Online Task Assignment Problems with Reusable Resources

TL;DR

This paper introduces an online task assignment model with reusable agents and multiple task accommodations, proposing a $1/2$-competitive algorithm and analyzing its performance under rejection constraints, supported by numerical experiments.

Contribution

We develop a novel online algorithm for reusable resource task assignment with proven competitive ratios and extend analysis to rejection constraints, addressing practical applications.

Findings

The algorithm achieves a $1/2$-competitive ratio, which is proven to be tight.

Under rejection constraints, the competitive ratio is at least 1/3.

Numerical experiments validate the effectiveness of the proposed algorithm.

Abstract

We study online task assignment problem with reusable resources, motivated by practical applications such as ridesharing, crowdsourcing and job hiring. In the problem, we are given a set of offline vertices (agents), and, at each time, an online vertex (task) arrives randomly according to a known time-dependent distribution. Upon arrival, we assign the task to agents immediately and irrevocably. The goal of the problem is to maximize the expected total profit produced by completed tasks. The key features of our problem are (1) an agent is reusable, i.e., an agent comes back to the market after completing the assigned task, (2) an agent may reject the assigned task to stay the market, and (3) a task may accommodate multiple agents. The setting generalizes that of existing work in which an online task is assigned to one agent under (1). In this paper, we propose an online algorithm that is $1/2$-competitive for the above setting, which is tight. Moreover, when each agent can reject assigned tasks at most $\Delta$ times, the algorithm is shown to have the competitive ratio $\Delta/(3\Delta-1)\geq 1/3$. We also evaluate our proposed algorithm with numerical experiments.