Multiple Criteria Discrete Dynamic Programming

Dynamic programming is classically concerned with maximization of the value assigned by a real-valued function defined over sequences of decisions. Multi-criteria (multi-objective) dynamic programming extends the approach to a vector-valued criterion function. The main purpose of the paper is to give new definitions of separability and monotonicity which allow to extend the theory of discrete multiobjective dynamic programming. The vector principle of optimality and theorems applied in decomposition methods are formulated. Numerical algorithms for such problems are briefly described. The paper ends with examples which illustrate the numerical aspects of the procedures.