA in the way in which relative efficiency is measured. The focus is on the benchmark selection procedure (Hougaard, 2002). The measurement of
  8. 8. inefficiency is a secondary issue. It is advantageous from a managerial viewpoint in that it provides more relevant performance information, suggests where to improve performance for the individual companies and it allows for a more substantive analysis of the effect of external variables on the inefficiency scores. Such analysis should be performed in each direction4 separately with marginal analysis, conditional analyses, and multivariate analyses of variance. For policy makers this information is useful. Also, potential improvements idea (Asmild, 2003) is introduced. The focus is on analyzing managerial performance by estimating the improvement potential taken separately for each company. After establishing a standard of excellence through benchmark selection procedure and by estimating the firm's improvement potential, the analyst can choose the firm he prefers and evaluate the multifactor performance of every firm that the assessed firm competes against. Performance evaluation against the most preferred firm can be achieved by using the Cobb- Douglass weighted product model (Cobb, 1928) or by any other Multiple Criteria Decision Making procedure5. It is also important to monitor the firms multifactor performance through time by applying different variations of directional Malmquist productivity change index proposed in (Caves, 1982). 4. Multi-directional benchmarking models: methodology and an illustrative example Unit of assessment is the entity whose relative (comparative) efficiency we wish to measure against other entities of its kind, known as benchmark units. Suppose there are n benchmark units. Unit of assessment and benchmark units transform inputs into outputs. The identification of the inputs and the outputs as well as environmental factors that impact the transformation process is crucial for economic applications. Suppose m inputs and s outputs was selected. Let the input and output data for benchmark unit j, ( j = 1,2,..., n ) be x j = ( x1 j , x 2 j ,..., x mj ) and y j = ( y1 j , y 2 j ,..., y sj ) , respectively. We can identify benchmark unit j [ ] with vector ( x j , y j ) ∈ M 1,m + s . The benchmark unit’s input-data matrix is X = xij ∈ M mn and the 4 In our approach, the analyst should choose directions and benchmarks through definition of competitive firms or by incorporating subjective standard of excellence. 5 We argue it is wrong to evaluate performance against the benchmark frontier, like in (Bogetoft, 2004) or other benchmarking papers.
  9. 9. [ ] output-data matrix is Y = y rj ∈ M sn . Also, let the input and output data for unit of assessment be x = ( x1 , x 2 ,..., x m ) and y = ( y1 , y 2 ,..., y s ) , respectively. We can identify unit of assessment with vector ( x, y ) ∈ M 1,m + s . In other words, unit of assessment and benchmark units are “black boxes”, illustrated in Figure 4. Unit Outputs Inputs of assessment Figure 4 Unit of assessment is black box that transforms inputs into outputs A model that measures the unit of assessment ( x, y ) performance in terms of output vector y proportional expansion potential against benchmark units while inputs are fixed at their current levels is given by the linear program (Charnes, 1978), (Zhu, 2003) σ * = max{σ | Xλ ≤ x, Yλ = σy, λ ≥ 0} . (1) σ ,λ A model that measures the unit of assessment ( x, y ) output q specific expansion potential against benchmark units while keeping other inputs and outputs at their current levels is given by the linear program (Zhu, 2000), (Zhu, 2003)  n n  σ q* = max σ q | ∑ λ j y qj = σ q y q , q ∈ { ,2,..., s}, ∑ λ j y kj ≥ y k , k ≠ q, Xλ ≤ x, λ ≥ 0 1 (2) σ q ,λ  j =1 j =1  Letting I ( y ) be the subjective output expansion “benchmark direction point” for the inefficient unit of assessment ( x, y ) , its performance against benchmark units can be measured by E MBD ( x, y ) = t * I ( y ) − y 1 , (3) where t * = max{t | Xλ ≤ x, Yλ = y + t ( I ( y ) − y ), λ ≥ 0} . (4) t ,λ
  10. 10. When all variables are measured on the same monetary scale, the value E MBD ( x, y ) directly indicates the monetary loss connected with unit of assessment ( x, y ) inefficiency against chosen benchmark units. Let's look at our example with just three economic variables: value-added, equity and employment. As we know, we can identify unit of assessment with vector ( y , k , l ) . Let Y , K and L represent benchmark unit’s value-added, equity and employment vector, respectively. The reference technology Farrell polyhedral cone is defined by {( y, k , l ) ∈ R 3 + | y ≤ Yλ , k ≥ Kλ , l ≥ Lλ , λ ≥ 0 . } (5) Let’s look at the business performance improvement in Hicks direction y * = max{y | y = Yλ , Kλ ≤ k , Lλ ≤ l , λ ≥ 0} , (6) y ,λ and the business performance improvement in Harrod direction σ * = max{σ | Yλ = σy, Kλ = σk , Lλ ≤ l , λ ≥ 0} . (7) σ ,λ We know (Kumar, 2002) that the “real world” business improvement direction is somewhere between two extreme cases, (6) and (7). So, for subjectively chosen s ∈ [0,1], business managers solve { } t * = max t | t ( sy * + (1 − s )σ * y ) ≥ Yλ , Kλ ≤ sk + (1 − s )σ * k , Lλ ≤ l , λ ≥ 0 . t ,λ (8) For unit of assessment ( y , k , l ) we identified its target input-output levels (t * ( sy * + (1 − s )σ * y ), sk + (1 − s )σ * k , l ) . (9) We can multiply this vector with a desirable positive number if we find such target more realistic. Our simple procedure suggests that Pareto-efficient units of assessment with undercapitalized labor can perform better if they add more capital input in creating value-added process. From a strategic planning perspective, we found the suggested target input-output levels to be much more effective than standard Data Envelopment Analysis target levels. There is no Data Envelopment Analysis model that allows for input expansion possibility. This is in fact a serious restriction because the greatest goal of every company is to achieve an improvement in productivity as well as an increase in its employment simultaneously. As we can see from Figure 5, inefficient units of assessment have different improvement directions, dependant on their current capital-labor ratio and analyst preferences. Improvement potential will be discussed in our future papers.
  11. 11. C E 0 Figure 5 Improvement directions and target input-output levels 5. Strategic groups and multi-directional benchmarking The first step in structural analysis within industries (Porter, 1979) is the mapping of the industry into strategic groups. A strategic group (Porter, 1998) is the group of firms in an industry following the same or a similar strategy along the strategic dimensions. Strategic dimensions include specialization, brand identification, push versus pull, channel selection, product quality, technological leadership, vertical integration, cost position, service, price policy, leverage, relationship with parent company and relationship to home and host government. The strategic dimensions are related and thus classifying firms into strategic groups requires judgments about what degree of difference in strategic dimensions are important. Clearly, the strategic groups (Hatten, 1987) are the groups of the firms that have the similar costs of the change in strategy and could be interpreted as the penalty costs of moving from one strategic group to another. Reasons for this are group-specific mobility barriers, factors that deter the movement of firms from one strategic position to another. Mobility barriers are the leading reason why some firms in the industry will be consistently more profitable than others. There is no conclusive empirical evidence that exists between the firm’s performance and affiliation to some strategic group. Some critique (Ketchen, 1996) suggests that methodology for treating the data is inadequate because strategy is multidimensional. Anyhow, the literature using multidimensional deterministic frontiers to determine strategic groups (Prior, 2006) is scarce although the advantages of the methodology are revealed in (Day, 1995). According to the methodology, the firm’s current trade-offs among inputs (capabilities) and outputs (dimensions of scope) indicate its capacity to respond to market disturbances and to adapt to new competitive
  12. 12. market conditions. If a firm lies on the frontier, it is labeled a strategic leader. If not, it is a strategic follower of the firm’s benchmark firms. Also, MDB can be used to obtain marginal rates of substitution between inputs and the marginal rates of transformation between outputs the same way as suggested in (Prior, 2006). Such rates can be used to approximate the trade off between the two inputs or outputs in the process of subjective valuation of inputs and outputs relative importance. To illustrate how the deterministic frontiers reflect the firm’s strategy, let’s take a look at the Croatian banking sector frontiers in the years 1995. (red) and 2000. (blue). As in (Jemrić, 2002), we used deposits as input because they are paid for in part by interest payments, and the funds raised provide the banks with the raw material for investments. As outputs we used consumer credit loans and “risk free” investments. Figure 6 illustrates frontier rotation. This is obviously a consequence of the change in the strategic leader bank’s strategy after the Croatian banking sector crisis in 1998. Although it is obvious that the largest Croatian commercial bank (green) replaced consumer credit loans with “risk free” investments, Farrell efficiency index indicate growth and frontier shift index (Färe, 1994) indicate “technological set-back”. The process of splitting the change in strategy from performance will be discussed in our future papers. RFI 0 CCL Figure 6 Rotation of the frontier reflects change in the best practice firm’s strategy
  13. 13. 6. Performance measurement in multi-directional benchmarking A variety of ranking the units of assessment and formulating the units of assessment strategy mathematical algorithms can assist the analysts to gain insight and understanding about the problems they face. But after modeling the problem and performing the computer analysis, decision-making often remains a difficult task. The ideal model that would entirely substitute the analyst’s creativity can’t be developed. Thus, the analyst had to use many models or even methodologies during the analysis, which would each from its own perspective, create a detailed image about every unit of assessment. Every model advises the decision maker what to do from its own perspective by the incorporated way of thinking. When the analyst understands the way of thinking incorporated into the models, their results should give him an enhanced insight and sharper intuition into what to do. It is very important to be aware that models just recommend decisions, and people make them. Generally, in decision making involving multiple criteria, the basic problem stated by the analysts concerns the way by which the final decision should be made. The success of unit’s of assessment analysis requires tools for measuring their achievements that contain all accomplished results. Such tools had to unleash measuring unit of assessment impact relatively toward their precedent impact, the same as measuring every unit of assessment impact relatively toward impact of operating units by which is sensible to compare. Since modern analyses pretend to reach more quality evaluation of overall state in units of assessment with as little as possible different indicators or models, and more realistically state the quality of their performance, we have to suggest the methodology that we rate the best for this purpose. It is known (Portela, 2004) that the use of distance functions as a means to calculate total factor productivity change may introduce some bias in the analysis. For example, the Malmquist TFP index (Färe, 1994) relies on radial measures and does not account for slacks. In real world applications, slacks are often important sources of inefficiency. Some authors tried to solve this problem through the use of non-radial efficiency measures. The most recent survey of these measures can be found in (Thrall, 2000) and a new types of distance functions (slacks based, hyperbolic and geometric) are proposed in (Tone, 2001), (Färe, 2002) and (Portela, 2004). The TFP index proposed in (Portela, 2004) gives a clear and simple economic interpretation, but suffers from the restriction that no input or output is more important than the other. We generalized their measure by ex-ante incorporating analyst preferences. Multi-criteria decision-making has developed many procedures for deriving the weights of criteria from decision-maker's subjective judgments. The main problem refers to how the final ranking should be made. The objective of this section is to propose, as a supplement and generalization of one-dimensional productivity indicator, a modification of the TFP measure introduced in (Portela, 2004). We generalize the TFP measure and propose this generalization as the most logical for the final ranking of the unit’s of assessment. The proposed procedure seems to be more advantageous to users than any other existing procedure. Let the vector x t = ( x1t , x2 ,..., xm ) ∈ R+ correspond to unit of assessment inputs used to t t m produce a unit of assessment output vector y t = ( y1t , y 2 ,..., y st ) ∈ R+ in a technology involving n t s units of assessment in period t. Let the vector P ( x t ) = ( P ( x1t ), P ( x 2 ),..., P ( x m )) ∈ R+ correspond t t m to unit of assessment target input vector and let the vector P( y t ) = ( P ( y1t ), P( y 2 ),..., P( y st )) ∈ R+ t s correspond to unit of assessment target output vector. Assume that the target vector can be any
  14. 14. vector at the production frontier and that target levels can be calculated through any known procedure. Let the number u i correspond to the weight of i-th input relative importance to the m analyst. Denote with u = (u1 , u 2 , K, u m ), ∑ u i = 1 the vector of input weights. Let the number v j i =1 correspond to the weight of j-th output relative importance to the analyst. Denote with s v = (v1 , v 2 ,K , v s ), ∑ v j = 1 the vector of output weights. Assume that the weighted product j =1 m model can be used to express aggregated performance value of inputs WPI ( x t ; u ) = ∏ ( xi ) ui t i =1 s vj and outputs WPO( y t ; v) = ∏ ( y j ) . Then we define Generalized Geometric Distance Function t j =1 WPI ( P ( x t ); u ) WPO ( y t ; v) (GGDF) as GGDF ( x t , y t ; u , v) = ⋅ , and Generalized Total Factor WPI ( x t ; u ) WPO ( P ( y t ); v) WPI ( x t ; u ) WPO ( y t +1 ; v) Productivity (GTFP) as GTFP ( x t , y t , x t +1 , y t +1 ) = ⋅ . Notice that GGDF WPI ( x t +1 ; u ) WPO ( y t ; v) account for all sources of inefficiency and GTFP is fit for various decompositions will be discussed in our future papers. Like in every decision making problem involving multiple criteria, the basic problem stated by analysts concerns the way by which the final decision should be made. In this paper we propose to ex-ante incorporate analyst preferences in deterministic frontier models by deriving input and output weights with inference procedure described in (Chu, 1979) or (Lootsma, 1991). 7. Concluding remarks The underlying assumption of basic DEA models is that no input or output is more important than the other. This assumption can be restrictive for the analysis. In such situations, the unit of assessment that achieves the best value towards less important criterion (equity to value-added ratio) is technically efficient, even if its performance is relatively bad in comparison to benchmark units by more important criterions (like labor to value-added ratio). So, technical efficiency in basic DEA models may not be a good enough indicator of performance and not an appropriate measure for monitoring and control purposes. We tried not to ignore relationships between economic variables. The idea to incorporate expert analyst judgments and preferences into analysis is motivated with case studies that prove this assumption is sometimes unrealistic. The idea is to correct the frontier by ex-post introducing the analyst explicit preferences into analysis. Also, the sources of inefficiency can be hidden if radial direction is used. We must remember that our primary task is to reveal them and to use this information for planning purposes. Therefore, our procedure is trying to reveal sources of inefficiency. Another modeling
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