Markovian assignment decision process

A finite-state, discrete-time Markovian decision process, in which, each action in each state is a feasible solution to a state dependent assignment problem, is considered. The objective is to maximize the additive rewards realized by the assignments over an infinite time horizon. In the undiscounted case, the average gain per transition and in the discounted case, the discounted total gain respectively, are maximized. Properties of optimal solutions in the two cases are characterized and finite algorithms are presented.