ON THE MULTIFACETED COMPLEXITIES OF FAIR RESOURCE ALLOCATION PROBLEMS IN NETWORK SYSTEMS AND HOW TO ADDRESS THEM VIA MATHEMATICAL PROGRAMMING

Abstract

The challenge of fair resource allocation within supply and demand network systems represents a critical issue in the realm of cyber-physical-social systems (CPSS). Addressing this problem is essential for enhancing societal well-being and optimizing decision-making processes in complex, interconnected environments. This dissertation aims to provide a comprehensive study on this topic, utilizing mathematical programming techniques to navigate the intricacies of fair resource allocation.

Initially, the dissertation underscores the significance of resource allocation, emphasizing its real-life implications and fundamental role in promoting social equity. The exploration begins with a detailed examination of fairness in resource allocation, highlighting the delicate balance between fairness and efficiency. The work further delves into the difficulty of defining global fairness, leading to an in-depth analysis of fair resource allocation problems and the nuances of fair division. Drawing from mathematics, economics, game theory, and operations research, the study offers an interdisciplinary perspective on these issues.

A key focus of the dissertation is the investigation of utility allocation schemes, where stakeholders perceive different utility values from resource allocations. To illustrate these dynamics, concepts from game theory such as fair cake-cutting are employed. The research also explores the multi-dimensional trade-offs between fairness and efficiency, aiming to find optimal solutions that balance these competing objectives through a Multi-objective Mixed-Integer Linear Optimization model to achieve Pareto optimal allocations.

The dissertation further examines decentralized decision-making in resource allocation within network systems, particularly in hierarchical structures. A two-level resource allocation setting is analyzed, with the primary decision-maker optimizing fairness-based metrics and a secondary decision-maker pursuing cost-efficiency. To mitigate performance losses in fairness, a Mixed-Integer Linear Bilevel Optimization approach is proposed.

Lastly, the study addresses resource allocation problems under uncertainty, focusing on the utilities generated by end users. Using stochastic programming, specifically Two-stage Mixed-Integer Linear Programming, the dissertation explores the sensitivity of resource allocations to uncertainty and its implications for decision-makers.

In summary, this dissertation advances the understanding and methodologies for fair resource allocation in network systems, offering valuable insights and practical implications for CPSS management.