The On-Demand Tourist Paths Problem Teodor Gabriel Crainic Dept. management et technologie Universit´ e du Qu´ ebec `a Montr´ eal and Center for Research on Transportation Universit´ e de Montr´ eal Nicoletta Ricciardi Giovanni Storchi Dept. di Statistica, Probabilit`a e Statistiche Applicate Universit` a degli Studi di Roma “La Sapienza” Abstract The aim of this paper is to study how to organize the paths or activities on demand of tourist in artistic towns, with the objective of satisfying the demand of visit. Museums, churches, streets and places of interest or attraction are considered, in order to define a ”desirability” for the tourist. The index of desirability of a place is defined by parameters such as the importance, popularity, typology, the average visiting time and some descriptive attributes. This index is associated to each nodes or link of the graph as a label. The current city representation has to be processed such each visiting type of monument or activity is defined. Two main set of paths may be required: Sequential-activity paths, where each of the activity specified by the user have to be performed in the order given by the user; and Mixed-activity paths, where there is no particular request on the sequence on activities. The goal is to find the best path according to the user-specified preferences. The label of each activity is updated using the usual path labelling techniques, adjusted to account for the type of path computed. Key words : Tourist paths, Routing, Shortest paths, A*.