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.

Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.

A Novel Enhanced Russell Graph Efficiency Measure in Network DEA

Hitherto, the presented models for measuring the efficiency score of multi-stage decision-making units (DMUs) either are nonlinear or require to specify the weights for combining their divisional efficiencies. The nonlinearity leads to high computational complexity for these models, especially when used for problems with enormous dimensions, and also assigning various weights to the divisional efficiencies causes to obtain different efficiency scores for the multi-stage network system. To tackle these problems, this study contributes to network DEA by introducing a novel enhanced Russell graph (ERG) efficiency measure for evaluating the general two-stage series network structures. Then, the proposed model is extended into the general multi-stage series network structures. This study also describes the managerial and economic implications of measuring the efficiency score of the multi-stage DMUs and provides two numerical and empirical examples for illustrating the use of our proposed model.

A Scenario-based Model for Resource Allocation with Price Information

In this paper, we consider the problem of allocating resources among Decision Making Units (DMUs). Regarding the concept of overall (cost) efficiency, we consider three different scenarios and formulate three Resource Allocation (RA) models correspondingly. In the first scenario, we assume that overall efficiency of each unit remains unchanged. The second scenario is related to the case where none of overall efficiency scores is deteriorated. We improve the overall efficiencies by a pre-determined percentage in the last scenario. We formulate Linear Programming problems to allocate resources in all scenarios. All three scenarios are illustrated through numerical and empirical examples.

Efficiency Analysis of Higher Education Institutions: Use of Categorical Variables

This paper focuses on the Data Envelopment Analysis (DEA) based efficiency evaluation to find the impact of two-step categorical impact on the enrollment efficiency of colleges in Bihar, one of the largest states of India. The objective of the study is to find the impact of factors, other than college-specific, on the efficiency of the colleges. The proposed research includes colleges funded and managed through seven state public universities. To follow the homogeneity condition of DEA, colleges providing courses of Arts (languages and humanities only), Science, and Commerce only, have been selected. The numbers of students enrolled in undergraduate and postgraduate courses are considered as two outputs. Numbers of teaching and non-teaching staff are considered as inputs. Colleges have been classified into two categories based on their presence in the rural or urban areas. The efficiency of a college due to any categorical value is calculated as the ratio of overall efficiency and efficiency calculated with similar categorical Decision-Making Units (DMUs) only. The impact of both the categorical variables, affiliation to university and geographical presence, has been analyzed through the hypothesis testing with the null hypothesis that there is no impact of category on the efficiency of DMUs due to a categorical variable.

Ranking of decision making units using the imperialist competitive algorithm in DEA

One of the challenging and important subjects in Data Envelopment Analysis (DEA) is the ranking of Decision Making Units (DMUs). In this paper, a new method for ranking the efficient DMUs is firstly proposed by utilizing the DEA technique and also developing a capable metaheuristic, imperialist competitive algorithm, derived from social, political, and cultural phenomena. Efficient DMUs are known as colonizers, and the virtual units, which are within their regions of exclusive domination, are considered as colonies. Efficient units are ranked by utilizing the factor of competition among imperialists to attract each other’s colonies. One advantage of proposed method is that, without solving any mathematical, and complex solution approaches, all extreme and non-extreme units are ranked only by comparing the pairs.

Aggregate Efficiency Dynamics in Lithuanian Dairy Farms

In this paper, we attempt to identify the major groups of decision making units (dairy farms) contributing to the aggregate efficiency change. We also suggest identifying influential peers in order to gain more insights into possible development strategies within a sector. The empirical application focuses on specialist dairy farms in Lithuania. The farm-level data cover the period 2004-2016. The results indicate the presence of structural changes and resulting shifts in the aggregate efficiency. Based on the results of decomposition of the covariance term and identification of the influential peers, two models can be followed by Lithuanian dairy farms, namely “pure” family farms with lower operational scale and large farms involving hired labour.

Performance measurement of decision making units through interval efficiency with slacks-based measure: an application to tourist hotels in Taipei

Data envelopment analysis (DEA) is widely used to evaluate the performance of a group of homogeneous decision making units (DMUs). Considering the uncertainty, interval DEA has been introduced to fit into more situations. In this paper, an interval efficiency method based on slacks-based measure is proposed to solve the uncertain problems in DEA. Firstly, the maximum and minimum efficiency values of the evaluated DMU are calculated by the furthest and closest distance from the evaluated DMU to the projection points on the Pareto-efficient frontier, respectively. Then, the AHP method is used for the full ranking of DMUs. The paper uses the pairwise comparison relationship between each pair of DMUs to construct the interval multiplicative preference relations (IMPRs) matrix. If the matrix does not meet the consistency condition, a method to obtain consistency IMPRs is introduced. According to the consistency judgment matrix, the full ranking of DMUs can be obtained. Finally, we apply our method to the performance evaluation of 12 tourist hotels in Taipei in 2019.