  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.
