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A slacks-based nonlinear DEA model with integer data : an application to departments of the Islamic Azad University, Karaj Branch in Iran

Moazenzadeh Zahra, Saati Saber, Saen Reza Farzipoor, Matin Reza Kazemi, Sohraee Sevan

Operations Research and Decisions

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2022

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Vol. 32, No. 3

80--91

EN

Although Data Envelopment Analysis (DEA) assumes that inputs and outputs take non-negative real values, in some realworld cases, data are integer-valued. In some situations, rounding a fractional value to the closest integer can lead to a misleading evaluation of efficiency and in some cases may lead to an infeasible projection point. To date, various radial and non-radial models have been presented. This paper proposes a slacks-based non-linear model that guarantees an integer-valued reference point for all integer targets. Also, the reference point of each target is feasible under the proposed model. The lack of a need to round answers to the closest whole value is an advantage of this method. In addition, the results of this model are compared with other models. An example is used to clarify the suggested method.

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Detecting congestion in DEA by solving one model

Shadab Maryam, Saati Saber, Farzipoor Saen Reza, Khoveyni Mohammad, Mostafaee Amin

Operations Research and Decisions

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2021

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Vol. 31, No. 1

77--96

EN

The presence of input congestion is one of the key issues that result in lower efficiency and performance in decision-making units (DMUs). So, determination of congestion is of prime importance, and removing it improves the performance of DMUs. One of the most appropriate methods for detecting congestion is Data Envelopment Analysis (DEA). Since the output of inefficient units can be increased by keeping the input constant through projecting on the weak efficiency frontier, it is unnecessary to determine the congested inefficient DMUs. Therefore, in this case, we solely determine congested vertex units. Towards this aim, only one LP model in DEA is proposed and the status of congestion (strong congestion and weak congestion) obtained. In our method, a vertex unit under evaluation is eliminated from the production technology, and then, if there exists an activity that belongs to the production technology with lower inputs and higher outputs compared with the omitted unit, we say vertex unit evidences congestion. One of the features of our model is that by solving only one LP model and with easier and fewer calculations compared to other methods, congested units can be identified. Data set obtained from Japanese chain stores for a period of 27 years is used to demonstrate the applicability of the proposed model and the results are compared with some previous methods.

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A novel Data Envelopment Analysis model with complex numbers : measuring the efficiency of electric generators in steam power plants

Esfandiari Mahmood, Saati Saber, Navabakhsh Mehrzad, Khalili-Damghani Kaveh

Operations Research and Decisions

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2019

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Vol. 29, No. 4

41--52

EN

The output of a generator in power plant is the electricity, and it consists of two parts, active and reactive power. These quantities are expressed as complex numbers in which the real part is the active power and the imaginary part is the reactive power. Reactive power plays an important role in an electricity network. Ignoring it will exclude a lot of information. With regard to the importance of the generators in power plants, surely, calculating the efficiency of these units is of great importance. Data Envelopment Analysis (DEA) is a nonparametric approach to measure the relative efficiency of Decision-Making Units (DMUs). Since the generators data are complex numbers, thus, if we the use classical DEA models in order to measure the efficiency of the generators in power plants, the reactive power cannot be considered, and the measurement is limited to the real number of electric power. In this paper, a new DEA model with complex numbers is developed in order to assess the performance of the power plant generators.