⚡ electrical engineering

Normalization Method Selection to Enhance Sustainable Manufacturing Decision-Making in Benefit and Cost-based Aspects of MCDM

This study systematically evaluates and prioritizes normalization methods for multi-criteria decision-making in sustainable manufacturing, identifying Enhanced Accuracy and Max–Min Weitendorf's linear normalization as the most robust techniques for ensuring data consistency and reliability across both benefit and cost-based optimization scenarios.

Original authors: Gezaei Abera Asmelash, Luna Geo Kitila, Emmanuel Duc, Getasew Ashagrie Tadesse

Published 2026-10-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Gezaei Abera Asmelash, Luna Geo Kitila, Emmanuel Duc, Getasew Ashagrie Tadesse

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the complex world of modern manufacturing, creating a product is rarely just about making something that works. It is about balancing a delicate scale of competing needs: keeping costs low, ensuring the process is safe for workers, minimizing harm to the environment, and maintaining high quality. To make these difficult choices, engineers and managers rely on a structured way of thinking called multi-criteria decision-making. This approach allows them to weigh many different factors at once, from the price of raw materials to the amount of carbon a factory emits. However, these factors speak different languages. One might be measured in dollars, another in degrees of heat, and a third in a simple score of satisfaction. Trying to compare a dollar amount directly to a temperature reading is like trying to add apples to hours; the numbers are so different in size and meaning that the comparison becomes confusing and unreliable. To fix this, experts use a process called normalization, which translates all these diverse measurements into a single, common language so they can be compared fairly.

The problem is that there is no single agreed-upon way to translate these numbers. Just as different translators might interpret a sentence in slightly different ways, different mathematical methods for normalization can lead to different final rankings of which manufacturing option is best. If the translation method is flawed, the decision-maker might choose a factory process that looks good on paper but is actually risky or inefficient in reality. This uncertainty is dangerous because it can lead to wasted money, environmental damage, or unsafe working conditions. A new study from researchers at Addis Ababa University and SIGMA Clermont in France sets out to solve this specific problem. They wanted to find out which translation method is the most reliable for turning messy, real-world manufacturing data into clear, trustworthy decisions.

To do this, the researchers did not simply look at one specific factory or one single product. Instead, they built a rigorous testing ground using a wide variety of hypothetical scenarios. They imagined decision matrices containing four different options, or alternatives, and tested them against seven distinct types of data conditions. These conditions covered every possible way numbers can behave in the real world: data that is strictly positive, data that includes zero, data that is strictly negative, and data that mixes all these types together. They also tested situations where the total sum of the numbers was zero, or where the sum of their reciprocals was zero. By running fourteen different normalization methods through these seven challenging scenarios, they could see which methods held up and which ones broke down. They were looking for a method that would consistently produce results within a standard, understandable range of zero to one, without producing impossible numbers or crashing when faced with difficult data.

The investigation revealed that many of the methods commonly used today are surprisingly fragile. Several popular approaches, including those based on simple sums or logarithmic scales, failed completely when the data included zero or negative numbers. In some cases, these methods produced results that were mathematically undefined or exploded into massive, meaningless values. For instance, a method that worked perfectly for positive numbers might collapse entirely if a single zero appeared in the dataset. Other methods, while mathematically consistent, produced results that were so skewed toward the largest numbers that they drowned out the smaller, yet important, differences between options. The study showed that relying on these unstable methods introduces a hidden risk into the decision-making process, potentially leading engineers to choose the wrong technology or the wrong supplier based on a mathematical glitch rather than a true reflection of performance.

After systematically eliminating the methods that failed or produced unstable results, the researchers identified two standout performers that consistently delivered reliable outcomes across all seven scenarios. The top recommendation is a method called Enhanced Accuracy normalization. This approach proved to be the most robust, maintaining stability even when the data was mixed, negative, or included zeros. It successfully kept all the translated values within a tight, predictable range, ensuring that no single extreme number could unfairly dominate the final decision. The second-best option is a method known as Max–Min Weitendorf's linear normalization. Like the first, it consistently kept results within the standard zero-to-one range and handled both cost-based and benefit-based criteria with equal skill. While it is slightly more sensitive to extreme values than the top choice, it remains a highly reliable tool for general use.

The findings of this research offer a clear path forward for anyone involved in sustainable manufacturing. By adopting the Enhanced Accuracy method, or the Max–Min Weitendorf method as a strong alternative, decision-makers can significantly reduce the uncertainty that often plagues their evaluations. This does not mean the decision becomes easy, but it ensures that the data being used is trustworthy. When the numbers are translated correctly, the final choice reflects the true performance of the options, rather than an artifact of a poor calculation method. This clarity is essential for building a manufacturing sector that is not only efficient but also safe and sustainable for the long term. The study concludes that by choosing the right tool for the job, engineers and policymakers can make decisions that are more accurate, less risky, and better aligned with the goals of a sustainable future.

Technical Summary: Normalization Method Selection to Enhance Sustainable Manufacturing Decision-Making

Problem Statement
In the context of manufacturing sustainability, Multi-Criteria Decision-Making (MCDM) is essential for evaluating complex systems involving social, environmental, economic, and technical dimensions. However, these assessments face a critical challenge: decision criteria often exhibit wide variations in magnitude, measurement units, and preference directions (benefit vs. cost). This data heterogeneity creates significant difficulties in comparison and analysis, leading to uncertainty, inconsistency, and potential rank reversals in decision outcomes.

The paper identifies that a primary source of this decision risk is not the MCDM model structure itself, but the numerical distortions introduced during the data normalization process. Existing literature often lacks a systematic, scenario-based framework to evaluate how different normalization methods behave under extreme or limiting conditions (e.g., zero variance, mixed signs, or zero sums). Consequently, the selection of normalization methods is frequently arbitrary, based on convention or software defaults, which compromises the reliability and accuracy of sustainable manufacturing decisions.

Methodology
To address these gaps, the study employs a structured, scenario-based analytical framework to systematically evaluate and compare widely used normalization methods. The methodology proceeds through the following steps:

Method Selection: Based on a comprehensive literature review, 14 benefit- and cost-based normalization methods were identified and filtered for comparative analysis. These include Sum-based Linear, Vector, Max, Logarithmic, Min-Linear, Max-Min, Max-Min (Weitendorf's Linear), Stopp, Nonlinear (Peldschus), Z-Score, Enhanced Accuracy, and Lai & Hwang methods.
Scenario Definition: Seven distinct entry-value scenarios (cases) were defined to test the robustness of these methods against various numerical conditions:
- Case 1: Strictly positive values ( $x_{ij} > 0$ ).
- Case 2: Positive values including zero ( $x_{ij} \ge 0$ ).
- Case 3: Strictly negative values ( $x_{ij} < 0$ ).
- Case 4: Non-positive values including zero ( $x_{ij} \le 0$ ).
- Case 5: Mixed rational numbers.
- Case 6: Sum of input values equals zero ( $\sum x_{ij} = 0$ ).
- Case 7: Sum of reciprocals equals zero ( $\sum (1/x_{ij}) = 0$ ).
Evaluation Criteria: Each method was applied to these seven cases under both benefit and cost optimization aspects. The performance was assessed based on:
- Numerical Validity: Whether the method produces defined values or results in errors (e.g., division by zero).
- Boundedness: Whether the normalized values fall within the standard, interpretable range of [0, 1].
- Stability: Consistency of performance across all seven scenarios without extreme inflation, sign inversion, or loss of discrimination.

Key Results
The comparative analysis yielded distinct performance tiers among the 14 methods:

Top Performers:
- Enhanced Accuracy Normalization: Identified as the most robust method. It consistently produced normalized values within a stable, short range across all seven cases for both benefit and cost criteria. It successfully avoided division-by-zero errors, controlled outliers, and preserved the relative ordering of alternatives without allowing extreme values to dominate.
- Max–Min Weitendorf's Linear (WL) Normalization: Ranked second. This method consistently bounded values within the standard [0, 1] range across all cases. While highly reliable, it showed slightly higher sensitivity to extreme values compared to the Enhanced Accuracy method.
Moderate Performers:
- Vector Normalization: Demonstrated mathematical consistency but exhibited a bias toward high-magnitude criteria, potentially distorting rankings in datasets with disparate scales.
- Z-Score and Lai & Hwang Normalization: Provided stable results but were noted for limited dynamic range or sign inconsistencies that complicate interpretation in ranking-based MCDM.
Underperforming/Invalid Methods:
- Methods such as Logarithmic, Min-Linear, Stopp, and standard Max-Min normalization were found to be unreliable. They frequently failed in specific scenarios (particularly those involving zero or negative values), produced undefined results, generated values outside the [0, 1] range, or caused extreme numerical inflation (e.g., values in the millions or exponentials).

Key Contributions

Systematic Framework: The paper establishes a scenario-based framework for evaluating normalization methods, moving beyond simple dataset comparisons to test fundamental numerical behavior under boundary conditions.
Prioritization Guide: It provides a clear, prioritized ranking of normalization methods for general-purpose MCDM applications in manufacturing sustainability, offering a structured selection tool for decision-makers.
Risk Mitigation: By identifying methods that minimize uncertainty propagation and numerical distortion, the study offers a mechanism to reduce decision risk associated with data heterogeneity.

Significance and Claims
The authors claim that the adoption of the identified superior methods (Enhanced Accuracy and Max–Min WL) directly enhances the accuracy, reliability, and consistency of sustainable manufacturing decisions. By ensuring that normalized data remains within standard bounds and preserves preference structures, these methods support more accurate risk assessment and resource allocation.

The study positions normalization not merely as a technical pre-processing step, but as a critical determinant of decision accuracy. The proposed framework is intended to assist engineers, managers, and policymakers in selecting the most appropriate normalization technique for their specific data characteristics, thereby improving the overall quality of sustainability assessments and supporting broader socio-economic development goals, including the UN Sustainable Development Goals (SDGs). The paper concludes that while the selection of an MCDM method is important, the choice of a robust normalization method is equally critical to ensuring valid and sustainable outcomes.

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