Design a Win-Win Strategy That Is Fair to Both Service Providers and Tasks When Rejection Is Not an Option

TL;DR

This paper proposes a fair online matching strategy for task assignment that balances service provider workload and task waiting time, ensuring no task rejection due to overload.

Contribution

It introduces a novel approach modeling task assignment as a bipartite graph minimax problem, with efficient solutions and heuristics validated by real data simulations.

Findings

Linear programming approach effectively minimizes maximum workload.

Heuristics based on the LP perform well in simulations.

The method balances fairness and efficiency in task assignment.

Abstract

Assigning tasks to service providers is a frequent procedure across various applications. Often the tasks arrive dynamically while the service providers remain static. Preventing task rejection caused by service provider overload is of utmost significance. To ensure a positive experience in relevant applications for both service providers and tasks, fairness must be considered. To address the issue, we model the problem as an online matching within a bipartite graph and tackle two minimax problems: one focuses on minimizing the highest waiting time of a task, while the other aims to minimize the highest workload of a service provider. We show that the second problem can be expressed as a linear program and thus solved efficiently while maintaining a reasonable approximation to the objective of the first problem. We developed novel methods that utilize the two minimax problems. We conducted extensive simulation experiments using real data and demonstrated that our novel heuristics, based on the linear program, performed remarkably well.