An LP-based heuristic for a time-constrained routing problem

In this paper we present an LP-based heuristic for the solution of a Time Constrained Routing problem arising from innovative services accessible via World Wide Web. The problem consists of scheduling the visit of a tourist to a given geographical area in order to maximize his satisfaction degree whilst respecting time windows restrictions. We refer to this problem as the Intelligent Tourist Problem (ITP). ITP is formulated as a Set Packing problem with side constraints. Due to the huge number of variables in the formulation, the LP-relaxation is solved by a ‘column-and-row generation’ approach. Then we run an MIP solver over the active columns to get a feasible solution. Computational experience on real-world instances is reported showing the effectiveness of the proposed approach.