In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) DIRECTIONAL DISTANCE FUNCTION through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH DIRECTIONAL DISTANCE FUNCTION. We prove that the proposed measures are translation invariant and unit invariant. In addition, we present effective enumeration algorithms to compute them. Our proposed measures have several practical advantages such as: (a) providing closest Pareto-efficient observed targets (b) incorporating the decision maker’s preference information into efficiency analysis and (c) being flexible in computer programming. We illustrate the newly developed approach with a real world data set.

We present an integrated data envelopment analysis (DEA) and Malmquist productivity index (MPI) to evaluate the performance of decision making units (DMUs) by using a DIRECTIONAL DISTANCE FUNCTION with undesirable interval outputs. The MPI calculation is performed to compare the efficiency of the DMUs in distinct time periods. The uncertainty inherent in real-world problems is considered by using the best and worst-case scenarios, defining an interval for the MPI and reflecting the DMUs’ advancement or regress. The optimal solution of the robust model lies in the efficiency interval, i. e., it is always equal to or less than the optimal solution in the optimistic case and equal to or greater than the optimal solution in the pessimistic case. We also present a case study in the banking industry to demonstrate applicability and efficacy of the proposed integrated approach.

In conventional DEA methods, all inputs and outputs are assumed to be continuous. However, the implied presumption of continuous data may not maintain an acceptable level of precision in practical data. Many practical situations such as number of teachers in a school, number of students in a college, or research papers only take integer values. Presented work presumes subsets of input and output variables in traditional , ve-pronged axioms in DEA model to be integer values for the , rst time in the , eld. An additional e, ort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the , rst phase produces more precise e, ciency values and the best benchmark in its second phase, i. e. the nearest integer point to the e, ciency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of e, ciency values obtained with this model compared to prior models that is show in table 1. And in Table 2, the values of the slack are compared with each other.

Background: The ongoing advancements in modern society have negatively impacted air quality, and India is one of the worst affected countries. This study aimed to evaluate the efficiency of maintaining air quality in 10 major Indian cities. Methods: The present study employed a DIRECTIONAL DISTANCE FUNCTION (DDF) within the framework of data envelopment analysis (DEA) to evaluate the efficiency of 10 major cities including Chennai, Delhi, Bengaluru, Ahmedabad, Hyderabad, Jaipur, Lucknow, Patna, Gurugram, and Thiruvananthapuram from January 01, 2018 to December 31, 2019. Results: The results indicate that air pollution is a significant issue in most cities in India. Thiruvananthapuram, Bengaluru, and Chennai were identified as the most efficient cities in terms of air quality for both 2018 and 2019 whereas Ahmedabad was noted as a purely inefficient city during the same period. Moreover, it was revealed that cities in the northern (Delhi, Lucknow, Patna), western (Ahmedabad), and northwestern (Jaipur, Gurugram) parts of India had higher levels of air pollution compared to the southern (Chennai, Bengaluru, Hyderabad, Thiruvananthapuram) part of India. Conclusion: There are significant disparities in air quality efficiency among the cities, revealing that southern cities perform better than their northern, western, and northwestern counterparts. It emphasizes the need for targeted interventions to improve air quality, particularly in cities like Delhi, Ahmedabad, and Jaipur.

In this paper we develop an approach that synthesizes the best features of the two main methods in the estimation of production efficiency. Specifically, our approach first allows for statistical noise, similar to Stochastic frontier analysis, and second, it allows modeling multiple-inputs-multiple-outputs technologies without imposing parametric assumptions on production relationship, similar to what is done in non-parametric methods. The methodology is based on the theory of local maximum likelihood estimation and extends recent works of Kumbhakar et al. We will use local-spherical coordinate system to transform multi-input multi-output data to more flexible system which we can use in our approach. We also illustrate the performance of our approach with simulated example.

In this paper, two methods named DISTANCE and triangle methods are extended to evaluate the quality of approximation of the Pareto set from solving bi-objective problems. In order to use evaluation methods, a bi-objective problem is needed to define. It is considered the problem of scheduling jobs in a hybrid flow shop environment with sequence-dependent setup times and the objectives of minimizing both the makespan and the total tardiness. The bi-objective genetic algorithm in literature is applied to solve this problem belongs to NP-hard class. In the structure of algorithm, 3 and 4 alternatives for dispatching rules and neighborhood search structure have been introduced respectively. Therefore, twelve algorithms are derived from a combination of dispatching rules and neighborhood search structures. After the execution of algorithms, efficient sets are compared through several evaluation methods. Computational results show that the FIFO rule is the best alternative for the dispatching rule in order to find the job sequence for the second to end stages.