Online Task Assignment Problems with Reusable Resources

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 ∆ times, the algorithm is shown to have the competitive ratio ∆/(3∆ − 1) ≥ 1/3. We also evaluate our proposed algorithm with numerical experiments.

Online Task Assignment Problems with Reusable Resources

“…Due to the space limitation, we omit some results and the details of the proofs; see the full version (Sumita et al 2022). Below let us describe technical highlights of the proof of our algorithms.…”

Equity Promotion in Online Resource Allocation

“…Other related works. There are a few works that have considered online resource allocation in different contexts, see, e.g., allocation of public housing for lower-income families (Benabbou et al 2018), distribution of emergence aid for natural disasters like wildfires (Wang, Bier, and Sun 2019), task assignment in crowdsourcing platform (Chatterjee et al 2018;Sumita et al 2022), online set selection with fairness and diversity constraints (Stoyanovich, Yang, and Jagadish 2018), online resource-allocation problems with limited choices in the long-chain design (Asadpour, Wang, and Zhang 2020), and income inequality among rideshare drivers, see, e.g., (Lesmana, Zhang, and Bei 2019;Sühr et al 2019).…”