Towards Fairness in Online Service with k Servers and its Application on Fair Food Delivery

TL;DR

This paper introduces the k-FOOD problem, a realistic generalization of the k-SERVER problem for online service scenarios like food delivery, and proposes algorithms to optimize fairness and efficiency in such settings.

Contribution

It formulates the k-FOOD and FAIR k-FOOD problems, proves their NP-hardness, and develops an optimal offline algorithm and an effective online algorithm for real-world applications.

Findings

The online algorithm DOC4FOOD outperforms existing fair food delivery algorithms.

The proposed algorithms are effective on real-world and synthetic datasets.

Both k-FOOD and FAIR k-FOOD are strongly NP-hard.

Abstract

The k-SERVER problem is one of the most prominent problems in online algorithms with several variants and extensions. However, simplifying assumptions like instantaneous server movements and zero service time has hitherto limited its applicability to real-world problems. In this paper, we introduce a realistic generalization of k-SERVER without such assumptions - the k-FOOD problem, where requests with source-destination locations and an associated pickup time window arrive in an online fashion, and each has to be served by exactly one of the available k servers. The k-FOOD problem offers the versatility to model a variety of real-world use cases such as food delivery, ride sharing, and quick commerce. Moreover, motivated by the need for fairness in online platforms, we introduce the FAIR k-FOOD problem with the max-min objective. We establish that both k-FOOD and FAIR k-FOOD problems are strongly NP-hard and develop an optimal offline algorithm that arises naturally from a time-expanded flow network. Subsequently, we propose an online algorithm DOC4FOOD involving virtual movements of servers to the nearest request location. Experiments on a real-world food-delivery dataset, alongside synthetic datasets, establish the efficacy of the proposed algorithm against state-of-the-art fair food delivery algorithms.