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

Abstract

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.

Figures (6)

• Figure 1: The x b-VGA-EA method to assess DMUs.
• Figure 2: The b-VGA-MCDM method to select the best alternative.
• Figure 3: Comparing the solutions of PT and TS3 models.
• Figure 4: Comparing the solutions of TS1 and TS2 models.
• Figure 5: Comparing the solutions of sTS1 and sTS2 models in assessing $DMU_B$.