Sensitivity Analysis of Inefficient Decision-Making Units in Data Envelopment Analysis (DEA) with a Focus on Boilers: A Case StudyYazdanpanahAlirezaDepartment of Mathematics, Shiraz branch, Islamic Azad University, Shiraz, Iran.
This paper focuses on the sensitivity analysis of inefficient Decision-Making Units (DMUs) in Data Envelopment Analysis (DEA), particularly on boilers. The main objective of this study is to identify and evaluate the efficiency of boilers across various industries and to propose a modified model for their sensitivity analysis. Boiler performance criteria are inputs and outputs, and a case study is presented within an industrial plant. The paper introduces an enhanced DEA-based model to assess the sensitivity of inefficient boilers. The proposed model determines the instability radius of boilers concerning changes in inputs and outputs. Employing managerial coefficients offers greater flexibility in adapting strategies. A case study is implemented in a power plant.
Data envelopment analysisPower plant boilersEfficient and inefficient decision-making unitsCounterparty credit riskBidirectional consistency constraintIntroduction
In the power generation industry, boilers are key components for energy production and thermal power supply. These systems utilize thermal energy to generate steam, which drives turbines and produces electricity. Given the growing importance of environmental and economic issues, improving boiler efficiency has become crucial in reducing operational costs and minimizing pollutant emissions. Therefore, accurate evaluation of these units'units' performance is essential [1]–[4].
In this context, Data Envelopment Analysis (DEA) is applied as a non-parametric method to assess the efficiency of Decision-Making Units (DMUs). DEA identifies efficient and inefficient units by analyzing input and output data to define efficiency frontiers. However, one major limitation of traditional DEA applications is the lack of adequate sensitivity analysis-meaning it does not sufficiently examine how changes in inputs and outputs may lead to improvements in the performance of inefficient units [5]–[7].
This paper aims to develop a modified model for analyzing inefficient boilers within the DEA framework. By introducing coefficients that allow greater flexibility in adjusting inputs and outputs, this model helps decision-makers design more targeted improvement strategies. The process involves identifying and analyzing boilers' instability radius, which can then be used to propose solutions that bring inefficient units closer to the efficiency frontier.
A case study is conducted in an industrial power plant, focusing on boilers that have been identified as inefficient due to performance fluctuations. The sensitivity analysis is based on practical variations in inputs, such as fuel and water consumption, and outputs, such as steam production and emission levels. The results of this study can serve as a guide for power plant management and other similar industries to enhance productivity and reduce environmental impacts.
Ultimately, this research emphasizes the importance of utilizing advanced techniques, such as modified DEA models, to achieve higher efficiency and optimize resource consumption in boilers and other industrial equipment. Industries will be better equipped to analyze performance data and make more effective strategic decisions with the proposed model.
Theoretical Foundations
Efficiency analysis in organizations and the improvement of products and services have always been primary concerns for managers and researchers. In this regard, methods such as data mining and DEA have been introduced as effective tools for performance and efficiency evaluation. This section explores various approaches used in efficiency and sensitivity analysis within the DEA framework, especially concerning inefficient DMUs.
Introduction to Data Envelopment Analysis
Charnes and colleagues [8] first introduced DEA in 1978 as a method for measuring task efficiency using linear programming. The initial DEA model enabled researchers to analyze the performance of DMUs by incorporating multiple inputs and outputs. This method compares similar units and establishes operational efficiency frontiers [8].
Sensitivity Analysis in Data Envelopment Analysis
Sensitivity analysis within the DEA framework investigates the impact of input and output variable changes on the final efficiency assessment of DMUs. This approach was proposed by Charnes et al. [9] in 1985 and has since been developed further. Research such as Neralic [10] and studies by Zhu and Seiford [11] have deepened this area, making it possible to analyze both individual and group data variations.
Sensitivity Analysis Models
Several models have been developed for sensitivity analysis in DEA. For instance, the model proposed by Cooper and colleagues in [12] focuses specifically on inefficient DMUs. This model recommends using managerial coefficients instead of traditional models to better design performance improvement strategies. Other models include synchronous and asynchronous change analyses in inputs and outputs, enabling managers to develop strategic plans for efficiency and service enhancement [13].
Application of Data Envelopment Analysis in Industry
The current paper proposes a modified sensitivity analysis model for inefficient boilers based on DEA, which is investigated through a case study in the power industry. This study aims to optimize boiler performance by identifying gaps and analyzing expectations versus actual output data.
General view for powerplant.
This figure is shown in the PDF version of the article.
Methodology and Findings
Logical input and output variables were first identified for 10 boilers to conduct the case study on boilers, representing their operational performance in a power plant. The aim was to evaluate their efficiency using the DEA model (Table 1).
Sample Inputs and Outputs in Boilers.
This table is shown in the PDF version of the article.
II. Water consumption (m³/day): The volume of water used for steam generation and cooling operations. III. Operating costs (USD/day): Includes maintenance, labor, and energy expenses.
IV. Maintenance time (hrs/month): Time required to repair and replace key components.
Outputs:
I. Steam output (tons/day): The amount of steam generated contributes to electricity production and industrial processes.
II. Power output (MWh/day): The amount of electricity each boiler generates.
III. Emission levels (relative to standards): Emissions such as CO₂ and particulate matter, measured against permitted thresholds.
Data Analysis
Using the data in Table 1, DEA can be applied to identify inefficient boilers and recommend efficiency improvements, which may include:
I. Optimization of fuel and water consumption based on the best-performing boilers.
II. Reduction in operational costs and maintenance time to enhance productivity.
III. Management and reduction of emissions to comply with environmental standards.
IV. These insights can support power plant managers in making optimal decisions to improve boiler efficiency and productivity.
Sampling and Data Analysis
This section presents the case study on industrial boilers, focusing on relevant inputs and outputs to assess their efficiency and improve performance.
The case study focuses on industrial boilers within a power plant (Table 2). The main objective is to identify and analyze performance weaknesses using the modified DEA model and sensitivity analysis to propose improvement strategies.
Inputs:
I. Fuel consumption: Amount of fossil fuel or natural gas used, directly impacting operational costs and CO₂ emissions.
II. Water consumption: The volume of water needed for steam generation and temperature regulation affects the system's thermal efficiency.
Outputs:
I. Steam output (tons/hour): The volume of steam produced reflects the system's thermal performance.
Data Analysis Process
The collected data were compiled via monitoring systems and processed using specialized optimization software.
Step 1. (Data collection and normalization) Input and output data were recorded over a specific period and normalized to ensure accurate comparisons between boilers.
Step 2. (Identifying performance gaps) Performance gaps were identified by analyzing the differences between the inputs consumed and the outputs produced by inefficient boilers.
Step 3. (Applying the DEA model) The DEA model was implemented with managerial coefficients to evaluate current boiler efficiency and identify inefficient units.
Input and output data for the 10 Boilers.
This table is shown in the PDF version of the article.
Modeling
In this study, only two inputs (water and fuel) and one output (steam production) are considered to simplify calculations and data segmentation. As shown in Fig. 1, other criteria may be included in earlier or future stages or as part of a complementary project. The Counterparty Credit Risk (CCR) and Bidirectional Consistency Constraint (BCC) methods were applied, primarily emphasizing the BCC method.
CCR model
The CCR model is one of the earliest and simplest DEA models used to measure the relative efficiency of DMUs. It assumes Constant Returns to Scale (CRS). The CCR model aims to maximize the weighted ratio of outputs to inputs such that this ratio is ≤1 for all other units [14], [15].
Steps of sensitivity analysis using the CCR method
The initial linear programming model is based on Formula (1), where xik and yrk represent inputs and outputs for unit kkk, and uuu and vvv are the weights for outputs and inputs, respectively.
∑r=1 μryrk
max = s . (1)
∑r=1 ϑixik
Initial efficiency calculation
First, the relative efficiency of each boiler is calculated. These efficiency values help identify which boilers require improvement.
Performing sensitivity analysis
After identifying inefficient boilers, input and output values are altered to assess their impact on efficiency. In other words, we evaluate how reducing/increasing inputs like fuel or water or changing outputs like steam production influences overall efficiency. This aims to determine the stability radius (see Table 3).
CCR model calculation results.
This table is shown in the PDF version of the article.
As shown in Table 3, only Boiler B09 is efficient. The Farrell efficiency diagram (Fig. 2) illustrates this.
Farel DEA model result.
This figure is shown in the PDF version of the article.
BCC Model
The BCC model (Formula 2) is a modified version of CCR based on Variable Returns to Scale (VRS). In this study, the input-oriented BCC model aims to reduce inputs while maintaining maximum output.
∑r=1 μryrk
max = s , (2)
∑r=1 ϑixik
min∑i=1 ϑi xik + w, (3) ∑r=1 μryrk = 1, (4) ∑r=1 μryrk − ∑i=1 ϑixik − w ≤ 1, (5) μr& xik ≥ 0, j = 1~n, W = free. (6) In this model, a free variable W is added to the CCR formula, and the equation is solved accordingly depending on whether an input-oriented or output-oriented perspective is used.
BCC model results.
This table is shown in the PDF version of the article.
As observed in Table 4, in addition to Boiler B9, Boilers B3, B6, B7, and B10 are also efficient under the BCC model. Boilers B1, B2, B4, B5, and B8 remain inefficient. Reference Boilers and Benchmarking (Table 5). In the BCC model, inefficient boilers are compared to efficient ones to determine which units can serve as references. These reference units act as performance benchmarks for improvement.
Reference Boilers for inefficient units.
This table is shown in the PDF version of the article.
Key Findings
I. Efficiency evaluation: Boiler B10 can become efficient with only a minor reduction in water usage (~1.7 m³/day), showing that small operational adjustments can yield substantial improvements.
Required adjustments for improving inefficient Boilers.
This table is shown in the PDF version of the article.
II. Least efficient Boiler: B5 is identified as the most inefficient, requiring the largest reductions in both water and fuel to reach the efficiency frontier.
III. Sensitivity insights: For example, reducing B1'sB1's fuel by 3.5 tons/day and water by 6.5 m³/day significantly improves efficiency.
These targeted adjustments offer practical guidance for operators and maintenance teams to prioritize actions.
Conclusion
The DEA method is a powerful tool for evaluating performance and identifying inefficiencies. It offers efficient insights without relying on rigid assumptions about the production function. Its flexibility in adjusting input and output weights allows managers to fine-tune operational plans and enhance overall system performance.
Significance of Sensitivity Analysis
Sensitivity analysis is especially valuable for operational decision-making, as it reveals how small input/output changes can lead to significant performance improvements. This particularly applies to power generation and manufacturing industries, where operational costs are high, and optimization is critical.
By incorporating additional inputs and outputs into future models, a more comprehensive analysis of boiler performance can be achieved. Ongoing research is being conducted in this area to expand the model's model's capabilities.
Applications
The results of this study can be used to develop optimization programs aimed at reducing costs and increasing efficiency. This approach contributes to environmentally conscious strategies by minimizing resource consumption and maximizing useful outputs.
Ultimately, integrating DEA and sensitivity analysis has proven to be a comprehensive strategy for enhancing boiler performance. Facilities can significantly improve efficiency and effectiveness by making intelligent adjustments to inputs and outputs. This not only reduces operational costs but also supports better resource management and lowers environmental impact.
Recommendations
Based on the efficiency analysis of the boilers and the results obtained, the following recommendations are proposed to improve their performance:
I. Recommendations: Based on the efficiency analysis of the boilers and the results obtained, the following recommendations are proposed to improve their performance:
II. Scheduled maintenance planning: It is recommended that the maintenance schedule be carefully reviewed to ensure optimal system operation. Minimizing downtime and extending boiler lifespan can lead to overall efficiency gains.
III. Input and output engineering: Considering the role of inputs and outputs in DEA, efforts should focus on optimizing fuel and water usage. Enhancing steam and power output through energy efficiency techniques is also suggested.
IV. Enhanced staff training: Continuous training of personnel in optimal boiler operation and maintenance practices can significantly impact system performance. Boiler-specific training programs can address energy-saving and resource-management techniques.
V. Utilization of advanced technologies: Implementing modern control and monitoring technologies—such as automation and Internet of Things (IoT) systems-can help improve energy efficiency and reduce resource consumption.
VI. Decision-making based on sensitivity analysis: Managers should treat sensitivity analysis as a key decision-making tool. Operational priorities and action plans based on minor input/output adjustments can result in tangible improvements.
VII. Financial resource management: Reviewing operational expenses and identifying cost-cutting opportunities-without sacrificing service quality-can help boost boiler efficiency.
These recommendations can be incorporated into a comprehensive management strategy to improve boiler performance and resource efficiency. In addition to cost savings and stakeholder satisfaction, these actions can positively influence environmental sustainability and energy productivity.
Funding
This research received no external funding.
Data Availability
The data supporting the findings of this study are available from the corresponding author upon reasonable request.
Conflicts of Interest
The author declares no conflict of interest.
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