TLDR: A new method called Ordinal Virtual Gap Analysis (Ord-VGA) is proposed to assess and rank alternatives based on multiple criteria. This approach effectively handles both quantitative (cardinal) and qualitative (ordinal) data, accounts for heterogeneity among decision-making units, and removes subjective biases, offering a robust and transparent solution for complex decision problems.
In today’s complex world, making informed decisions often means evaluating various options, or ‘Decision-Making Units’ (DMUs), against multiple criteria. Whether it’s choosing the best laptop or assessing the energy efficiency of different regions, these evaluations can be challenging. Traditional methods like Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), and Multiple Criteria Decision-Making (MCDM) have been widely used, but they often come with limitations. These methods can rely on assumptions, be influenced by subjective judgments, and struggle to incorporate both quantitative (numerical) and qualitative (like Likert scale ratings) data effectively. A significant challenge also arises when the DMUs being compared are not perfectly uniform, a condition known as heterogeneity.
Addressing these critical gaps, researchers Fuh-Hwa Franklin Liu and Su-Chuan Shih have introduced a novel approach for multi-criteria assessment (MCA). Their new methodology, detailed in their paper “A NEW APPROACH FOR MULTICRITERIA ASSESSMENT IN THE RANKING OF ALTERNATIVES USING CARDINAL AND ORDINAL DATA”, proposes a robust solution that combines two specific Virtual Gap Analysis (VGA) models: the best-practice Pure Technical (obPT) and the super-virtual gap of Pure Technical (osPT) models.
A Two-Stage Evaluation Process
The core of this innovative approach lies in its two-stage evaluation framework:
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Stage I: Identifying Top-Tier Performers (using the obPT model)
This initial stage systematically assesses all DMUs to identify those that are performing at their best, exhibiting a ‘virtual gap’ of zero. These are classified as ‘top-tier’ DMUs. Unlike traditional methods, this stage does not assume that all DMUs operate under identical input-output structures, making it suitable for heterogeneous units. -
Stage II: Selecting the Best Alternative (using the osPT model)
Once the top-tier DMUs are identified, the second stage further evaluates and ranks them. The osPT model calculates a ‘super-virtual gap’ for each of these high-performing units. This super-virtual gap essentially measures how much a DMU can ‘degrade’ its performance before it loses its efficiency. The DMU with the smallest negative super-virtual gap is then determined to be the absolute best, demonstrating superior performance and resilience.
Key Advantages of the New Approach
This novel MCA method offers several significant advantages:
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Assumption-Free: It is built on linear programming principles and operates without making restrictive underlying assumptions, enhancing its reliability.
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Handles Mixed Data: It seamlessly integrates both cardinal (quantitative, like weight or sales figures) and ordinal (qualitative, like Likert scale ratings for brand perception or user satisfaction) data, which is crucial for real-world scenarios.
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Unified Goal Price: All diverse measurement units are converted into a ‘virtual currency,’ allowing for a unified and unbiased assessment of performance metrics.
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Removes Subjectivity: The method is designed to eliminate subjective biases and personal judgments that often plague traditional evaluation techniques.
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Accounts for Heterogeneity: It effectively handles differences among DMUs, ensuring accurate evaluations even when units have varying input-output configurations.
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Efficient and Scalable: The computational method is efficient, capable of quickly identifying the best DMU from decision matrices with numerous units.
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Graphical Visualization: The evaluation outcomes can be clearly illustrated using 2D graphical intuition, providing transparency and easy understanding of the results.
Real-World Demonstrations
The effectiveness and transparency of the proposed method are demonstrated through comprehensive numerical examples. These include evaluating six different laptop models based on mixed quantitative and qualitative criteria, and analyzing the energy efficiency of 29 Chinese provinces using a combination of cardinal and Likert scale data. These examples highlight the method’s accuracy and its practical applicability in diverse fields.
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Conclusion and Future Outlook
This innovative multi-criteria assessment methodology provides a robust and adaptive solution for complex evaluation challenges, particularly those involving heterogeneous DMUs and mixed data types. By removing subjective biases and operating without restrictive assumptions, it offers a more comprehensive and dependable framework for decision-making. The researchers believe this approach will encourage continued advancement and stimulate progress in automated decision systems and decision support systems, with future research opportunities including identifying the worst-performing alternatives and integrating additional constraints from other MCA methodologies.
