New Approach in Fixed Resource Allocation and Target Setting Using Data Envelopment Analysis with Common Set of Weights

One of the mathematical programming techniques is data envelopment analysis (DEA), which is used for evaluating the efficiency of a set of similar decision-making units (DMUs). Fixed resource allocation and target setting with the help of DEA is a subject that has gained much attention from researchers. A new model was proposed by determining a common set of weights (CSW). All DMUs were involved with the aim of achieving higher efficiency in every DMU after the procedure. The minimum resources and targets allocated to each DMU were commensurate to the efficiency of that DMU and the share of DMU in the input resources and the output productions. To examine the proposed method, other methods in the DEA literature were examined as well, and then, the efficiency of the method was demonstrated through a numerical example.

Fuzzy clustering of homogeneous decision making units with common weights in data envelopment analysis

Data Envelopment Analysis (DEA) is the most popular mathematical approach to assess efficiency of decision-making units (DMUs). In complex organizations, DMUs face a heterogeneous condition regarding environmental factors which affect their efficiencies. When there are a large number of objects, non-homogeneity of DMUs significantly influences their efficiency scores that leads to unfair ranking of DMUs. The aim of this study is to deal with non-homogeneous DMUs by implementing a clustering technique for further efficiency analysis. This paper proposes a common set of weights (CSW) model with ideal point method to develop an identical weight vector for all DMUs. This study proposes a framework to measuring efficiency of complex organizations, such as banks, that have several operational styles or various objectives. The proposed framework helps managers and decision makers (1) to identify environmental components influencing the efficiency of DMUs, (2) to use a fuzzy equivalence relation approach proposed here to cluster the DMUs to homogenized groups, (3) to produce a common set of weights (CSWs) for all DMUs with the model developed here that considers fuzzy data within each cluster, and finally (4) to calculate the efficiency score and overall ranking of DMUs within each cluster.

Evaluating the Eco-Efficiency of Wastewater Treatment Plants: Comparison of Optimistic and Pessimistic Approaches

The assessment of wastewater treatment plant (WWTP) performance has gained the interest of water utilities and water regulators. Eco-efficiency has been identified as a powerful indicator, as it integrates economic and environmental variables into a single index. Most previous studies have employed traditional data envelopment analysis (DEA) for the evaluation of WWTP eco-efficiency. However, DEA allows the selection of input and output weights for individual WWTPs for the calculation of eco-efficiency scores. To overcome this limitation, we employed the double-frontier and common set of weights methods to evaluate the eco-efficiency of a sample of 30 WWTPs in Spain. The WWTPs were ranked based on eco-efficiency scores derived under several scenarios including best- and worst-case scenarios; this approach to performance assessment is reliable and robust. Twenty-six of the 30 WWTPs were not classified as eco-efficient, even under the most favorable scenario, indicating that these facilities have substantial room for the reduction of costs and greenhouse gas emissions. The ranking of WWTPs varied according to the scenario used for evaluation, which has notable consequences when eco-efficiency scores are used for regulatory purposes. The findings of this study are relevant for water regulators and water utilities, as they demonstrate the importance of weight allocation for eco-efficiency score estimation.

A Proposed Extended Version of the Hadi-Vencheh Model to Improve Multiple-Criteria ABC Inventory Classification

The ABC classification problem is approached as a ranking problem by the most current classification models; that is, a group of inventory items is expressed according to its overall weighted score of criteria in descending order. In this paper, we present an extended version of the Hadi-Vencheh model for multiple-criteria ABC inventory classification. The proposed model is one based on the nonlinear weighted product method (WPM), which determines a common set of weights for all items. Our proposed nonlinear WPM incorporates multiple criteria with different measured units without converting the performance of each inventory item, in terms of converting each criterion into a normalized attribute value, thereby providing an improvement over the model proposed by Hadi-Vencheh. Our study mainly includes various criteria for ABC classification and demonstrates an efficient algorithm for solving nonlinear programming problems, in which the feasible solution set does not have to be convex. The algorithm presented in this study substantially improves the solution efficiency of the canonical coordinates method (CCM) algorithm when applied to large-scale, nonlinear programming problems. The modified algorithm was tested to compare our proposed model results to the results derived using the Hadi-Vencheh model and demonstrate the algorithm’s efficacy. The practical objectives of the study were to develop an efficient nonlinear optimization solver by optimizing the quality of existing solutions, thus improving time and space efficiency.

A Proposed Extended Version of the Hadi-Vencheh Model to Improve Multiple Criteria ABC Inventory Classification

In this paper, we present an extended version of the Hadi-Vencheh model for multiple criteria ABC inventory classification. The proposed model is a nonlinear weighted product model (WPM) which determines a common set of weights for all the items. Our proposed nonlinear WPM incorporates multiple criteria with different measure units, without converting the performance of each inventory item in terms of each criterion into a normalized attribute value, thereby providing an improvement over the model proposed by Hadi-Vencheh. Our study mainly includes various criteria for ABC classification, and demonstrates an efficient algorithm for solving nonlinear programming problems in which the feasible solution set does not have to be convex. The algorithm presented in this study improves the solution efficiency of the Canonical Coordinates Method (CCM) algorithm substantially when applied to large scale, nonlinear programming problems. The modified algorithm was tested to compare our proposed model results to the results derived using the Hadi-Vencheh model and demonstrate the algorithm's efficacy. The practical implications of the study are to develop an efficient nonlinear optimization solver by optimizing the quality of existing solutions, thus improving time and space efficiency.

Solving the fully fuzzy multi-objective transportation problem based on the common set of weights in DEA

A transportation problem basically deals with the problem which aims to minimize the total transportation cost or maximize the total transportation profit of distributing a product from a number of sources or origins to a number of destinations. While, in general, most of the real life applications are modeled as a transportation problem (TP) with the multiple, conflicting and incommensurate objective functions. On the other hand, for some reason such as shortage of information, insufficient data or lack of evidence, the data of the mentioned problem are not always exact but can be fuzzy. This type of problem is called fuzzy multi-objective transportation problem (FMOTP). There are a few approaches to solve the FMOTPs. In this paper, a new fuzzy DEA based approach is developed to solve the Fully Fuzzy MOTPs (FFMOTPs) in which, in addition to parameters of the MOTPs, all of the variables are considered fuzzy. This approach considers each arc in a FFMOTP as a decision making unit which produces multiple fuzzy outputs using the multiple fuzzy inputs. Then, by using the concept of the common set of weights (CSW) in DEA, a unique fuzzy relative efficiency is defined for each arc. In the following, the unique fuzzy relative efficiency is considered as the only attribute for the arcs. In this way, a single objective fully fuzzy TP (FFTP) is obtained that can be solved using the existing standard algorithms for solving this kind of TPs. A numerical example is provided to illustrate the developed approach.