Action-Evolution Petri Nets: a Framework for Modeling and Solving Dynamic Task Assignment Problems

TL;DR

This paper introduces Action-Evolution Petri Nets (A-E PN), a unified, executable modeling framework for dynamic task assignment problems that enables learning near-optimal policies via Reinforcement Learning.

Contribution

It proposes A-E PN as an integrated modeling and solving framework, bridging existing formalisms and facilitating policy learning without extra modeling effort.

Findings

A-E PN can model various dynamic task assignment problems.

The framework enables learning close-to-optimal policies.

Demonstrated effectiveness on three archetypical problems.

Abstract

Dynamic task assignment involves assigning arriving tasks to a limited number of resources in order to minimize the overall cost of the assignments. To achieve optimal task assignment, it is necessary to model the assignment problem first. While there exist separate formalisms, specifically Markov Decision Processes and (Colored) Petri Nets, to model, execute, and solve different aspects of the problem, there is no integrated modeling technique. To address this gap, this paper proposes Action-Evolution Petri Nets (A-E PN) as a framework for modeling and solving dynamic task assignment problems. A-E PN provides a unified modeling technique that can represent all elements of dynamic task assignment problems. Moreover, A-E PN models are executable, which means they can be used to learn close-to-optimal assignment policies through Reinforcement Learning (RL) without additional modeling effort. To evaluate the framework, we define a taxonomy of archetypical assignment problems. We show for three cases that A-E PN can be used to learn close-to-optimal assignment policies. Our results suggest that A-E PN can be used to model and solve a broad range of dynamic task assignment problems.