Shortest path tour problem with time windows

This paper aims at studying a new variant of the shortest path tour problem, where time window constraints are taken into account. This is the first work dealing with the shortest path tour problem with time windows. The problem is formally described and its theoretical properties are analyzed. We prove that it belongs to the NP-hard class of complexity by polynomial reduction from the knapsack problem. An optimal solution approach based on the dynamic programming paradigm is devised. Labelling algorithms are defined along with well-tailored pruning strategies based on cost and time. The correctness of the bounding strategies is proven and the empirical behavior is analyzed in depth. In order to evaluate the performance of the proposed approach, extensive computational experiments have been carried out on a significant set of test problems derived from benchmarks for the shortest path tour problem. Sensitivity analysis is carried out by considering both algorithmic and instance parameters.