Promoting Fair Online Resource Allocation with Indivisible Units

TL;DR

This paper introduces new online policies for allocating indivisible resources fairly under uncertainty, achieving optimal fairness guarantees and highlighting the importance of distributional assumptions and partial allocations.

Contribution

It develops the RCB algorithm for stationary demands and proves optimal fairness guarantees, showing the benefits of stationarity and partial allocations over all-or-nothing policies.

Findings

Optimal fairness guarantee of 1/(1+R_beta) for arbitrary arrivals.

RCB achieves tight guarantees in stationary cases.

All-or-nothing policies cannot match these fairness guarantees.

Abstract

Allocating scarce, indivisible resources to diverse groups under uncertainty is a central challenge in operations research, where efficiency-focused methods often underserve marginalized populations. We study the Fair Online Resource Allocation with Indivisible Units (FORA-IU) problem, in which an unpredictable sequence of demands must be served from a strictly fixed inventory, and ask what fairness guarantees are achievable under different distributional and structural assumptions. We adopt a fairness criterion based on the expected filling ratio (FE-FR-beta), which balances each group's expected allocation against its expected demand and priority weight. We design online policies that calibrate acceptance probabilities to the remaining budget, analyze both arbitrary time-varying and stationary arrivals, introduce the Random Cyclic Blocks (RCB) algorithm tailored to the stationary case, and study the effect of restricting policies to all-or-nothing allocations. For arbitrary time-varying arrivals, our policy achieves the optimal universal fairness guarantee of 1/(1+R_beta), where R_beta denotes the priority-weighted system load. For time-invariant arrivals, RCB achieves the exact finite-horizon guarantee [1-(1-R_beta/T)^T]/R_beta, which is at least (1-e^{-R_beta})/R_beta and is also tight. We further show that all-or-nothing allocation policies cannot match these guarantees. These findings demonstrate that distributional stationarity strictly improves the fairness frontier, and that partial fulfillment is a necessary condition for attaining optimal fairness in online indivisible resource allocation.