Resource Allocation of Cooperative Alternatives Using the Analytic Hierarchy Process and Analytic Network Process with Shapley Values

Abstract

Cooperative alternatives need complex multi-criteria decision-making (MCDM) consideration, especially in resource allocation, where the alternatives exhibit interdependent relationships. Traditional MCDM methods like the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) often overlook the synergistic potential of cooperative alternatives. This study introduces a novel method integrating AHP/ANP with Shapley values, specifically designed to address this gap by evaluating alternatives on individual merits and their contributions within coalitions. Our methodology begins with defining problem structures and applying AHP/ANP to determine the criteria weights and alternatives’ scores. Subsequently, we compute Shapley values based on coalition values, synthesizing these findings to inform resource allocation decisions more equitably. A numerical example of budget allocation illustrates the method’s efficacy, revealing significant insights into resource distribution when cooperative dynamics are considered. Our results demonstrate the proposed method’s superiority in capturing the nuanced interplay between criteria and alternatives, leading to more informed urban planning decisions. This approach marks a significant advancement in MCDM, offering a comprehensive framework that incorporates both the analytical rigor of AHP/ANP and the equitable considerations of cooperative game theory through Shapley values.

Keywords

• Analytic Hierarchy Process
• Analytic Network Process
• Shapley values
• cooperative alternatives
• resource allocation