Optimal Stationary Policies in General State Space Markov Decision Chains with Finite Action Sets

The result of Sennott [9] on the existence of optimal stationary policies in countable state Markov decision chains with finite action sets is generalized to arbitrary state space Markov decision chains. The assumption of finite action sets occurring in a global countable action space allows a particularly simple theoretical structure for the general state space Markov decision chain. Two examples illustrate the results. Example 1 is a system of parallel queues with stochastic work requirements, a movable server with controllable service rate, and a reject option. Example 2 is a system of parallel queues with stochastic controllable inputs, a movable server with fixed service rates, and a reject option.