Route planning problem under fuzzy sightseeing times and satisfaction values of sightseeing places

This paper proposes a personal tour planning problem with uncertain traveling times and satisfaction values of sightseeing places dependent on sightseeing. Since traveling times are dependent on the time of day, it is difficult to represent this uncertain model using the general static network model. In this paper, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. Using the proposed TEN-based model, it is possible to construct various variations of traveling times and satisfactions values of sightseeing places in a single static network. Furthermore, uncertain sightseeing times are represented as fuzzy variables and the proposed model is formulated as a fuzzy 0-1 mixed integer programming problem, and also equivalently transformed into several existing tour planning problems using some natural assumptions in fuzzy programming.