Multiple Criteria Data Envelopment Analysis Research Articles

A new multiple criteria data envelopment analysis with variable return to scale: Applying bi-dimensional representation and super-efficiency analysis

It is known that, in general, in practical real-world problems, when the number of Decision- Making Units (DMUs) is not large enough compared to the total number of input and output parameters, the traditional DEA models with Constant Return to Scale – CRS and with Variable Return to Scale – VRS have a weak power of discrimination, producing solutions that identify many DMUs as being efficient, in addition to obtaining unrealistic weight distributions. In this context, it is recommended to work with Multiple Criteria Data Envelopment Analysis - MCDEA models. So far, all MCDEA models available in the literature adopt CRS approach. This paper proposes a New Multiple Criteria Data Envelopment Analysis (NMCDEA) – VRS model, as well as performs a super-efficiency analysis for this model. Furthermore, through bi- dimensional graphic representations, a geometric demonstration is provided, showing that, in fact, the proposed model is a good representation of situations in which it is interesting to consider a VRS behavior. The results obtained through the optimization of instances available in the literature, for real instances, as well as the sensitivity analysis carried out, indicated that the NMCDEA-VRS has a much greater power of discrimination compared to the classic DEA–VRS model.

Goal programming and multiple criteria data envelopment analysis combined with optimization and Monte Carlo simulation: An application in railway components

AbstractThis work has been developed in a large steel industry in Brazil, which produces railway and industrial components, and whose aim was to reduce casting defects. Usually, in industrial processes, identifying the causes of defects and their control are relatively complex activities, due to the many variables involved. In this context, the production processes of seven products, involving 38 process variables (inputs and outputs), have been evaluated adopting a new and innovative procedure. Initially, using a Weighted Goal Programming ‐ Multiple Criteria Data Envelopment Analysis (WGP‐MCDEA) model, we identified the most relevant input and output variables, and the studied company validated the results. Next, using the multiple regression technique, empirical functions were constructed for two response variables chosen by the company – number of external cracks and number of internal cracks. Then, to model the real processes adequately, we introduced the occurrence of uncertainty on the coefficients of these functions, considering them as random variables, according to triangular probability functions. Finally, applying the optimizer Optquest, optimization via Monte Carlo simulation (OvMCS) was performed, and with the Ordinary Least Square technique, we obtained the best fit for the two response variables. Specialists from the company validated the proposed procedure. They found that the values of input and output variables obtained by OvMSC, as well as the values of the response variables, belonged to the database available in the ERP system of the company. These results showed that the procedure proposed herein provided feasible and useful solutions to improve the industrial processes under study.

Multiple Criteria DEA-Based Ranking Approach With the Transformation of Decision-Making Units

Though various ranking methods in the data envelopment analysis (DEA) context have emerged since the conventional DEA was introduced, none of them has not been accepted as a universal or a superior method for ranking decision-making units (DMUs). The DEA-based ranking methods show some shortcomings as the numbers of inputs and outputs for DMUs increase. To overcome such shortcomings, this paper proposes a two-step procedure of ranking DMUs more effectively and consistently. In the first step, the multi-objective programming (MOP) is applied for the multiple criteria DEA to transform the original DMUs into the new simpler DMUs with two inputs and a single output, regardless of the numbers of inputs and outputs that the original DMUs use and produce. With the transformed DMUs, some conventional DEA based-methods for ranking DMUs are applied in the second step. A numerical example demonstrates the efficient performance of the proposed method.

Multiple Criteria DEA-Based Ranking Approach With the Transformation of Decision-Making Units

Though various ranking methods in the data envelopment analysis (DEA) context have emerged since the conventional DEA was introduced, none of them has not been accepted as a universal or a superior method for ranking decision-making units (DMUs). The DEA-based ranking methods show some shortcomings as the numbers of inputs and outputs for DMUs increase. To overcome such shortcomings, this paper proposes a two-step procedure of ranking DMUs more effectively and consistently. In the first step, the multi-objective programming (MOP) is applied for the multiple criteria DEA to transform the original DMUs into the new simpler DMUs with two inputs and a single output, regardless of the numbers of inputs and outputs that the original DMUs use and produce. With the transformed DMUs, some conventional DEA based-methods for ranking DMUs are applied in the second step. A numerical example demonstrates the efficient performance of the proposed method.

Application of Integrated Multiple Criteria Data Envelopment Analysis to Humanitarian Logistics Network Design

This paper considers a humanitarian logistics network (HTLN) design problem, including the emergency relief facilities (ERFs) location-allocation decision for the efficient distribution of emergency supplies from the ERFs to the affected areas. A goal programming (GP) approach is applied to consider the multiple objectives simultaneously. Solving the GP model with a given weight assigned to each goal yields a single HTLN scheme, so there will be various schemes available by solving the GP with multiple values of the weights. For evaluating these schemes and identifying the most efficient one, we apply the data envelopment analysis (DEA) methods considering each scheme as a decision-making unit (DMU). Since the classical DEA (C-DEA) intrinsically aims to identify efficient DMUs and the efficient frontier, the use of C-DEA may not lead to a full ranking in many situations. There are several independent evaluation approaches to increasing discriminating power. Among them, this study integrates the multiple criteria DEA (MC-DEA) with the following three DEA methods, (i) stratification DEA (S-DEA), (ii) cross-efficiency DEA (CE-DEA), and (iii) super-efficiency DEA (SE-DEA), to make the most use of each method’s strengths. Through a case study of designing the HTLN system for South Carolina, the procedure of implementing the integrated multiple criteria DEA (IMC-DEA) method is demonstrated. It is observed that the IMC-DEA method performs well in terms of designing the HTLN system and would help the decision-makers consider more efficient options and make a final decision.

Global Criterion Approach for the Solution of Multiple Criteria Data Envelopment Analysis Model: An Application at Packaging Waste Collection and Separation Facilities

Adverse effects of packaging waste on the environment and economic losses resulting from the use of untouched resources have made the recycling process compulsory. The success of the collection and separation of packaging waste, which are the most important phases in the recycling process, depends on the effective management of these processes. In this paper, we analyzed the efficiency of 14 collection and separation facilities. A Global- Multiple Criteria Data Envelopment Analysis model (G-MCDEA) based on a global criterion method was proposed for the solution of the multiple criteria data envelopment analysis model, which is organized as a three-objective multiple objective linear programming model. With the proposed model, the three objective functions were transformed into a single objective function, and the normalized grades of the distance from the ideal solution was calculated for each decision making unit. In this was it was determined which objective was closer to the global activity achieved.

Improving manufacturing cycle efficiency through new multiple criteria data envelopment analysis models: an application in green and lean manufacturing processes

The Green & Lean Manufacturing organisational strategy emphasises waste and environmental impact reduction, efficiency increase, quality improvement, and cycle time reduction by eliminating non-value-added activities. Usually, companies adopt the Manufacturing Cycle Efficiency indicator to identify and make improvements to meet Lean Manufacturing requirements. This work proposes an innovative approach based on Multiple Criteria Data Envelopment Analysis to calculate a new indicator, hereby called Value-Added Activities in Manufacturing Processes, to measure the efficiency of productive processes through Green Manufacturing concepts. This new indicator was applied in a company with the purpose of validating and testing it. The Levene’s test was used to statistically validate the proposed procedure. As an immediate advantage of this new indicator, it was possible for managers to insert more information, such as incorporating aspects associated with Green Manufacturing, in the calculation of the Manufacturing Cycle Efficiency, making it more consistent and representative of what is happening in practice. Among this additional piece of information on the real processes analysed, it is worth mentioning, for example, the volume of scrap generated, the amount of sales invoicing, the quantity of work in process, and the quantity of finished products in stock. Specialists in Green & Lean Manufacturing, managers of the studied company, validated the results of the new indicator because they observed greater adherence to the practice of these new calculated values, when compared to the traditionally adopted calculations. Also highlighted, are other advantages of the new indicator such as the establishment of an efficiency ranking between the productive processes analysed and the determination of feasible goals to turn processes identified as inefficient into efficient ones.

Improving the discrimination power with a new multi-criteria data envelopment model

Data envelopment analysis (DEA) allows evaluation of the relative efficiencies of similar entities, known as decision making units (DMUs), which consume the same types of resources and offer similar types of products. It is known that under certain circumstances, when the number of DMUs does not meet the DEA Golden Rule, that is, this number is not sufficiently large compared to the total number of inputs and outputs, traditional DEA models often yield solutions that identify too many DMUs as efficient. In fact, this weak discrimination power and unrealistic weight distribution presented by DEA models remain a major challenge, leading to the development of models to improve this performance, such as: multiple criteria data envelopment analysis (MCDEA), bi-objective multiple criteria data envelopment analysis, goal programming approaches to solve weighted goal programming (WGP–MCDEA) and extended–MCDEA. This paper proposes a new MCDEA model which is based on goal programming, with and without super efficiency concepts, and presents test results that show its advantages over the above cited models. A set of problems from the literature and real-world applications are used in these tests. The results show that the new MCDEA model provides better discrimination of DMUs in all tested problems, and provides a weight dispersion that is statistically equal to that obtained by other MCDEA models. An additional feature of the proposed model is that it allows the identification of the input and output variables that are most important to the problem, to make it easier for the decision maker to improve the efficiency of the DMUs involved. This is very useful in practice, because in general, the available resources are scarce, so it is a further advantage of the proposed MCDEA model over the others tested.

EFFICIENCY ASSESSMENT OF CENTRAL AIRPORTS IN BRAZIL

> In this paper, we asses the efficiency of Brazilian airports, based on Data Envelopment Analysis (DEA). Although previous studies applied DEA to Brazilian airports, herein we consider DEA´s homogeneity assumption, according to which units are assumed to operate in similar environments. As airport environment differs significantly throughout the country, we limit our analysis to six central airports. Still, our results are valuable nationwide, because these airports handle half of all flights departing from Brazil. As classic DEA is not recommended for small data sets, we use Multiple Criteria DEA, which has more discriminatory power. In our study, we found that only two airports in the State of Sao Paulo are efficient, whereas the other central airports are under-utilized, with an efficiency score of less than 50%. Results found in this study could serve as an important tool for public politics, as well as for private decisions in the airport sector. KEYWORDS. Airport efficiency; central airports; Brazilian air transport; Multiple Criteria Data Envelopment Analysis. MSC: 90B06

A Discriminant Analysis and Goal Programming Approach to solve the Multiple Criteria Data Envelopment Analysis Model

A Discriminant Analysis and Goal Programming Approach to solve the Multiple Criteria Data Envelopment Analysis Model

Bi-Objective Multiple Criteria Data Envelopment Analysis combined with the Overall Equipment Effectiveness: An application in an automotive company

The mass production companies need to seek high efficiency in the use of equipment and human resources, as well as in the consumption of their inputs. One of the key methods to address these challenges is the adoption of Overall Equipment Effectiveness, derived from Total Productive Maintenance. This work aims to propose a new efficiency indicator, called Overall Machinery Effectiveness, to be applied in an automotive company in Brazil that adopted Overall Equipment Effectiveness indicator. The studied company made available production data from ten months, associated to two Press machines, generating twenty Decision Making Units for Data Envelopment Analysis and Bi-Objective Multiple Criteria Data Envelopment Analysis models application. As results, Press #2 was identified as being the most critical because, among the first ten DMUs in the efficiency ranking, seven are associated to Press #1. The targets values recommended by the new indicator were considered feasible to be implemented by the company, thus validating in practice the new proposed procedure for the management of machines effectiveness. Moreover, the identification of the relevant variables (input and output) for the Press #1, and Press #2, allowed the decision maker to act in the best way to increase their efficiency.

An extended multiple criteria data envelopment analysis model

Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries.

A goal programming approach to solve the multiple criteria DEA model

The lack of discrimination power and the inappropriate multipliers schemes remain major issues in data envelopment analysis (DEA). To overcome these problems, the multiple criteria DEA (MCDEA) model was introduced in the late 1990s, drawing from a multiple objective perspective. However, because the objectives of the MCDEA model are generally conflicting, an optimal solution satisfying all objectives simultaneously often does not exist. Within this context, goal programming (GP) approaches were proposed to solve the MCDEA model. This paper focuses specifically on the GP formulation, known as GPDEA. However, recently, the GPDEA models were found to be invalid, and no alternative formulation, under a GP framework, was proposed. Therefore, the aim here is to develop a formulation for adequately solving the MCDEA model using weighted GP. In order to do so, we point out inconsistencies in the existing GPDEA models, and we present the WGP-MCDEA model.

A multiple criteria approach to two-stage data envelopment analysis

Two-stage data envelopment analysis (DEA) models are commonly used in the evaluation and benchmarking of sustainable operations and processes across multiple research fields. To date, however, little attention has been given to the unrealistic weight distribution and weak discrimination power in the modeling and evaluation of the two-stage sustainable operations when using two-stage DEA models. In order to overcome this methodological weakness, we use the multiple criteria DEA (MCDEA) approach in the evaluation of the two-stage processes. The outcome is a multiple criteria two-stage DEA model which yields more realistic weights for the inputs and outputs and thus has better discrimination power than traditional two-stage DEA models. The developed model is tested and validated by assessing the sustainable design performances of a sample of car product designs.

Studies of some duality properties in the Li and Reeves model

In 1999, Li and Reeves presented the so-called MCDEA (Multiple Criteria Data Envelopment Analysis) model. This model is in fact a three objective linear model. It may be used to improve the discriminatory power of the DEA models, as well as generate a more reasonable distribution of the inputs and outputs weights. Besides the classical optimization of the efficiency index, Li and Reeves introduced two other objective functions, called minisum and minimax. Despite of being an important approach, it does not provide benchmarks or targets for inefficient DMUs. Benchmarks and targets are one of the most important DEA features and in standard DEA are determined using the dual (envelope) model. In this paper, we introduce an approach of the MCDEA dual formulation taking into account only two objective functions at each time. Combining both partial models we suggest benchmarks for each inefficient DMU.

Greenfield distribution network expansion strategy with hierarchical GA and MCDEA under uncertainty

Abstract Distribution network expansion planning (DNEP) is becoming more complex in nature. Addition of new load centers, due to increasing conversion of greenfield areas into habitats, have generated need of more intense and highly structured planning strategies. Micro level work on distribution expansion planning has been ignored by most of the researchers mainly in Indian scenario. Since practical distribution networks are quite large, number of candidates (load centers) will be more and, hence, number of variables (electrical parameters and new load center feasible connections with the existing system) are remarkable. Optimizing a large system may result in significant decrease of accuracy and increase of computation time. For deciphering this issue, segmentation procedure has been applicable. For this purpose, a sensitivity analysis has been applied to find dependent variables. It is obvious that a correct segmentation can decrease computation time (as a single task is operated in segments simultaneously) while accuracy decreases negligibly. In present work, a scheme has been introduced to connect three greenfield load centers with existing primary distribution system by using hierarchical genetic algorithm (HGA). HGA is an integrated approach of analytical hierarchical process and genetic algorithm. The paper reports best selection of investment with finest voltage profile and least losses while maintaining radiality of the system. DNEP has been done at micro level and proposed methodology has been tested on a small dimension practical distribution system. The novelty of this paper is to optimize the best possible selection of connection of new load centers with existing system with the help of AHP and GA and results have been verified with advance optimal tool multiple criteria data envelopment analysis (MCDEA). HGA and MCDEA are applied to practical nine bus distribution system and the results are presented and compared.

Goal-Programming-Based Procedure for Calculating Positive Multipliers Under a Multiple Criteria Data Envelopment Analysis Framework: An Application to UEFA EURO 2012

One of the motivations for the arise of the multiple criteria data envelopment analysis (MCDEA) model was the need to yield more reasonable input-output multipliers than those derived from standard data envelopment analysis (DEA), without using priori information. The problem of unreasonable multipliers occurs when some production units are efficient in standard DEA simply because the optimization problem allows those units to select few inputs/outputs to attach positive multipliers, discarding all of the others. Notwithstanding, MCDEA may fail in providing multipliers schemes free of non-null values. Therefore, in this paper, we propose an alternative procedure, based on goal programming, for calculating positive multipliers within a MCDEA framework. This procedure is applied to a previously reported problem, concerning the performance evaluation of national teams that participated in the 2012 UEFA European Football Championship (UEFA EURO 2012), where the MCDEA model has not succeeded in providing strictly positive multipliers schemes. The results derived by the proposed procedure indicate that, to assure non-null multipliers, it is necessary a mild detachment of non-dominated solutions.

PEMILIHAN GABUNGAN PRODUK MENGGUNAKAN SIMULASI BERKOMPUTER DAN ANALISIS PENYAMPULAN DATA

A combination of product selection is one of the decision that are difficult to be determined especially in SME’s food manufacturing company that produces different types of food products. Making a wrong decision in the combination of product selection will affect company profitability. In this study, computer simulation, Multiple Criteria Data Envelopment Analysis (MCDEA), BCC output-oriented and cross efficiency is proposed to determine the efficient combination of product alternatives and to rank the combination of product alternatives. Six combinations of product alternatives are identified and with the assistance of computer simulation, inputs and outputs are generated. Inputs used are cost and work in process while revenue, average operator utilization and total production are outputs. The study was conducted at one of SME’s food manufacturing companies. The results show that the production of the same types of food product is chosen as the best combination of products. The proposed methods are systematic and comprehensive, especially when adopt to SME’s.

Multiple Criteria Data Envelopment Analysis – An Application to UEFA EURO 2012

In this work, we evaluate the final performance of UEFA EURO 2012 national teams, by means of a methodology that combines Data Envelopment Analysis and Multiple Objective Linear Programming, known as MCDEA (Multiple Criteria Data Envelopment Analysis). Nonetheless, the formulation herein proposed is an extension of the original MCDEA model, as it considers the radial output orientation. The use of the MCDEA model seeks to improve the discrimination power among the evaluated units (national teams), a well-known limitation of traditional DEA models. The results reveal that the MCDEA framework actually enhanced the discrimination, considerably reducing the number of efficient units.

A bi-objective weighted model for improving the discrimination power in MCDEA

Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach.