An input relaxation model for evaluating congestion in fuzzy DEA

This paper develops a BCC input relaxation model for identifying input congestion as a severe form of inefficiency of decision-making units in fuzzy data envelopment analysis. The possibility approach is presented to obtain the models equivalent to fuzzy models. We use a one-model approach to determine input congestion based on the BCC input relaxation model. A numerical example is given to illustrate the proposed model and identify the congestion with precise and imprecise data. The proposed model is also used to determine the congestion in 16 hospitals using four fuzzy inputs and two fuzzy outputs with a symmetrical triangular membership function

Fuzzy Data Envelopment Analysis Approach for Ranking of Stocks with an Application to Tehran Stock Exchange

The main goal of this paper is to propose a new approach for efficiency measurement and ranking of stocks. Data envelopment analysis (DEA) is one of the popular and applicable techniques that can be used to reach this goal. However, there are always concerns about negative data and uncertainty in financial markets. Since the classical DEA models cannot deal with negative and imprecise values, in this paper, possibilistic range directional measure (PRDM) model is proposed to measure the efficiencies of stocks in the presence of negative data and uncertainty with input/output parameters. Using the data from insurance industry, this model is also implemented for a real case study of Tehran stock exchange (TSE) in order to analyse the performance of the proposed method

Optimization of the supplier selection process in prefabrication using BIM

Prefabrication offers substantial benefits including reduction in construction waste, material waste, energy use, labor demands, and delivery time, and an improvement in project constructability and cost certainty. As the material cost accounts for nearly 70% of the total cost of the prefabrication project, to select a suitable material supplier plays an important role in such a project. The purpose of this study is to present a method for supporting supplier selection of a prefabrication project. The proposed method consists of three parts. First, a list of assessment criteria was established to evaluate the suitability of supplier alternatives. Second, Building Information Modelling (BIM) was adopted to provide sufficient information about the project requirements and suppliers’ profiles, which facilitates the storage and sharing of information. Finally, the Analytic Hierarchy Process (AHP) was used to rank the importance of the assessment criteria and obtain the score of supplier alternatives. The suppliers were ranked based on the total scores. To illustrate how to use the proposed method, it was applied to a real prefabrication project. The proposed method facilitates the supplier selection process by providing sufficient information in an effective way and by improving the understanding of the project requirements

Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

A fuzzy data envelopment analysis based on credibility theory for estimating road safety

Road accidents as a global challenge, imposing irreparable financial and human life losses in almost all countries, especially in developing countries, annually. According to world health organization (WHO), if this trend continues, road accidents will become the 7th cause of human death by 2030. Thus, road safety policy makers have been trying to use safety promotion and preventative actions. In this paper, the road safety performance of Iranian provinces is studied. To evaluate road safety efficiency scores, data envelopment analysis based on road safety (DEA-RS) method in two deterministic and non-deterministic situations is used. To consider the uncertainty in input and output data, this paper develops credibility DEA-RS (CreDEA-RS) model. In fact, the constraints of DEA-RS model are considered as credibility constraints and a counterpart credibility DEA-RS (CreDEA-RS) model is proposed for evaluating road safety of provinces of Iran. According to the results, provinces located in mountainous and forest areas such as Gilan had a much weaker performance than provinces in desert areas such as Yazd

An Application of Data Envelopment Analysis in the Selection of the Best Response for the Drilling of Carbon Fiber-reinforced Plastic Composites

In the drilling operation, defects such as delamination at exit and entry are very disturbing responses that impact the efficiency of the drilling process. Without control, an exponential growth in the amount of drilled components with defect quantities may result. Thus, the process engineer has input in attaining the desired production levels for components in the drilling process. Consequently, this article deploys a novel method of data envelopment analysis to evaluate the relative efficiency of the drilling process in reducing the defects possible in the producing components from the CFRP composites. The high-speed steel drill bits were utilized to process the CFPs, while the responses considered are the entry and exit determination, thrust force, and torque, among others. Literature experimental data in twenty-seven experimental counts were summarized into fewer groups and processed through the data envelopment analysis method. The results show that capturing the CFRP composite responses is feasible, providing an opportunity for enhanced efficiency and a situation where undesirable defects in the CFRP composite production process may be eradicated. The article’s uniqueness and primary value are in being the foremost article in offering an updated vast representation of the comparative efficiency of CFRP composite parameters within the literature for the composite area. The work adds value to the CFRP composite literature by envisaging and understanding the comparative efficiency for the parameters, identifying and separating the best from the worst decision-making unit. It also reveals how the parameters are linked by their relative placements. The article's novelty is that using data envelopment to compare the efficiency in reducing drilling defects such as entry and exit determination, among others. The method’s utility is to provide information for cost-effective drilling operations during the planning and control phases of the operation

A New Dynamic Random Fuzzy DEA Model to Predict Performance of Decision Making Units

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) which ‎consume the same types of inputs and producing the same types of outputs. Believing that future planning and predicting the ‎efficiency are very important for DMUs, this paper first presents a new dynamic random fuzzy DEA model (DRF-DEA) with ‎common weights (using multi objective DEA approach) to predict the efficiency of DMUs under mean chance constraints and ‎expected values of the objective functions. In the initial proposed†â€DRF-DEA model, the inputs and outputs are assumed to be ‎characterized by random triangular fuzzy variables with normal distribution, in which data are changing sequentially. Under this ‎assumption, the solution process is very complex. So we then convert the initial proposed DRF-DEA model to its equivalent multi-‎objective stochastic programming, in which the constraints contain the standard normal distribution functions, and the objective ‎functions are the expected values of functions of normal random variables. In order to improve in computational time, we then ‎convert the equivalent multi-objective stochastic model to one objective stochastic model with using fuzzy multiple objectives ‎programming approach. To solve it, we design a new hybrid algorithm by integrating Monte Carlo (MC) simulation and Genetic ‎Algorithm (GA). Since no benchmark is available in the literature, one practical example will be presented. The computational results ‎show that our hybrid algorithm outperforms the hybrid GA algorithm which was proposed by Qin and Liu (2010) in terms of ‎runtime and solution quality. â€

Stochastic non-parametric efficiency measurement and yardstick competition in electricity regulation

Stochastic non-parametric efficiency measurement constructs production or cost frontiers that incorporate both inefficiency and stochastic error. This results in a closer envelopment of the mean performance of the companies in the sample and diminishes the effect of extreme outliers. This paper uses the Land, Lovell and Thore (1993) model incorporating information on the covariance structure of inputs and outputs to study efficiency across a panel of 14 electricity distribution companies in the UK during the 1990s. The purpose is to revisit the 1999 distribution price control review carried out by the UK regulator. The regulator’s benchmarking is contrasted with the stochastic nonparametric efficiency results and with other comparative efficiency models offering close envelopment of the data. Some conclusions are offered about the possible regulated price effects in the UK case

Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs

Data envelopment analysis (DEA) is a well-known non-parametric technique primarily used to estimate radial efficiency under a set of mild assumptions regarding the production possibility set and the production function. The technical efficiency measure can be complemented with a consistent radial metrics for cost, revenue and profit efficiency in DEA, but only for the setting with known input and output prices. In many real applications of performance measurement, such as the evaluation of utilities, banks and supply chain operations, the input and/or output data are often stochastic and linked to exogenous random variables. It is known from standard results in stochastic programming that rankings of stochastic functions are biased if expected values are used for key parameters. In this paper, we propose economic efficiency measures for stochastic data with known input and output prices. We transform the stochastic economic efficiency models into a deterministic equivalent non-linear form that can be simplified to a deterministic programming with quadratic constraints. An application for a cost minimizing planning problem of a state government in the US is presented to illustrate the applicability of the proposed framework