A modified DEA cross efficiency method with negative data and its application in supplier selection

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

     

On the relation between Wiener index and eccentricity of a graph

Journal of Combinatorial Optimization - The relation between the Wiener index W(G) and the eccentricity $$\varepsilon (G)$$ of a graph G is studied. Lower and upper bounds on W(G) in terms of...     

The Beta Exponential-Geometric Distribution

A new four-parameter distribution with decreasing, increasing, and upside-down bathtub failure rate called the beta exponential-geometric distribution is proposed. The new distribution, generated from the logit of a beta random variable, extends the exponential-geometric distribution of Adamidis and Loukas (1998 Adamidis , K. , Loukas , S. ( 1998 ). A lifetime distribution with decreasing failure rate . Statistics and Probability Letters 39 : 35 – 42 .[Crossref], [Web of Science ®] , [Google Scholar]) and some other distributions. A comprehensive mathematical treatment of this distribution is provided. Some expressions for the moment generating function, moments, order statistics, and Rényi entropy of the new distribution are derived. Estimation of the stress-strength parameter is also obtained. The model parameters are estimated by the maximum likelihood method and Fisher information matrix is discussed. Finally, an application to a real data set is illustrated.     

A two-step robust estimation of the process mean using M-estimator

Parameter estimation is the first step in constructing control charts. One of these parameters is the process mean. The classical estimators of the process mean are sensitive to the presence of outlying data and subgroups which contaminate the whole data. In existing robust estimators for the process mean, the effects of the presence of the individual outliers are being considered, while, in this paper, a robust estimator is being proposed to reduce the effect of outlying subgroups as well as the individual outliers within a subgroup. The proposed estimator was compared with some classical and robust estimators of the process mean. Although, its relative efficiency is fourth among the estimators tested, its robustness and efficiency are large when the outlying subgroups are present. Evaluation of the results indicated that the proposed estimator is less sensitive to the presence of outliers and the process mean performs well when there are no individual outliers or outlying subgroups.     

A robust R control chart based on a two-step estimator of the process dispersion

ABSTRACT

Control charts are the frequently used tools for monitoring and controlling the processes. Classical control charts are sensitive to existing contaminated data which may be presented in the data collected from the processes. Thus, these charts are not able to control the processes precisely when the data are contaminated. Robust control charts are those which are less sensitive to contamination. Some robust control charts for monitoring the process variability were proposed in the past which are robust to some sorts of contamination. In this paper a new robust R control chart is proposed which is less sensitive to wide range of contaminations, i.e. general and local contaminations. Simulation studies are performed to compare the performance of the proposed control chart with some classical and robust control charts, using ARL and MSD as criteria for comparisons purposes. The simulation results show a very good performance of the proposed chart when both types of contaminations exist.     

Predicting losses of residential structures in the state of Florida by the public hurricane loss evaluation model

As an environmental phenomenon, hurricanes cause significant property damage and loss of life in coastal areas almost every year. Although a number of commercial loss projection models have been developed to predict the property losses, only a handful of studies are available in the public domain to predict damage for hurricane prone areas. The state of Florida has developed an open, public model for the purpose of probabilistic assessment of risk to insured residential property associated with wind damage from hurricanes. The model comprises three components; viz. the atmospheric science component, the engineering component and the actuarial science component. The atmospheric component includes modeling the track and intensity life cycle of each simulated hurricane within the Florida threat area. Based on historical hurricane statistics, thousands of storms are simulated allowing determination of the wind risk for all residential Zip Code locations in Florida. The wind risk information is then provided to the engineering and actuarial components to model damage and average annual loss, respectively. The actuarial team finds the county-wise loss and the total loss for the entire state of Florida. The computer team then compiles all information from atmospheric science, engineering and actuarial components, processes all hurricane related data and completes the project. The model was submitted to the Florida Commission on Hurricane Loss Projection Methodology for approval and went through a rigorous review and was revised as per the suggestions of the commission. The final model was approved for use by the insurance companies in Florida by the commission. At every stage of the process, statistical procedures were used to model various parameters and validate the model. This paper presents a brief summary of the main components of the model (meteorology, vulnerability and actuarial) and then focuses on the statistical validation of the same.     

Authors’ responses to the discussion on “Predicting losses of residential structures in the state of Florida by the Public Hurricane Loss Evaluation Model”

Hurricanes threaten the Florida coast line every year and are capable of causing catastrophic losses. The Public Hurricane Loss Model was developed in response to the need for having an open transparent model to predict the above losses. The results were summarized in the paper “Predicting Losses of Residential Structures in the State of Florida by the Public Hurricane Loss Model” which was subsequently a subject of discussion by experts in Meteorology, Engineering, Actuarial Sciences and Statistics. The present paper presents a response to the discussions on the above mentioned article.