Online Task Assignment Problems with Reusable Resources
This addresses resource allocation in dynamic markets like ridesharing, offering theoretical guarantees for practical applications, though it builds incrementally on prior work by generalizing to multiple agents per task and agent rejections.
The paper tackles the online task assignment problem with reusable resources, such as in ridesharing and crowdsourcing, by proposing an algorithm that achieves a tight 1/2-competitive ratio for maximizing expected profit, and extends to cases with agent rejection limits, achieving at least a 1/3 ratio.
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 $Δ$ times, the algorithm is shown to have the competitive ratio $Δ/(3Δ-1)\geq 1/3$. We also evaluate our proposed algorithm with numerical experiments.