Chance-constrained Data Envelopment Analysis Model Research Articles

Measuring the Energy and Carbon Emission Efficiency of Regional Transportation Systems in China: Chance-Constrained DEA Models

In China, the transportation sector contributes about 18% of the total carbon emissions. This research contributes to measuring the energy and carbon emission efficiency (ECEE) of regional transportation systems (RTS) in China considering uncertain carbon emissions. A radial chance-constrained data envelopment analysis (DEA) model is developed to estimate the overall efficiency, and a nonradial chance-constrained DEA model is presented to evaluate the pure energy efficiency (PEE) and the pure carbon emission efficiency (PCEE). We prove that the proposed chance-constrained DEA models can effectively address the uncertain carbon emissions when measuring efficiency. We find that most of China’s RTS have low ECEE and the inefficiencies are mainly due to the lower gasoline utilization efficiency and the lower kerosene utilization efficiency. In addition, east China performs better than central China, and central China performs better than west China. In China, the unbalanced regional development of the ECEE in transportation corresponds with the unbalanced regional economic development. We provide some valuable suggestions based on the evaluation of the potential cuts in each kind of energy and the potential decreases in carbon emissions.

A joint chance-constrained data envelopment analysis model with random output data

Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the technical efficiency performances of a set of comparable decision-making units that transform multiple inputs into multiple outputs. The conventional DEA models are based on crisp input and output data, but real-world problems often involve random output data. The main purpose of the paper is to propose a joint chance-constrained DEA model for analyzing a real-world situation characterized by random outputs and crisp inputs. After developing the model, we carry out the following: First, we obtain an upper bound of this stochastic non-linear model deterministically by applying a piecewise linear approximation algorithm based on second-order cone programming; Second, we obtain a lower bound with use of a piecewise tangent approximation algorithm, which is also based on second-order cone programming; and then we use a numerical example to demonstrate the applicability of the proposed joint chance-constrained DEA framework.

Measuring the relative performance of forest management units: a chance-constrained DEA model in the presence of the nondiscretionary factor

In this study, we develop a marginal chance-constrained data envelopment analysis (DEA) model in the presence of nondiscretionary inputs and hybrid outputs for the first time. We call it a stochastic nondiscretionary DEA model (SND-DEA), and it is developed to measure and compare the relative efficiency of forest management units under different environmental management systems. Furthermore, we apply an output-oriented DEA technology to both deterministic and stochastic scenarios. The required data are collected from 24 forest management plans (as decision-making units) and included four inputs and an equal amount of outputs. The findings of this practical research show that the modified SND-DEA model in different probability levels gives us apparently different results compared with the output from pure deterministic models. However, when we calculate the correlation measures, the probability levels give us a strong positive correlation between stochastic and deterministic models. Therefore, approximately 40% of the forest management plans based on the applied SND-DEA model should substantially increase their average efficiency score. As the major conclusion, our developed SND-DEA model is a suitable improvement over previous developed models to discriminate the efficiency and (or) inefficiency of decision-making units to hedge against risk and uncertainty in this type of forest management problem.

Chance-constrained data envelopment analysis modeling with random-rough data

Data envelopment analysis (DEA) is a useful management tool for measuring the relative efficiency of decision making units (DMUs) which consumes multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally indispensable in classical DEA models, real-world problems often involve random and/or rough input and output data. We present a chance-constrained DEA model with random and rough (random-rough) input and output data and propose a deterministic equivalent model with quadratic constraints to solve the model. The main contributions of this paper are fourfold: (3.1) we propose a DEA model for problems characterized by random-rough variables; (3.2) we transform the proposed chance-constrained model with random-rough variables into a deterministic equivalent non-linear form that could be simplified as a deterministic model with quadratic constraints; (3.3) we perform sensitivity analysis to investigate the stability and robustness of the proposed model; and (3.4) we use a numerical example to demonstrate the feasibility and richness of the obtained solutions.

A new chance-constrained DEA model with birandom input and output data

The purpose of conventional Data Envelopment Analysis (DEA) is to evaluate the performance of a set of firms or Decision-Making Units using deterministic input and output data. However, the input and output data in the real-life performance evaluation problems are often stochastic. The stochastic input and output data in DEA can be represented with random variables. Several methods have been proposed to deal with the random input and output data in DEA. In this paper, we propose a new chance-constrained DEA model with birandom input and output data. A super-efficiency model with birandom constraints is formulated and a non-linear deterministic equivalent model is obtained to solve the super-efficiency model. The non-linear model is converted into a model with quadratic constraints to solve the non-linear deterministic model. Furthermore, a sensitivity analysis is performed to assess the robustness of the proposed super-efficiency model. Finally, two numerical examples are presented to demonstrate the applicability of the proposed chance-constrained DEA model and sensitivity analysis.

Developing a new chance-constrained DEA model for suppliers selection in the presence of undesirable outputs

Supplier selection is a significant and widely studied theme since it has a significant influence on purchasing management in supply chain. Slacks- based measure - undesirable output (SBM-undesirable output) model is one of the new models in data envelopment analysis (DEA). In many real-world applications, data are often stochastic. A successful approach to address uncertainty in data is to replace deterministic data via random variables, leading to chance-constrained DEA. In this paper, a SBM-undesirable output model is developed to assist the decision makers to determine the most appropriate suppliers in the presence of both undesirable factors and stochastic data, and also its deterministic equivalent which is a non-linear programme is derived. Furthermore, it is shown that the deterministic equivalent of the stochastic SBM-undesirable output model can be converted into a quadratic programme. In addition, sensitivity analysis of the SBM-undesirable output model is discussed with respect to changes on parameters. A case study demonstrates the application of the proposed model.

DATA ENVELOPMENT ANALYSIS WITH FUZZY RANDOM INPUTS AND OUTPUTS: A CHANCE-CONSTRAINED PROGRAMMING APPROACH

In this paper, we deal with fuzzy random variables for inputs and outputs in Data Envelopment Analysis (DEA). These variables are considered as fuzzy random flat LR numbers with known distribution. The problem is to find a method for converting the imprecise chance-constrained DEA model into a crisp one. This can be done by first, defuzzification of imprecise probability by constructing a suitable membership function, second, defuzzification of the parameters using an α-cut and finally, converting the chance-constrained DEA into a crisp model using the method of Cooper (4).