Subhash C Ray Department of Economics University of Connecticut Storrs CT
|
|
- Elfrieda Austin
- 5 years ago
- Views:
Transcription
1 CATEGORICAL AND AMBIGUOUS CHARACTERIZATION OF RETUNS TO SCALE PROPERTIES OF OBSERVED INPUT-OUTPUT BUNDLES IN DATA ENVELOPMENT ANALYSIS Subhash C Ray Department of Economics University of Connecticut Storrs CT subhash.ray@uconn.edu (Abstract) This paper shows how one can determine the returns to scale properties of every feasible input-output bundle efficient or otherwise. Specifically, we identify different regions within the production possibility set where increasing, constant, or diminishing returns to scale hold with respect to both inputs and outputs. We also identify regions where the nature of returns to scale is ambiguous and depends on the direction of proection on to the frontier. It is also shown that when the production possibility set is convex, a comparison of the input- and output-oriented efficiency measures reveals the nature of (local) returns to scale when increasing returns prevails at the input-oriented proection or diminishing returns holds at the output-oriented proection of an inefficient input-output bundle. Keywords: Most Productive Scale Size; Convex Technologies, Nonparametric Efficiency Analysis JEL Classification Codes: D2; C6 Revised: April 2009 The paper has benefited from insightful comments from Subal Kumbhakar and from two referees on an earlier version of the manuscript. The usual disclaimer applies.
2 CATEGORICAL AND AMBIGUOUS CHARACTERIZATION OF RETUNS TO SCALE PROPERTIES OF INPUT-OUTPUT BUNDLES IN DATA ENVELOPMENT ANALYSIS In the nonparametric Data Envelopment Analysis (DEA) literature, there are three alternative (but equivalent) approaches to identifying the nature of local returns to scale at any given input-output bundle on the frontier of the production possibility set: (i) a primal approach due to Banker (984), (ii) a dual approach due to Banker, Charnes, and Cooper (984), and (iii) a nesting approach due to Färe, Grosskopf, and Lovell (FGL) (985). In a later paper, Kerstens and Vanden Eeckaut (KVE) (999) combined FGL s nesting approach with Varian s (990) concept of goodness-of-fit in nonparametric models to propose a slightly different method of determining the nature of local returns to scale. It is well known that when the technology exhibits constant returns to scale (CRS) globally, input- and output oriented radial measures of technical efficiency are identical. By implication, if this equality does not hold for every input-output bundle, the technology is characterized by variable returns to scale (VRS). In their paper on Generalized Measures of Farrell Efficiency, Førsund and Halmarsson (979) invoked Frisch s (965) second law of beam variation to note that whenever the input-oriented radial measure of technical efficiency is greater (less) than the corresponding output-oriented measure, the scale elasticity is greater (less) than unity. As noted by KVE (999), the Førsund and Halmarsson paper has received far less attention than it deserves in the subsequent returns to scale and scale efficiency literature. It is to be noted, however, that their scale elasticity is a weighted average of point elasticities along the segment of the production frontier that lies between the input-and the output-oriented proections of an inefficient inputoutput bundle. As such, this elasticity measure does not provide any unequivocal information about the local returns to scale at the input- or the output-oriented proection. When a firm is found to be operating in the region of increasing returns to scale, an implied udgment is that it is smaller than its optimal size. Similarly, a firm operating in the region of diminishing returns to scale is considered to be too large. However, the concept of local returns to scale is meaningful only for efficient input-output bundles. For an inefficient bundle, one must consider its efficient proection on to the frontier. It is often the case that the input- and the output-oriented proections lie in two different regions of the frontier one exhibiting increasing and the other exhibiting diminishing returns to scale. This can be a source of confusion about whether the firm is too small or too large. Such confusion arises mainly because returns to scale properties are evaluated at an efficient proection, but udgment about the size of the firm is usually made about its actual input-output bundle. The obectives of this paper are twofold. First, we show how one can determine the returns to scale properties of every feasible input-output bundle efficient or otherwise. Specifically, we identify different regions within the production possibility set where increasing, constant, or diminishing returns to scale hold See Ray (2004, chapter 3). 2
3 with respect to both inputs and outputs. We also identify regions where the nature of returns to scale is ambiguous and depends on the direction of proection on to the frontier. The second contribution of this paper is to show that, when the production possibility set is convex, a comparison of the input- and outputoriented efficiency measures reveals the nature of (local) returns to scale when increasing returns prevails at the input-oriented proection or diminishing returns holds at the output-oriented proection of an inefficient input-output bundle. The paper unfolds as follows. Section 2 provides some basic concepts and definitions and proves a lemma showing that if the production possibility set is convex, increasing returns to scale (IRS) cannot follow diminishing returns to scale. An implication of this lemma is that increasing returns to scale prevails at all points on the frontier until a most productive scale size (MPSS) is attained. Similarly, diminishing returns holds at all efficient bundles larger than the (largest) MPSS. Section 3 describes how a DEA model can be utilized to find the MPSS for any feasible input-output bundle and what we can conclude about the observed size of a firm. Section 4 shows that, in some cases, a comparison of input- and output-oriented measures of technical efficiency of an inefficient bundle can reveal the nature of returns to scale at the input- or the output-oriented proection. Section 5 summarizes the main conclusions. 2. The Methodological Background Basic Concepts and Definitions: The production technology faced by firms in an industry producing output vectors ( from input vectors (x) can be described by the production possibility set T = {( x, : xr ; yr ; y can be produced from x}. () n m An input-output bundle (x, is considered feasible if and only if (, T. x Following the convention in DEA, we assume that the production possibility set is convex and also that both inputs and outputs are freely disposable. The frontier of the production possibility set (also known as the graph of the technolog is G ( x, :( x, T; ( x, T; ( x, T. (2) The input-oriented technical efficiency of a feasible input-output bundle (x, is min :( x, G. (3) x Similarly, the output-oriented technical efficiency of the same bundle is, where y max:( x, G. (4) Obviously, and. 3
4 Banker (984) generalized Frisch s (963) concept of the technically optimal production scale to define a most productive scale size (MPSS) in the context of multiple-input multiple-output technology 2. An inputoutput bundle (x,y ) G is a most productive scale size if, for any non-negative scalars α and β such that (βx, αy ) G,. Thus, (x,y ) is a point on the frontier of the production possibility set where average productivity attains a maximum in the single-output single-input case or ray average productivity reaches a maximum in the multiple-output multiple-input case. Locally constant returns to scale holds at an input-output bundle ( x, G, if there is a real number 0 (however small) such that ( x, G and, for. Locally increasing returns to scale holds if ( x, G and, for. Similarly, locally diminishing returns to scale holds if ( x, G and, for. Banker (984) has shown that locally constant returns to scale holds at an MPSS. It is possible, however, that the maximum (ra average productivity is attained at multiple levels (scales) of input. For such technologies, locally constant returns to scale holds at every input (bundle) within this range. In such cases, of particular interest are the smallest and the largest MPSS bundles. We now prove the following lemma to show that locally increasing returns holds at every scale smaller than the smallest MPSS and locally diminishing returns holds at every scale greater than the largest MPSS. Lemma: For any convex productivity possibility set T, if there exist non-negative scalars α and β such that α >β >, and both ( x, and ( x, G, then for every γ and δ such that <δ<β and ( x, G. Proof: Because ( x, and ( x, are both feasible, by convexity of T, for every ( 0,),(( ( ) ) x, ( ( ) ) is also feasible. Now select such that ( ). Further, define ( ). Using these notations, ( x, T. But, because ( x, G,. However, because,. Hence,. An implication of this lemma is that, when the production possibility set is convex, if the technology exhibits locally diminishing returns to scale at smaller input scale, it cannot exhibit increasing returns at a bigger input scale. This is easily understood in the single-input single-output case. When both x and y are 2 See also Banker and Thrall (992) and Banker et al. (2004). 4
5 scalars, average productivity at ( x, is y x and at ( x, y it is. Thus, when, average x productivity has increased. The above lemma implies that for every input level x in between x and x, average productivity is greater than y x. Thus, average productivity could not first decline and then increase as the input level increased from x to x. Two results follow immediately. First, locally increasing returns to scale holds at every input-output bundle (x, G that is smaller than the smallest MPSS. Second, locally diminishing returns to scale holds at every input-output bundle (x, G that is greater than the largest MPSS. To see this, let x =bx and y = ay, where (x, y ) is the smallest MPSS for the given input and output mix. Because (x, is not an MPSS, a. Further, assume that b <. Define ( ) and. Then (x, y ) = (βx, α and. b b Because ray average productivity is higher at a larger input scale, by virtue of the lemma, locally increasing returns to scale holds at (x,. Next assume that b >. Again, because (x, is not an MPSS, b a <. That is ray average productivity has fallen as the input scale is increased from x to x = bx. Then, by virtue of the lemma, ray average product could not be any higher than b a at a slightly greater input scale, a x (+ε)x. But, because (x, is not an MPSS, ray average product cannot remain constant as the input scale is slightly increased. Hence, ray average product must fall as the input scale is slight increased from x. Thus, locally diminishing returns to scale holds at every (x, G, when x is larger than the largest MPSS. (Insert Figure here) In Figure, the two axes measure the levels of input and output in the one input-one output case and the graph is merely the production function. In the multiple-output multiple-input case, the two axes show the input and output scale for some given input- and output-mix. The broken line ABCDEF in Figure shows the graph of some hypothetical technology. All points between (and including C and D) represent an MPSS. In this figure, C represents the smallest and D the largest MPSS. All points to the left of C exhibit locally increasing returns to scale. Locally diminishing returns to scale holds at any point to the right of D. For the inefficient input-output bundle shown by the point R, R x is its input-oriented technically efficient proection on to the graph. Increasing returns to scale holds at R x. Similarly, the point R y is its output oriented proection where diminishing returns to scale holds. 3. Using the Most Productive Scale Size for a Benchmark In the DEA literature on scale efficiency, the main interest has been on testing whether a specific inputoutput bundle is an MPSS. Surprisingly, there has been little interest in finding out what is an MPSS for that input-output bundle when the answer is in the negative. In this section, it is shown how a DEA model 5
6 currently available in the literature 3 can be used not only to determine whether an input-output bundle (x 0, y 0 ) is an MPSS but also to identify the bundle (x, y ) which is an MPSS for (x 0, y 0 ). For this, we use the observed input-output data (x, y ) (=,2,,N) to solve the following DEA problem considered by Cooper, Thompson, and Thrall (996): Subect to Maximize 0 x x ; y y 0 ; (5) ;,, (,2,..., N) 0. Because (x 0, y 0 ) is assumed to be a feasible input-output bundle, ( ) is a feasible solution for this problem. Hence, the optimal value is always greater than or equal to.when exceeds unity, we know that (x 0, y ) is not an MPSS. But we can also conclude that ( x, y ) is an MPSS. We first assume that the MPSS is unique and deal with the case of multiple MPSS presently. When the bundle (x 0, y 0 ) is not itself an MPSS, so that. possibilities: (i) ; (ii) ; and (iii). There are three distinct (Insert Figure 2 here) Figure 2 shows the three different cases graphically. It should be noted that in this diagram (as would be the case in Figure for a multi-output multi-input case) the broken line ABCDE is a fixed-proportions graph of the technology and is defined as: G ( x, y ) (, ) :( x, y ) G;, 0. (6) The point C (α= α, β=β ) is the unique MPSS. The actual input-output bundle (x 0, y 0 ), can be represented by the point (α=, β= ) in this diagram. At every point in region () to the southwest of C, both the input and output scales are smaller than the MPSS (i.e., α and β ). Therefore, if the actual bundle (α=, β=) lies in this region, the firm is unambiguously exhibiting increasing returns to scale. If it is an efficient bundle lying on the frontier, increasing returns holds at that point. If it is an inefficient bundle that lies below the 3 See, for example, Cooper, Seiford, and Tone (2004). 6
7 frontier, increasing returns holds at both the input- and the output-oriented proections. In a perfectly analogous way, at every point in region (2) to the northeast of C, the input and output scales are both larger than the MPSS. Hence, if (α=, β=) falls in this area, the observed bundle exhibits categorically diminishing returns to scale. Points in region (3) to the southeast of C, however, are problematic. On the one hand, for any point located in this area, the input scale is larger than the MPSS (β ). This implies diminishing returns to the input scale as is evident from the fact that an output-oriented efficient proection would lie to the right of C on the frontier. At the same time, the output scale is smaller than the MPSS (α ) and the input-oriented oriented proection is to the left of C implying increasing returns to the output scale. This is exactly the situation shown by the point R in Figure. It is an inherent dilemma in technologies where variable returns to scale apply: not only the measured technical efficiency but also the returns to scale characterization depends on whether the analysis is output- or input-oriented. Before we move on to the case of multiple MPSS, it would be useful to take a closer look at the DEA problem in (5). As such, the obective function is nonlinear. However, it can be easily transformed into a linear programming problem. Define t and μ = tλ ( =, 2,,N). Note that non-negativity of β and λ s ensures that t and μ s are also non-negative. Problem (5) can, therefore, be reformulated as the following linear programming problem: Maximize Subect to 0 x x ; 0 y y ; (7) t; t, (,2,..., N) 0. From the optimal solution of this problem we can derive and. One can then infer the nature of returns to scale from these values of α and β. An interesting point to note here is that because t has no restriction other than non-negativity, (6) actually is an output oriented CCR problem. Hence, when at the optimal solution of this problem, we can conclude that β is less than unity and diminishing returns to scale holds at the output-oriented proection on to the VRS frontier. This is what can also be readily derived from Banker s (984) primal approach with an output-oriented DEA model. But without a corresponding value of α as well, we cannot conclude anything about returns to scale at the input-oriented proection. t t 7
8 Next we consider the possibility of multiple MPSS. This is depicted graphically in Figure 3. Here both C and C 2 are MPSS and so are their convex combinations lying on the line segment connecting them. At C, (, ) is the smallest MPSS. Similarly, ( 2, 2 ) at C 2 is the largest MPSS. It is obvious that when (6) has a unique optimal solution (in particular, t is unique), there cannot be multiple MPSS. For multiple optimal solutions, the largest across all optimal solutions of (6) corresponds to the smallest t MPSS,. Similarly, 2 corresponds to the smallest t at an optimal solution. Note that across all optimal solutions the value of the obective function is the same ( ). Hence,, t where s.t. t max 0 x x ; 0 y y ; (8) (,2,..., N) 0. Similarly,, where 2 2 t t min 2 s.t. 0 x x ; 0 y y ; (9) Once (,2,..., N) 0. and 2 have been determined from (8) and (9), the corresponding values of are readily obtained as and. 2 2 (Insert Figure 3 here) As shown in Figure 3, the set of output-input scales (α, β) for which the input-output bundles (βx 0,αy 0 ) are feasible can be partitioned into six different regions defined below: 8
9 (i) In region () towards the southwest of the smallest MPSS (C ), ( ; ). When (x 0, y 0 ) falls in this region,. Hence, increasing returns to scale holds unambiguously. (ii) In region (2) to the northeast of the largest MPSS (C 2 ), ( ; ). If (x 0, y 0 ) falls in 2 2 this region,. Diminishing returns to scale holds unambiguously in this region. (iii) In region (3), 2 while 2. Points in this region lie between the smallest and the largest MPSS. It is interesting to note, that even if the point (α=, β= ) is not technically efficient and lies below the C C 2 line, both the input- and the output-oriented proection of the inefficient bundle will fall in the region of constant returns to scale. Thus, there is no scale inefficiency in this region even though there may be technical inefficiency,. (iv) In region (4), 2 ;. When the actual input-output bundle lies here, 2. The input bundle x 0 is larger than the largest MPSS hence the output oriented proection falls in the area of diminishing returns. At the same time, the actual output bundle is smaller than the smallest MPSS. Hence, increasing returns to scale holds at the input oriented proection. Thus, returns to scale cannot be unambiguously defined at the actual input-output bundle. (v) In region (5a), but. When the actual input-output bundle lies here, y 0 2 is smaller than the smallest MPSS and the input oriented proection falls in the area of increasing returns. At the same time, the actual input bundle lies between the smallest and the largest MPSS. Hence, constant returns to scale holds at the output oriented proection. Here also the returns to scale characterization depends on the orientation. (vi) In region (5b), 2 while 2. When the actual input-output bundle lies here, x 0 is larger than the largest MPSS. Hence the output oriented proection falls in the area of diminishing returns. At the same time, the actual output bundle lies between the smallest and the largest MPSS. Hence, constant returns to scale holds at the input oriented proection. Here the input bundle is too large. But the actual output bundle, if produced from the technically efficient input bundle would correspond to an MPSS.. 4. Comparing Input- and Output-oriented Measures of Technical Efficiency We now show what one can learn about the returns to scale properties of the input-output bundle (x 0, y 0 ) of an inefficient firm by comparing its input- and output-oriented technical efficiencies.. Proposition : If the input-oriented technical efficiency is greater than the output-oriented technical efficiency, then locally increasing returns to scale holds at the efficient input-oriented proection of (x 0, y 0 ). 9
10 Proof: The input-oriented proection of the bundle (x 0, y 0 ) on to G is (θ x 0, y 0 ) where θ is the measured level of input-oriented technical efficiency (τ x ). Similarly, the output-oriented proection is (x 0, φ y 0 ) and 0 0 the output-oriented technical efficiency is. Define the input bundle and the output y x x 0 0 bundle y y. Note that both the input-output bundles ( x 0, y 0 ) and ( x 0, y 0 ) are in G. Further, ( 0, y x ) can also be expressed as ( x, y ) where and. Now, x y implies. Note that, by construction, and. Thus, ray average productivity is higher at the bigger input scale 0 x. Hence, by virtue of the lemma, locally increasing returns to scale holds at the input-oriented efficient proection ( x 0, y 0 ). Proposition 2: If the output-oriented technical efficiency is greater than the input-oriented technical efficiency, then locally diminishing returns to scale holds at the efficient output-oriented proection of (x 0, y 0 ). Proof: Now suppose that τ y > τ x. That is, implying that. In other words, ray average productivity is lower at the output-oriented proection (x 0, φ y 0 ) than at the input-oriented proection (θ x 0, y 0 ). Hence, locally diminishing returns to scale holds at (x 0, φ y 0 ). It is obvious that compared to the procedure described in the previous section, this method of simply comparing the output- and input-oriented technical efficiencies to determine the nature of returns to scale has many limitations. First, it cannot be applied when the two efficiency measures are equal. Second, even though it can identify increasing returns at the input-oriented proection, one cannot detect increasing returns at the output-oriented proection. Similarly, it fails to determine if diminishing returns holds at the input-oriented proection. In spite of these limitations, this procedure has some advantages. First, this procedure is not affected by the presence of multiple optimal solutions of the relevant DEA models. Second, knowing that increasing returns holds at the input-oriented proection is by itself useful information because it implies that as an output target the bundle y 0 is too small. Similarly, when diminishing returns holds at the output-oriented proection, we can conclude that the input bundle is too large Summary 4 One may note in passing that the procedure proposed in Section 3 uses a CCR model. By contrast, in this section we use a BCC model. 0
11 When both the actual input and output bundles of a firm are smaller than their (smallest) MPSS, the firm is unambiguously too small and an increase in size will lead to higher productivity. Conversely, when both bundles are larger than the (largest) MPSS, the firm is too big. In some cases, the observed output scale is too small but the input scale is not. There are other cases, where the opposite is true. Also, comparison of input- and output-oriented technical efficiency measures can identify if the actual output scale is too small or the actual input scale is too large.
12 References: Banker, R.D. (984), Estimating the Most Productive Scale Size Using Data Envelopment Analysis, European Journal of Operational Research 7: (Jul Banker, R.D., A. Charnes, and W.W. Cooper (984), Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis, Management Science, 30:9 (September), Banker, R.D., W.W. Cooper, L. M. Seiford, R.M. Thrall, and J. Zhu (2004) Returns to Scale in different DEA Models ; European Journal of Operational Research 54: Banker, R.D. and R.M. Thrall (992) Estimating Most Productive Scale Size using Data Envelopment Analysis, European Journal of Operational Research,62, Cooper, W.W., R.G. Thompson, and R.M. Thrall (996) Introduction: Extensions and New Developments in DEA ; Annals of Operations Research, 66, pp Cooper, W.W., L. Seiford, and K. Tone (2004) Data Envelopment Analysis: A Comprehensive Text with Uses, Example Applications, References, and DEA Solver Software Norwell, MA: Kluwer Academic Publishers. Fare, R., S. Grosskopf, and C.A.K. Lovell (985) The Measurement of Efficiency of Production Boston: Kluwer-Nihoff. Førsund, F. and L.Halmarsson (979) Generalized Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants ; The Economic Journal;(89) 354, Frisch, R. (965) Theory of Production. Chicago: Rand McNally and Company. Kerstens, K. and P. Vanden Eeckaut (999) Estimating Returns to Scale Using Nonparametric Deterministic Technologies: A New Method Based on Goodness-of-Fit ; European Journal of Operational Research, 3(), Podinovski, V. (2004) Local and Global Returns to Scale in performance Measurement ; Journal of the Operations Research Society (2004) 55, Ray, S.C. (2004) Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research New York: Cambridge University Press Varian, H.R. (990), Goodness-of-Fit in Optimizing Models, Journal of Econometrics 46,
13 Output (level/scale) φy 0 Ry E F D C Rx R(x 0,y 0 ) y 0 B O A θx 0 x 0 Input (level/scale) Figure. Graph of the Technology and MPSS 3
14 4
15 Output Scale (α) D E α 2 C 2 2 α C 3 5b 5a 4 B 0 A β β 2 Input Scale (β) Figure 3: Multiple MPSS & Regions of Increasing, Constant, Decreasing, and Ambiguous Returns to Scale 5
Department of Economics Working Paper Series
Department of Economics Working Paper Series Comparing Input- and Output-Oriented Measures of Technical Efficiency to Determine Local Returns to Scale in DEA Models Subhash C. Ray University of Connecticut
More informationFurther discussion on linear production functions and DEA
European Journal of Operational Research 127 (2000) 611±618 www.elsevier.com/locate/dsw Theory and Methodology Further discussion on linear production functions and DEA Joe Zhu * Department of Management,
More informationEquivalent Standard DEA Models to Provide Super-Efficiency Scores
Second Revision MS 5035 Equivalent Standard DEA Models to Provide Super-Efficiency Scores C.A.K. Lovell 1 and A.P.B. Rouse 2 1 Department of Economics 2 Department of Accounting and Finance Terry College
More informationData Envelopment Analysis within Evaluation of the Efficiency of Firm Productivity
Data Envelopment Analysis within Evaluation of the Efficiency of Firm Productivity Michal Houda Department of Applied Mathematics and Informatics Faculty of Economics, University of South Bohemia in Česé
More informationOptimal weights in DEA models with weight restrictions
Loughborough University Institutional Repository Optimal weights in DEA models with weight restrictions This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation:
More informationThe Comparison of Stochastic and Deterministic DEA Models
The International Scientific Conference INPROFORUM 2015, November 5-6, 2015, České Budějovice, 140-145, ISBN 978-80-7394-536-7. The Comparison of Stochastic and Deterministic DEA Models Michal Houda, Jana
More informationA Slacks-base Measure of Super-efficiency for Dea with Negative Data
Australian Journal of Basic and Applied Sciences, 4(12): 6197-6210, 2010 ISSN 1991-8178 A Slacks-base Measure of Super-efficiency for Dea with Negative Data 1 F. Hosseinzadeh Lotfi, 2 A.A. Noora, 3 G.R.
More informationRevenue Malmquist Index with Variable Relative Importance as a Function of Time in Different PERIOD and FDH Models of DEA
Revenue Malmquist Index with Variable Relative Importance as a Function of Time in Different PERIOD and FDH Models of DEA Mohammad Ehsanifar, Golnaz Mohammadi Department of Industrial Management and Engineering
More informationDetermination of Economic Optimal Strategy for Increment of the Electricity Supply Industry in Iran by DEA
International Mathematical Forum, 2, 2007, no. 64, 3181-3189 Determination of Economic Optimal Strategy for Increment of the Electricity Supply Industry in Iran by DEA KH. Azizi Department of Management,
More informationMarginal values and returns to scale for nonparametric production frontiers
Loughborough University Institutional Repository Marginal values and returns to scale for nonparametric production frontiers This item was submitted to Loughborough University's Institutional Repository
More informationChance Constrained Data Envelopment Analysis The Productive Efficiency of Units with Stochastic Outputs
Chance Constrained Data Envelopment Analysis The Productive Efficiency of Units with Stochastic Outputs Michal Houda Department of Applied Mathematics and Informatics ROBUST 2016, September 11 16, 2016
More informationNEGATIVE DATA IN DEA: A SIMPLE PROPORTIONAL DISTANCE FUNCTION APPROACH. Kristiaan Kerstens*, Ignace Van de Woestyne**
Document de travail du LEM 2009-06 NEGATIVE DATA IN DEA: A SIMPLE PROPORTIONAL DISTANCE FUNCTION APPROACH Kristiaan Kerstens*, Ignace Van de Woestyne** *IÉSEG School of Management, CNRS-LEM (UMR 8179)
More informationResearch Article A Data Envelopment Analysis Approach to Supply Chain Efficiency
Advances in Decision Sciences Volume 2011, Article ID 608324, 8 pages doi:10.1155/2011/608324 Research Article A Data Envelopment Analysis Approach to Supply Chain Efficiency Alireza Amirteimoori and Leila
More informationCHAPTER 4 MEASURING CAPACITY UTILIZATION: THE NONPARAMETRIC APPROACH
49 CHAPTER 4 MEASURING CAPACITY UTILIZATION: THE NONPARAMETRIC APPROACH 4.1 Introduction: Since the 1980's there has been a rapid growth in econometric studies of capacity utilization based on the cost
More informationAN IMPROVED APPROACH FOR MEASUREMENT EFFICIENCY OF DEA AND ITS STABILITY USING LOCAL VARIATIONS
Bulletin of Mathematics Vol. 05, No. 01 (2013), pp. 27 42. AN IMPROVED APPROACH FOR MEASUREMENT EFFICIENCY OF DEA AND ITS STABILITY USING LOCAL VARIATIONS Isnaini Halimah Rambe, M. Romi Syahputra, Herman
More informationA DIMENSIONAL DECOMPOSITION APPROACH TO IDENTIFYING EFFICIENT UNITS IN LARGE-SCALE DEA MODELS
Pekka J. Korhonen Pyry-Antti Siitari A DIMENSIONAL DECOMPOSITION APPROACH TO IDENTIFYING EFFICIENT UNITS IN LARGE-SCALE DEA MODELS HELSINKI SCHOOL OF ECONOMICS WORKING PAPERS W-421 Pekka J. Korhonen Pyry-Antti
More informationPrediction of A CRS Frontier Function and A Transformation Function for A CCR DEA Using EMBEDED PCA
03 (03) -5 Available online at www.ispacs.com/dea Volume: 03, Year 03 Article ID: dea-0006, 5 Pages doi:0.5899/03/dea-0006 Research Article Data Envelopment Analysis and Decision Science Prediction of
More informationModeling undesirable factors in efficiency evaluation
European Journal of Operational Research142 (2002) 16 20 Continuous Optimization Modeling undesirable factors in efficiency evaluation Lawrence M. Seiford a, Joe Zhu b, * www.elsevier.com/locate/dsw a
More informationA Simple Characterization
95-B-1 A Simple Characterization of Returns to Scale in DEA l(aoru Tone Graduate School of Policy Science Saitama University Urawa, Saita1na 338, Japan tel: 81-48-858-6096 fax: 81-48-852-0499 e-mail: tone@poli-sci.saita1na-u.ac.jp
More informationMeasuring the efficiency of assembled printed circuit boards with undesirable outputs using Two-stage Data Envelopment Analysis
Measuring the efficiency of assembled printed circuit boards with undesirable outputs using Two-stage ata Envelopment Analysis Vincent Charles CENTRUM Católica, Graduate School of Business, Pontificia
More informationCentre for Efficiency and Productivity Analysis
Centre for Efficiency and Productivity Analysis Working Paper Series No. WP02/2013 Scale Efficiency and Homotheticity: Equivalence of Primal and Dual Measures Valentin Zelenyuk Date: February 2013 School
More informationSensitivity and Stability Radius in Data Envelopment Analysis
Available online at http://ijim.srbiau.ac.ir Int. J. Industrial Mathematics Vol. 1, No. 3 (2009) 227-234 Sensitivity and Stability Radius in Data Envelopment Analysis A. Gholam Abri a, N. Shoja a, M. Fallah
More informationNonparametric Measures of Capacity Utilization: A Dual Approach
Universit of Connecticut DigitalCommons@UConn Economics Working Papers Department of Economics October 22 onparametric Measures of Capacit Utilization: A Dual Approach Subhash C. Ra Universit of Connecticut
More informationCHAPTER 3 THE METHOD OF DEA, DDF AND MLPI
CHAPTER 3 THE METHOD OF DEA, DDF AD MLP 3.1 ntroduction As has been discussed in the literature review chapter, in any organization, technical efficiency can be determined in order to measure the performance.
More informationMULTI-COMPONENT RETURNS TO SCALE: A DEA-BASED APPROACH
Int. J. Contemp. Math. Sci., Vol. 1, 2006, no. 12, 583-590 MULTI-COMPONENT RETURNS TO SCALE: A DEA-BASED APPROACH Alireza Amirteimoori 1 Department of Mathematics P.O. Box: 41335-3516 Islamic Azad University,
More informationDepartment of Economics Working Paper Series
Department of Economics Working Paper Series A Simple Statistical Test of Violation of the Weak Axiom of Cost Minimization Subhash C. Ray University of Connecticut Working Paper 2004-17 February 2004 341
More informationABSTRACT INTRODUCTION
Implementation of A Log-Linear Poisson Regression Model to Estimate the Odds of Being Technically Efficient in DEA Setting: The Case of Hospitals in Oman By Parakramaweera Sunil Dharmapala Dept. of Operations
More informationSensitivity and Stability Analysis in Uncertain Data Envelopment (DEA)
Sensitivity and Stability Analysis in Uncertain Data Envelopment (DEA) eilin Wen a,b, Zhongfeng Qin c, Rui Kang b a State Key Laboratory of Virtual Reality Technology and Systems b Department of System
More informationNonparametric Analysis of Cost Minimization and Efficiency. Beth Lemberg 1 Metha Wongcharupan 2
Nonparametric Analysis of Cost Minimization and Efficiency Beth Lemberg 1 Metha Wongcharupan 2 For presentation at the AAEA Annual Meeting August 2-5, 1998 Salt Lake City, Utah 1 Research Assistant, Department
More informationSearching the Efficient Frontier in Data Envelopment Analysis INTERIM REPORT. IR-97-79/October. Pekka Korhonen
IIASA International Institute for Applied Systems Analysis A-2361 Laxenburg Austria Tel: +43 2236 807 Fax: +43 2236 71313 E-mail: info@iiasa.ac.at Web: www.iiasa.ac.at INTERIM REPORT IR-97-79/October Searching
More informationFinding the strong defining hyperplanes of production possibility set with constant returns to scale using the linear independent vectors
Rafati-Maleki et al., Cogent Mathematics & Statistics (28), 5: 447222 https://doi.org/.8/233835.28.447222 APPLIED & INTERDISCIPLINARY MATHEMATICS RESEARCH ARTICLE Finding the strong defining hyperplanes
More informationProperties of Inefficiency Indexes on Input, Output Space
Properties of Inefficiency Indexes on Input, Output Space by R. Robert Russell University of California, Riverside, and University of New South Wales and William Schworm University of New South Wales September
More informationA Unifying Framework for Farrell Profit Efficiency Measurement
A Unifying Framework for Farrell Profit Efficiency Measurement Rolf Färe a, Xinju He b, Sungko Li b, Valentin Zelenyuk c Abstract Measuring profit efficiency is a challenging task and many different approaches
More informationNonparametric production technologies with multiple component processes
Loughborough University Institutional Repository Nonparametric production technologies with multiple component processes This item was submitted to Loughborough University's Institutional Repository by
More informationData envelopment analysis
15 Data envelopment analysis The purpose of data envelopment analysis (DEA) is to compare the operating performance of a set of units such as companies, university departments, hospitals, bank branch offices,
More informationDEA WITH EFFICIENCY CLASSIFICATION PRESERVING CONDITIONAL CONVEXITY
DEA WITH EFFICIENCY CLASSIFICATION PRESERVING CONDITIONAL CONVEXITY by Timo Kuosmanen * Helsinki School of Economics and Business Administration Department of Economics and Management Science P.O. Box
More informationA ratio-based method for ranking production units in profit efficiency measurement
Math Sci (2016) 10:211 217 DOI 10.1007/s40096-016-0195-8 ORIGINAL RESEARCH A ratio-based method for ranking production units in profit efficiency measurement Roza Azizi 1 Reza Kazemi Matin 1 Gholam R.
More informationLITERATURE REVIEW. Chapter 2
Chapter 2 LITERATURE REVIEW This chapter reviews literature in the areas of productivity and performance measurement using mathematical programming and multi-level planning for resource allocation and
More informationINEFFICIENCY EVALUATION WITH AN ADDITIVE DEA MODEL UNDER IMPRECISE DATA, AN APPLICATION ON IAUK DEPARTMENTS
Journal of the Operations Research Society of Japan 2007, Vol. 50, No. 3, 163-177 INEFFICIENCY EVALUATION WITH AN ADDITIVE DEA MODEL UNDER IMPRECISE DATA, AN APPLICATION ON IAUK DEPARTMENTS Reza Kazemi
More informationUSING LEXICOGRAPHIC PARAMETRIC PROGRAMMING FOR IDENTIFYING EFFICIENT UNITS IN DEA
Pekka J. Korhonen Pyry-Antti Siitari USING LEXICOGRAPHIC PARAMETRIC PROGRAMMING FOR IDENTIFYING EFFICIENT UNITS IN DEA HELSINKI SCHOOL OF ECONOMICS WORKING PAPERS W-381 Pekka J. Korhonen Pyry-Antti Siitari
More informationSelective Measures under Constant and Variable Returns-To- Scale Assumptions
ISBN 978-93-86878-06-9 9th International Conference on Business, Management, Law and Education (BMLE-17) Kuala Lumpur (Malaysia) Dec. 14-15, 2017 Selective Measures under Constant and Variable Returns-To-
More informationA Note on the Scale Efficiency Test of Simar and Wilson
International Journal of Business Social Science Vol. No. 4 [Special Issue December 0] Abstract A Note on the Scale Efficiency Test of Simar Wilson Hédi Essid Institut Supérieur de Gestion Université de
More informationClassifying inputs and outputs in data envelopment analysis
European Journal of Operational Research 180 (2007) 692 699 Decision Support Classifying inputs and outputs in data envelopment analysis Wade D. Cook a, *, Joe Zhu b a Department of Management Science,
More informationEuropean Journal of Operational Research
European Journal of Operational Research 207 (200) 22 29 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Interfaces with
More informationAuthor Copy. A modified super-efficiency DEA model for infeasibility. WD Cook 1,LLiang 2,YZha 2 and J Zhu 3
Journal of the Operational Research Society (2009) 60, 276 --281 2009 Operational Research Society Ltd. All rights reserved. 0160-5682/09 www.palgrave-journals.com/jors/ A modified super-efficiency DEA
More informationThe directional hybrid measure of efficiency in data envelopment analysis
Journal of Linear and Topological Algebra Vol. 05, No. 03, 2016, 155-174 The directional hybrid measure of efficiency in data envelopment analysis A. Mirsalehy b, M. Rizam Abu Baker a,b, L. S. Lee a,b,
More informationRanking Decision Making Units with Negative and Positive Input and Output
Int. J. Research in Industrial Engineering, pp. 69-74 Volume 3, Number 3, 2014 International Journal of Research in Industrial Engineering www.nvlscience.com Ranking Decision Making Units with Negative
More informationChapter 11: Benchmarking and the Nonparametric Approach to Production Theory
1 APPLIED ECONOMICS By W.E. Diewert. 1 July, 2013. Chapter 11: Benchmarking and the Nonparametric Approach to Production Theory 1. Introduction Data Envelopment Analysis or (DEA) is the term used by Charnes
More informationFinding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies
Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies MARIA CONCEIÇÃO A. SILVA PORTELA csilva@porto.ucp.pt; portemca@aston.ac.uk Universidade Católica Portuguesa
More informationReview of Methods for Increasing Discrimination in Data Envelopment Analysis
Annals of Operations Research 116, 225 242, 2002 2002 Kluwer Academic Publishers. Manufactured in The Netherlands. Review of Methods for Increasing Discrimination in Data Envelopment Analysis LIDIA ANGULO-MEZA
More informationIntegrating Efficiency Concepts in Technology Approximation: A Weighted DEA Approach
Integrating Efficiency Concepts in Technology Approximation: A Weighted DEA Approach Kota Minegishi Department of Animal Science, University of Minnesota, Twin Cities Version. December 7, 2016 Abstract:
More informationESTIMATING ELASTICITIES OF INPUT SUBSTITUTION USING DATA ENVELOPMENT ANALYSIS NOAH JAMES MILLER
ESTIMATING ELASTICITIES OF INPUT SUBSTITUTION USING DATA ENVELOPMENT ANALYSIS by NOAH JAMES MILLER B.A., University of Oklahoma, 007 M.Sc., The London School of Economics, 011 A THESIS submitted in partial
More informationComplete Closest-Target Based Directional FDH Measures of Efficiency in DEA
Complete Closest-Target Based Directional FDH Measures of Efficiency in DEA Mahmood Mehdiloozad a,*, Israfil Roshdi b a MSc, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran,
More informationA reference-searching based algorithm for large-scale data envelopment. analysis computation. Wen-Chih Chen *
A reference-searching based algorithm for large-scale data envelopment analysis computation Wen-Chih Chen * Department of Industrial Engineering and Management National Chiao Tung University, Taiwan Abstract
More informationI N S T I T U T D E S T A T I S T I Q U E B I O S T A T I S T I Q U E E T S C I E N C E S A C T U A R I E L L E S (I S B A)
I N S T I T U T D E S T A T I S T I Q U E B I O S T A T I S T I Q U E E T S C I E N C E S A C T U A R I E L L E S (I S B A) UNIVERSITÉ CATHOLIQUE DE LOUVAIN D I S C U S S I O N P A P E R 2011/35 STATISTICAL
More informationA DEA- COMPROMISE PROGRAMMING MODEL FOR COMPREHENSIVE RANKING
Journal of the Operations Research Society of Japan 2004, Vol. 47, No. 2, 73-81 2004 The Operations Research Society of Japan A DEA- COMPROMISE PROGRAMMING MODEL FOR COMPREHENSIVE RANKING Akihiro Hashimoto
More informationTHE PERFORMANCE OF INDUSTRIAL CLUSTERS IN INDIA
THE PERFORMANCE OF INDUSTRIAL CLUSTERS IN INDIA Dr.E. Bhaskaran.B.E, M.B.A., Ph.D., M.I.E., (D.Sc)., Deputy Director of Industries and Commerce, Government of Tamil Nadu Introduction The role of micro,
More informationChapter 2 Output Input Ratio Efficiency Measures
Chapter 2 Output Input Ratio Efficiency Measures Ever since the industrial revolution, people have been working to use the smallest effort to produce the largest output, so that resources, including human,
More informationTHE MEASUREMENT OF EFFICIENCY
Chapter 2 THE MEASUREMENT OF EFFICIENCY This chapter is about the measurement of efficiency of production units. It opens with a section concerning basic definitions of productivity and efficiency. After
More informationGroups performance ranking based on inefficiency sharing
Available online at http://ijim.srbiau.ac.ir/ Int. J. Industrial Mathematics (ISSN 2008-5621) Vol. 5, No. 4, 2013 Article ID IJIM-00350, 9 pages Research Article Groups performance ranking based on inefficiency
More informationA Survey of Some Recent Developments in Data Envelopment Analysis
95-B-6 A Survey of Some Recent Developments in Data Envelopment Analysis W.W. Cooper and Kaoru Tone W.W. Cooper* and Kaoru Tone** A SURVEY OF SOME RECENT DEVELOPMENTS IN DATA ENVELOPMENT ANALYSIS*** Abstract:
More informationDecomposing Malmquist Productivity Indexes into Explanatory Factors
1 Decomposing Malmquist Productivity Indexes into Explanatory Factors September 16, 2013 Erwin Diewert, 1 Kevin Fox, Discussion Paper 13-09, School of Economics, School of Economics, University of New
More informationDarmstadt Discussion Papers in ECONOMICS
Darmstadt Discussion Papers in ECONOMICS Direct Targeting of Efficient DMUs for Benchmarking Jens J. Krüger Nr. 229 Arbeitspapiere der Volkswirtschaftlichen Fachgebiete der TU Darmstadt ISSN: 1438-2733
More informationPRIORITIZATION METHOD FOR FRONTIER DMUs: A DISTANCE-BASED APPROACH
PRIORITIZATION METHOD FOR FRONTIER DMUs: A DISTANCE-BASED APPROACH ALIREZA AMIRTEIMOORI, GHOLAMREZA JAHANSHAHLOO, AND SOHRAB KORDROSTAMI Received 7 October 2003 and in revised form 27 May 2004 In nonparametric
More informationMixed input and output orientations of Data Envelopment Analysis with Linear Fractional Programming and Least Distance Measures
STATISTICS, OPTIMIZATION AND INFORMATION COMPUTING Stat., Optim. Inf. Comput., Vol. 4, December 2016, pp 326 341. Published online in International Academic Press (www.iapress.org) Mixed input and output
More informationPRINCIPAL COMPONENT ANALYSIS TO RANKING TECHNICAL EFFICIENCIES THROUGH STOCHASTIC FRONTIER ANALYSIS AND DEA
PRINCIPAL COMPONENT ANALYSIS TO RANKING TECHNICAL EFFICIENCIES THROUGH STOCHASTIC FRONTIER ANALYSIS AND DEA Sergio SCIPPACERCOLA Associate Professor, Department of Economics, Management, Institutions University
More informationA New Method for Optimization of Inefficient Cost Units In The Presence of Undesirable Outputs
Available online at http://ijim.srbiau.ac.ir/ Int. J. Industrial Mathematics (ISSN 2008-5621) Vol. 10, No. 4, 2018 Article ID IJIM-01173, 8 pages Research Article A New Method for Optimization of Inefficient
More informationIndian Institute of Management Calcutta. Working Paper Series. WPS No. 787 September 2016
Indian Institute of Management Calcutta Working Paper Series WPS No. 787 September 2016 Improving DEA efficiency under constant sum of inputs/outputs and Common weights Sanjeet Singh Associate Professor
More informationDepartment of Social Systems and Management. Discussion Paper Series
Department of Social Systems and Management Discussion Paper Series No. 1128 Measuring the Change in R&D Efficiency of the Japanese Pharmaceutical Industry by Akihiro Hashimoto and Shoko Haneda July 2005
More informationSlack and Net Technical Efficiency Measurement: A Bootstrap Approach
Slack and Net Technical Efficiency Measurement: A Bootstrap Approach J. Richmond Department of Economics University of Essex Colchester CO4 3SQ U. K. Version 1.0: September 2001 JEL Classification Code:
More informationInvestigación Operativa. New Centralized Resource Allocation DEA Models under Constant Returns to Scale 1
Boletín de Estadística e Investigación Operativa Vol. 28, No. 2, Junio 2012, pp. 110-130 Investigación Operativa New Centralized Resource Allocation DEA Models under Constant Returns to Scale 1 Juan Aparicio,
More informationA Fuzzy Data Envelopment Analysis Approach based on Parametric Programming
INT J COMPUT COMMUN, ISSN 1841-9836 8(4:594-607, August, 013. A Fuzzy Data Envelopment Analysis Approach based on Parametric Programming S.H. Razavi, H. Amoozad, E.K. Zavadskas, S.S. Hashemi Seyed Hossein
More informationEstimating most productive scale size using data envelopment analysis
Estimating most productive scale size using data envelopment analysis 35 Rajiv D. BANKER Carnegie. Mellon Untt,erslt.v. School o/urban and Public Affairs. Pittsburgh. PA 15213, U.S.A. Received February
More informationA short training on efficiency and productivity analyses 1. Introduction
A short training on efficiency and productivity analyses 1. Introduction This two day training briefly reviews [upper-undergraduate level] production theory and introduces the concepts and methods of measuring
More informationSensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models. April Abstract
Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models by Léopold Simar and Paul W. Wilson April 1995 Abstract Efficiency scores of production units are generally
More informationSymmetric Error Structure in Stochastic DEA
Available online at http://ijim.srbiau.ac.ir Int. J. Industrial Mathematics (ISSN 2008-5621) Vol. 4, No. 4, Year 2012 Article ID IJIM-00191, 9 pages Research Article Symmetric Error Structure in Stochastic
More informationPROFIT FUNCTIONS. 1. REPRESENTATION OF TECHNOLOGY 1.1. Technology Sets. The technology set for a given production process is defined as
PROFIT FUNCTIONS 1. REPRESENTATION OF TECHNOLOGY 1.1. Technology Sets. The technology set for a given production process is defined as T {x, y : x ɛ R n, y ɛ R m : x can produce y} where x is a vector
More informationCentre for Efficiency and Productivity Analysis
Centre for Efficiency and Productivity Analysis Working Paper Series No. WP04/2018 Profit Efficiency, DEA, FDH and Big Data Valentin Zelenyuk Date: June 2018 School of Economics University of Queensland
More informationIPRODUCTION FUNCTIONSU) TEXAS UNIV AT AUSIN CENTER FOR ICYBERNETI CAUDIES ACHURNESET AL MAY 83CCS-459
AD-A41768 PAREOOPMALT EFFCIENCYANALYSISAND EMPIRICAL j IPRODUCTION FUNCTIONSU) TEXAS UNIV AT AUSIN CENTER FOR ICYBERNETI CAUDIES ACHURNESET AL MAY 83CCS-459 END 78 4 L MICROCO PY RESOLUTION TEST CHART
More informationA buyer - seller game model for selection and negotiation of purchasing bids on interval data
International Mathematical Forum, 1, 2006, no. 33, 1645-1657 A buyer - seller game model for selection and negotiation of purchasing bids on interval data G. R. Jahanshahloo, F. Hosseinzadeh Lotfi 1, S.
More informationIntegrating Efficiency Concepts in Technology Approximation: A Weighted DEA Approach. Kota Minegishi University of Maryland, College Park
Integrating Efficiency Concepts in Technology Approximation: A Weighted DEA Approach Kota Minegishi University of Maryland, College Park Contact: kminegishi@arec.umd.edu Selected Paper prepared for presentation
More informationMore Technical Efficiency and Data Envelopment Analysis (DEA)
More Technical Efficiency and Data Envelopment Analysis (DEA) based on OnFront, Reference Guide Coelli, et al., Introduction to Efficiency and Productivity Springer, 2005, Ch 6. April 22, 2008 Technology:
More informationFirms and returns to scale -1- John Riley
Firms and returns to scale -1- John Riley Firms and returns to scale. Increasing returns to scale and monopoly pricing 2. Natural monopoly 1 C. Constant returns to scale 21 D. The CRS economy 26 E. pplication
More informationConstrained Optimization and Lagrangian Duality
CIS 520: Machine Learning Oct 02, 2017 Constrained Optimization and Lagrangian Duality Lecturer: Shivani Agarwal Disclaimer: These notes are designed to be a supplement to the lecture. They may or may
More informationData Envelopment Analysis and its aplications
Data Envelopment Analysis and its aplications VŠB-Technical University of Ostrava Czech Republic 13. Letní škola aplikované informatiky Bedřichov Content Classic Special - for the example The aim to calculate
More informationA Rothschild-Stiglitz approach to Bayesian persuasion
A Rothschild-Stiglitz approach to Bayesian persuasion Matthew Gentzkow and Emir Kamenica Stanford University and University of Chicago September 2015 Abstract Rothschild and Stiglitz (1970) introduce a
More informationLinear Programming and Marginal Analysis
337 22 Linear Programming and Marginal Analysis This chapter provides a basic overview of linear programming, and discusses its relationship to the maximization and minimization techniques used for the
More informationLinear Programming. Operations Research. Anthony Papavasiliou 1 / 21
1 / 21 Linear Programming Operations Research Anthony Papavasiliou Contents 2 / 21 1 Primal Linear Program 2 Dual Linear Program Table of Contents 3 / 21 1 Primal Linear Program 2 Dual Linear Program Linear
More informationSpecial Cases in Linear Programming. H. R. Alvarez A., Ph. D. 1
Special Cases in Linear Programming H. R. Alvarez A., Ph. D. 1 Data Envelopment Analysis Objective To compare technical efficiency of different Decision Making Units (DMU) The comparison is made as a function
More informationModeling Dynamic Production Systems with Network Structure
Iranian Journal of Mathematical Sciences and Informatics Vol. 12, No. 1 (2017), pp 13-26 DOI: 10.7508/ijmsi.2017.01.002 Modeling Dynamic Production Systems with Network Structure F. Koushki Department
More informationMEMORANDUM. No 09/99. Monte Carlo Simulations of DEA Efficiency Measures and Hypothesis Tests. By Sverre A.C. Kittelsen
MEMORANDUM No 09/99 Monte Carlo Simulations of DEA Efficiency Measures and Hypothesis Tests By Sverre A.C. Kittelsen ISSN: 080-7 Department of Economics University of Oslo This series is published by the
More informationThe Difference Approach to Productivity Measurement and Exact Indicators November 25, 2017
1 The Difference Approach to Productivity Measurement and Exact Indicators November 25, 2017 Erwin Diewert and Kevin J. Fox, 1 Discussion Paper 17-08, Vancouver School of Economics, University of British
More informationStochastic Nonparametric Envelopment of Data (StoNED) in the Case of Panel Data: Timo Kuosmanen
Stochastic Nonparametric Envelopment of Data (StoNED) in the Case of Panel Data: Timo Kuosmanen NAPW 008 June 5-7, New York City NYU Stern School of Business Motivation The field of productive efficiency
More informationA METHOD FOR SOLVING 0-1 MULTIPLE OBJECTIVE LINEAR PROGRAMMING PROBLEM USING DEA
Journal of the Operations Research Society of Japan 2003, Vol. 46, No. 2, 189-202 2003 The Operations Research Society of Japan A METHOD FOR SOLVING 0-1 MULTIPLE OBJECTIVE LINEAR PROGRAMMING PROBLEM USING
More informationSummary of the simplex method
MVE165/MMG630, The simplex method; degeneracy; unbounded solutions; infeasibility; starting solutions; duality; interpretation Ann-Brith Strömberg 2012 03 16 Summary of the simplex method Optimality condition:
More informationLUENBERGER AND MALMQUIST PRODUCTIVITY INDICES: THEORETICAL COMPARISONS AND EMPIRICAL ILLUSTRATION
# Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research 2003. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden,
More informationDATA ENVELOPMENT ANALYSIS AND ITS APPLICATION TO THE MEASUREMENT OF EFFICIENCY IN HIGHER EDUCATION
DATA ENVELOPMENT ANALYSIS AND ITS APPLICATION TO THE MEASUREMENT OF EFFICIENCY IN HIGHER EDUCATION Jill Johnes* Department of Economics Lancaster University Management School Lancaster University Lancaster
More informationCENTER FOR CYBERNETIC STUDIES
TIC 1 (2 CCS Research Report No. 626 Data Envelopment Analysis 1% by (A. Charnes W.W. Cooper CENTER FOR CYBERNETIC STUDIES DTIC The University of Texas Austin,Texas 78712 ELECTE fl OCT04109W 90 - CCS Research
More information52 LIREZEE, HOWLND ND VN DE PNNE Table 1. Ecient DMU's in Bank Branch Eciency Studies. Study DMU's Number Ecient Percentage verage of inputs, DMU's Ec
c pplied Mathematics & Decision Sciences, 2(1), 51{64 (1998) Reprints vailable directly from the Editor. Printed in New Zealand. SMPLING SIZE ND EFFICIENCY BIS IN DT ENVELOPMENT NLYSIS MOHMMD R. LIREZEE
More informationEnumeration algorithms for FDH directional distance functions under different returns to scale assumptions
http://lem.cnrs.fr Document de travail du LEM Discussion paper LEM 2017-04 Enumeration algorithms for FDH directional distance functions under different returns to scale assumptions Kristiaan KERSTENS
More information