Minimizing Latency in Online Ride and Delivery Services

TL;DR

This paper develops approximation algorithms for complex variants of the minimum latency problem in online ride and delivery services, incorporating real-world constraints like source-destination pairs and release times, and validates them empirically.

Contribution

It introduces the first constant-factor approximation algorithms for these variants, extending classical minimum latency problems with practical constraints.

Findings

Constant-factor approximation algorithms developed.

Algorithms effectively handle source-destination and release-time constraints.

Empirical evaluation shows practical effectiveness on real taxi data.

Abstract

Motivated by the popularity of online ride and delivery services, we study natural variants of classical multi-vehicle minimum latency problems where the objective is to route a set of vehicles located at depots to serve request located on a metric space so as to minimize the total latency. In this paper, we consider point-to-point requests that come with source-destination pairs and release-time constraints that restrict when each request can be served. The point-to-point requests and release-time constraints model taxi rides and deliveries. For all the variants considered, we show constant-factor approximation algorithms based on a linear programming framework. To the best of our knowledge, these are the first set of results for the aforementioned variants of the minimum latency problems. Furthermore, we provide an empirical study of heuristics based on our theoretical algorithms on a real data set of taxi rides.