Dynamic programming with ordered structures: Theory, examples and applications

The paper presents a dynamic, discrete optimization model with returns in ordered structures. It generalizes multiobjective methods used in vector optimization in two ways: from real vector spaces to ordered structures and from the static model to the dynamic model. The proposed methods are based on isotone homomorphisms. These methods can be applied in dynamic programming with returns in ordered structures. The provided numerical example shows an application of fuzzy numbers and random variables with stochastic dominance in dynamic programming. The paper also proposes applications in the following problems: a problem of allocations in the market model, a location problem, a railway routing problem, and a single-machine scheduling problem.