arXiv subjects

Su-Chuan Shih

Publications and source records attributed to Su-Chuan Shih.

5 recordsLinked to original sources

arXiv2026

Virtual Gap Analysis procedures for Multi-Criteria Decision-Making and Efficiency Analysis Problems

Existing multi-criteria decision-making (MCDM) methods often face challenges when evaluating a large number of alternatives, leading to skewed results in selecting the optimal choice. Similarly, conventional efficiency analysis (EA) methods, such as Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), often yield incomplete solutions due to their reliance on theoretical assumptions. To address these limitations, we propose a novel EA method that integrates Virtual Gap Analysis (VGA) models to evaluate the performance of each decision-making unit (DMU) in relation to others based on best practices. Unlike DEA and SFA, our VGA models are linear programming-based, assumption-free, and capable of delivering robust and reliable solutions. The proposed method enables each DMU to identify achievable benchmarks for inputs and outputs. Based on the estimated virtual gaps, DMUs are classified as inefficient (with scores below one) or efficient (with scores of one or higher). Additionally, our new MCDM method incorporates existing MCDM techniques to analyze the few identified efficient DMUs, significantly reducing the effort required to select the best DMU.

math.OC↗

arXiv2026

Linear Programming for Multi-Criteria Assessment with Cardinal and Ordinal Data: A Pessimistic Virtual Gap Analysis

Multi-criteria Analysis (MCA) is used to rank alternatives based on various criteria. Key MCA methods, such as Multiple Criteria Decision Making (MCDM) methods, estimate parameters for criteria to compute the performance of each alternative. Nonetheless, subjective evaluations and biases frequently influence the reliability of results, while the diversity of data affects the precision of the parameters. The novel linear programming-based Virtual Gap Analysis (VGA) models tackle these issues. This paper outlines a two-step method that integrates two novel VGA models to assess each alternative from a pessimistic perspective, using both quantitative and qualitative criteria, and employing cardinal and ordinal data. Next, prioritize the alternatives to eliminate the least favorable one. The proposed method is dependable and scalable, enabling thorough assessments efficiently and effectively within decision support systems.

cs.AI↗

arXiv2025

A New Approach for Multicriteria Assessment in the Ranking of Alternatives Using Cardinal and Ordinal Data

Modern methods for multi-criteria assessment (MCA), such as Data Envelopment Analysis (DEA), Stochastic Frontier Analysis (SFA), and Multiple Criteria Decision-Making (MCDM), are utilized to appraise a collection of Decision-Making Units (DMUs), also known as alternatives, based on several criteria. These methodologies inherently rely on assumptions and can be influenced by subjective judgment to effectively tackle the complex evaluation challenges in various fields. In real-world scenarios, it is essential to incorporate both quantitative and qualitative criteria as they consist of cardinal and ordinal data. Despite the inherent variability in the criterion values of different alternatives, the homogeneity assumption is often employed, significantly affecting evaluations. To tackle these challenges and determine the most appropriate alternative, we propose a novel MCA approach that combines two Virtual Gap Analysis (VGA) models. The VGA framework, rooted in linear programming, is pivotal in the MCA methodology. This approach improves efficiency and fairness, ensuring that evaluations are both comprehensive and dependable, thus offering a strong and adaptive solution. Two comprehensive numerical examples demonstrate the accuracy and transparency of our proposed method. The goal is to encourage continued advancement and stimulate progress in automated decision systems and decision support systems.

cs.AI↗

arXiv2024

Algorithms for Multi-Criteria Decision-Making and Efficiency Analysis Problems

Multi-criteria decision-making (MCDM) problems involve the evaluation of alternatives based on various minimization and maximization criteria. Similarly, efficiency evaluation (EA) methods assess decision-making units (DMUs) by analyzing their input consumption and output production. MCDM and EA methods face challenges in managing alternatives and DMUs with varying capacities across different criteria (inputs and outputs). That leads to performance assessments often skewed by subjective biases in criteria weighting. We introduce two innovative scenarios utilizing linear programming-based Virtual Gap Analysis (VGA) models to address these limitations. This dual-scenario approach aims to mitigate traditional biases, offering robust solutions for comprehensively assessing alternatives and DMUs. Our methodology allows for the influential ranking of alternatives in MCDM problems and enables each DMU to adjust its input and output ratios to achieve efficiency.

math.OC↗

arXiv2023

Data envelopment analysis models or the virtual gap analysis model: Which should be used for identifying the best benchmark for each unit in a group?

Decision-making units (DMUs) in a group convert the same resources (i.e., input indices) into the same products (i.e., output indices) at different scales. Performance indices have different measurement units, and their market prices per unit are unobtainable. Data envelopment analysis (DEA) programs employ linear programming to estimate the virtual weight and best slack of every input and output index for each DMU, named DMU-o, to obtain the minimum relative inefficiency against the DMUs. DMU-o reduces each input's slack, the surplus, and expands each output's slack, the shortage, to the benchmark. Each DEA program specifies an artificial goal weight for each performance index. The relative inefficiencies in the primal and dual models are the sum of the weighted slacks and the virtual gap of the total virtual weighted inputs to the outputs, respectively. DEA programs have failed the uncountable attempts to conceive the artificial goal weight equal to the estimated virtual weight for each performance index; therefore, they have incomplete solutions that some of the slacks could not be aggregated into the efficiency score. Our new virtual gap analysis program assesses DMU-o comprehensively. The four-phase procedure ensures DMU-o has the achievable best benchmarks for implementation and its compatible best peers to learn. Each DMU is a point in the 2D geometric intuition of the virtual technology set in assessing DMU-o. The best peers and the improved DMU-o are on the best efficiency boundary. Inefficient DMUs are situated underneath the boundary.

math.OC↗