Theoretical Aspects of the Integrated Route Planning Problem ⋆ Carlos Cardonha ∗ Ricardo Herrmann ∗∗ Priscilla Avegliano ∗∗∗ IBM Research - Brazil Rua Tut´ oia 1157, 04007-005 S˜ao Paulo, SP ∗ (Tel: +55 11 2132-3934; e-mail: carloscardonha@br.ibm.com). ∗∗ (Tel: +55 11 2132-4883; e-mail: ricardo.herrmann@br.ibm.com). ∗∗∗ (Tel: +55 11 2132-5790; e-mail: pba@br.ibm.com). Abstract: In this article, we introduce the Integrated Route Planning Problem (IRPP), which deals with the assignment of touristic itineraries, composed of activities characterized by their capacity and opening time, to visitors that may have variable time availabilities and different levels of preference for the activities. We show that the IRPP is challenging from the computational point of view, present a mathematical programming formulation of the problem and discuss aspects of a solution method based on the column generation technique. We also show how some tools of probabilistic planning and agent-based modeling may be used to address important aspects of the problem. Keywords: optimization problems, mathematical programming, integer programming 1. INTRODUCTION With the recent technological advances, the access to personalized services that can be delivered electronically increased considerably. In particular, the large use of smartphones and social networks together with wide in- ternet availability made information and services about activities that are taking place in a certain region easily accessible not only to local residents, but also to current and potential visitors. Clearly, a visitor that is going to a city wants to have the most pleasant trip possible, which means that she wants to visit a set of attractions that is compatible with her’s and their’s time constraints. However, if every visitor has an egoistic behavior and/or if she is just unaware of what other visitors will do, we may have a situation where several attractions will be overflowed, reducing the quality of the tourists’ experience and eventually disrupting their itineraries. In this article, we investigate the Integrated Route Planning Problem (IRPP), which deals with the as- signment of touristic itineraries, composed of activities with limited capacity and time restrictions, to visitors with variable time availabilities and different levels of preference for the activities. It is clear that solving the problem in an integrated way (i.e., considering all the visitors’ profiles and generating itineraries for them simultaneously) allows for better global solutions and leverages solutions such as the ones proposed by Picot-Clem´ ent et al. [CMCN12]. Solutions for the IRPP provide a mathematical frame- work for recommender systems that can be used by mu- ⋆ This work was supported and partially funded by FINEP / MCTI, under subcontract no. 03.11.0371.00. nicipal tourism councils and agencies in the organization of routes that maximize their clients’ experience while re- specting capacity limitations of the suggested attractions. This article is organized as follows. In Section 2 we in- troduce the formal aspects of the Integrated Route Planning Problem and show that it is challenging from a computational point of view. In Section 3 we present a Mixed Integer Linear Programming formulation of the problem and discuss how it can be solved with the col- umn generation technique. Section 4 outlines alternative approaches, focused mainly on probabilistic planning and agent-based modeling, and their potential application to interesting extensions of the problem. Finally, we present our conclusions and discuss possible topics of future works in Section 5. 2. THE INTEGRATED ROUTE PLANNING PROBLEM We introduce now the mathematical description of the Integrated Route Planning Problem (IRPP) . We assume that time is measured in discrete units, so all the time-related values are integer numbers belonging to some set T = {0, 1,...,T }, T ∈ N. 2.1 Definition of the Parameters We are given a set A⊆ R 2 ×N 6 containing n activities. The coordinates of every tuple a in A consists of the following elements: • loc a denoting the location of activity a using its geographical coordinates (latitude and longitude); • κ a ∈ N, denoting the maximum number of tourists that may participate in a simultaneously; 6th IFAC Conference on Management and Control of Production and Logistics The International Federation of Automatic Control September 11-13, 2013. Fortaleza, Brazil 978-3-902823-50-2/2013 © IFAC 427 10.3182/20130911-3-BR-3021.00082