Travel itinerary problem

•An itinerary optimization problem is proposed to search itineraries with the lowest cost.•It is decomposed into a tour selection process and a number selection process.•An implicit enumeration algorithm is used to solve the optimal itinerary.•By integrating itinerary optimization and web crawler technology, a smart travel system is proposed.

In this study, we propose a travel itinerary problem (TIP) which aims to find itineraries with the lowest cost for travelers visiting multiple cities, under the constraints of time horizon, stop times at cities and transport alternatives with fixed departure times, arrival times, and ticket prices. First, we formulate the TIP into a 0–1 integer programming model. Then, we decompose the itinerary optimization into a macroscopic tour (i.e., visiting sequence between cities) selection process and a microscopic number (i.e., flight number, train number for each piece of movement) selection process, and use an implicit enumeration algorithm to solve the optimal combination of tour and numbers. By integrating the itinerary optimization approach and Web crawler technology, we develop a smart travel system that is able to capture online transport data and recommend the optimal itinerary that satisfies travelers’ preferences in departure time, arrival time, cabin class, and transport mode. Finally, we present case studies based on real-life transport data to illustrate the usefulness of itinerary optimization for minimizing travel cost, the computational efficiency of the implicit enumeration algorithm, and the feasibility of the smart travel system.