On fairness and efficiency in resource allocation problems

A key challenge in socially responsible operations is to balance fairness and efficiency. This thesis studies this trade-off in centralized resource allocation settings, where limited resources are allocated among multiple players under considerations of both efficiency and equity. Chapter 2 examines the operation of public housing allocation systems, motivated by the tension between mobility and fairness. Housing authorities must jointly manage move-in requests from households outside the public housing system and transfer requests from incumbent tenants whose needs have changed. While better matching can improve transfer mobility without increasing housing supply, prioritizing transfers may reduce opportunities for external applicants and thereby create fairness concerns. To address this trade-off, this chapter models each type of request as a queue, and adapts the dynamic matching queue framework developed by Gurvich and Ward (2014). Within this framework, we propose a periodic review policy, establish strong asymptotic optimality guarantees, relax a key assumption in the existing matching-queue literature, and illustrate the practical value of the approach using both real housing authority data and simulation experiments. Chapter 3 studies the efficiency loss that arises when fairness criteria are incorporated into resource allocation. Following the framework of Bertsimas et al. (2011), this chapter examines the price of fairness under proportional fairness and max-min fairness. It derives tight upper bounds for an arbitrary number of players with possibly unequal maximum achievable utilities, identifies the source of the gap in the existing bounds, and shows that the new bounds are asymptotically sharper. Chapter 4 extends this analysis to weighted proportional fairness, allowing heterogeneous priority weights across players. The chapter derives tight upper bounds on the associated efficiency loss and shows that the new bounds remain tight for arbitrary priority weights and general utility sets. The analysis also provides qualitative insights into how the price of fairness depends on the number of players and the structure of the priority weights.