1 Abstract The itinerary planning problem in an urban public transport system constitutes a common routing and scheduling decision faced by travelers. The objective of this paper is to present a new formulation and an algorithm for solving the itinerary planning problem, i.e., determination of the itinerary that lexicographically optimizes a set of criteria (i.e. total travel time, number of transfers, and total walking and waiting time) while departing from the origin and arriving at the destination within specified time windows. Based on the proposed formulation, the itinerary planning problem is expressed as a shortest path problem in a time schedule multimodal network with time windows and time dependent travel times. A dynamic programming based algorithm has been developed for the solution of the emerging problem. The special case of the problem involving a mandatory visit at an intermediate stop within a given time window is formulated as two nested itinerary planning problems which are solved by the aforementioned algorithm. The proposed algorithm has been integrated in a web based journey planning system while its performance has been assessed by solving real life itinerary planning problems defined on the Athens Urban Public Transport Network providing fast and accurate solutions. Index Terms itinerary planning, multimodal transportation network, multi-criteria, shortest path I. INTRODUCTION journey in an urban public transport system usually involves the combined use of the available public transport services. Each conventional urban public transport service is defined by a sequence of stops on a given route and a specified schedule. In this context, any journey may be realized by a path that consists of alternate interconnected route segments of the underlying public transport services. Manuscript received May 14, 2007. The research reported in this paper has been partially supported by the General Secretariat for Science and Technology of the Greek Ministry of Development, through the project Integrated Decision Support System for On-line, Real Time Trip Planning in Multimodal Transportation Systems (ENOSIS). K. G. Zografos is with the Transportation Systems and Logistics Laboratory, Department Management Science and Technology, Athens University of Economics and Business, Evelpidon 47A & 33 Lefkados, 113 62 Athens, Greece, Tel: +30 210 8203673-5, Fax: +30 210 8203684, Email: translog@aueb.gr . K. N. Androutsopoulos is a research associate in the Transportation Systems and Logistics Laboratory, Department Management Science and Technology, Athens University of Economics and Business. Any such path enhanced with a feasible schedule of traversing it, is called itinerary. It is evident that a journey may be realized by several alternative itineraries. A major decision that arises for the traveler relates to the selection of the itinerary that complies with his/her preferences and requirements. The major complexities of this type of decision relate to: i) the lack of information on the schedule and the routes of the public transport services, ii) the difficulty in determining feasible itineraries within the dense urban public transport network, and iii) the intensive task of assessing alternative feasible itineraries in terms of multiple traveling criteria. The provision of real time journey planning services through an online advanced public transport information system may alleviate the aforementioned difficulties [1], [2] and contribute to the enhancement of the usability and accessibility of the public transport services. During the past decade many advanced public transport information systems have been developed providing journey planning services with the objective of determining the shortest itineraries in terms of the travel time or the cost [3], [4]. Nowadays this type of services are directly accessible by the travelers through on-line web-based applications [2], [5], [6], [7] . The existing journey planning services aim to determine the itinerary between an origin-destination pair that optimizes one of the travel time, number of transfers, or walking time, given the preferable departure or arrival time stated by the user and considering constant (average) travel times. In general the itinerary planning problem constitutes a multi-criteria routing and scheduling problem, providing a traveler with many alternative itineraries for a specific urban journey. However, this implies that the user should take on the tedious task (especially for the user who is unfamiliar with the specific public transport system) of selecting an itinerary from a list of alternative solutions. This issue could be resolved by the incorporation of the lexicographical ordering in the solution process of the itinerary planning problem. Under this approach, more than one criteria are taken into account, while only a single solution is provided to the user. This paper provides a new formulation of the itinerary planning problem which apart from the lexicographically optimal itinerary aims to determine the optimal departure time of the journey. The proposed formulation enhances the existing trip planning models mentioned above by Algorithms for Itinerary Planning in Multimodal Transportation Networks Konstantinos G. Zografos, Konstantinos N. Androutsopoulos A