For a vector-valued Markov decision process with discounted reward criterion, we study the structure of its value spaces defined for all initial states. At first we discuss the relationship between the value spaces, i.e. we verify a linking property for optimality. We next show that if the...

We study a multi-objective shortest path problem. We formulate a multi-objective Markov decision process model for the problem and solve it by the policy improvement procedure. We first show by counter-examples the differences between the multi-objective shortest path problem and the...