How to spread service areas for better matching in space
Distance flexibility in spatial matching: the value of concentration
Data Structures and Algorithms
Summary
When services like deliveries or ride-hailing have areas where they can operate, deciding how to spread these areas is important. The authors studied how to best assign service distances to different locations before knowing exactly where demand or supply will be. They found that when the total allowed service distance is large, it’s better to spread it evenly, but when it’s small, focusing on a few spots helps more. This helps platforms plan ahead to fulfill the most demand possible under a distance budget.
What this means in practice
- •For logistics planners: Allocate service coverage areas efficiently to maximize demand fulfillment under distance limits before demand locations are known.
- •For urban transit managers: Design variable service radii in transit or shared mobility systems to improve coverage with limited travel distances or operational budgets.
A theory result. No direct application yet.
Authors
Taha Ameen, Sophie H. Yu
Abstract
In spatial matching markets, a supply unit's flexibility is measured by its service radius, the maximum distance at which it can serve demand. In dimensions $k \geq 2$, we study how a platform should allocate service radii among the supply nodes subject to a budget on their sum. The platform makes this choice before observing supply and demand locations, with the objective of maximizing the expected fulfilled demand. We show that the shape of a preferred allocation depends on the total budget: under suitable conditions, large budgets favor allocations that are more uniform in the sense of majorization, while small budgets favor concentration. We also characterize a non-uniform allocation that is asymptotically optimal for a very-sparse regime, and show that the uniform allocation is suboptimal in this regime. Our results provide theoretical explanations for the radius allocation questions raised by the numerical experiments in [ASY26b].