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.

翻译：动态任务分配旨在通过将到达的任务分配到有限资源上，最小化分配总成本。为获得最优任务分配，首先需要对分配问题进行建模。尽管存在马尔可夫决策过程和（着色）Petri网等独立形式化方法，可分别对问题的不同方面进行建模、执行和求解，但缺乏统一的建模技术。为填补这一空白，本文提出行动演化Petri网（A-E PN）作为建模和求解动态任务分配问题的框架。A-E PN提供了一种统一建模技术，可表达动态任务分配问题的所有要素。此外，A-E PN模型是可执行的，这意味着无需额外建模工作即可通过强化学习（RL）学习接近最优的分配策略。为评估该框架，我们定义了原型分配问题的分类体系。通过三个案例，我们证明A-E PN可用于学习接近最优的分配策略。研究结果表明，A-E PN可对广泛的动态任务分配问题进行建模和求解。