Action-Evolution Petri Nets: a Framework for Modeling and Solving Dynamic Task Assignment Problems
This addresses the problem of dynamic task assignment for researchers and practitioners by providing a unified modeling framework, though it is incremental as it builds on existing formalisms like Petri Nets and Markov Decision Processes.
The paper tackles the lack of an integrated modeling technique for dynamic task assignment problems by proposing Action-Evolution Petri Nets (A-E PN), a framework that unifies modeling and enables learning close-to-optimal policies through reinforcement learning, as demonstrated on three cases.
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.