Online Food Delivery to Minimize Maximum Flow Time
Xiangyu Guo, Shi Li, Kelin Luo, Yuhao Zhang

TL;DR
This paper addresses the challenge of minimizing maximum flow time in online food delivery, presenting new algorithms with competitive ratios and exploring the problem's computational hardness.
Contribution
It introduces an $O(1)$-competitive online algorithm for uncapacitated delivery on tree metrics and develops approximation algorithms under speed-augmentation models.
Findings
Hardness of approximation is $oldsymbol{ ilde{oldsymbol{ ext{Omega}}}(n)}$ for offline and online cases.
An $O(1)$-competitive online algorithm exists for uncapacitated delivery on trees.
Approximation algorithms are developed using speed-augmentation with factors related to TSP and CVRP.
Abstract
We study a common delivery problem encountered in nowadays online food-ordering platforms: Customers order dishes online, and the restaurant delivers the food after receiving the order. Specifically, we study a problem where vehicles of capacity are serving a set of requests ordering food from one restaurant. After a request arrives, it can be served by a vehicle moving from the restaurant to its delivery location. We are interested in serving all requests while minimizing the maximum flow-time, i.e., the maximum time length a customer waits to receive his/her food after submitting the order. We show that the problem is hard in both offline and online settings: There is a hardness of approximation of for the offline problem, and a lower bound of on the competitive ratio of any online algorithm, where is number of points in the metric. Our main…
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