Urban customized bus companies are increasingly motivated by design efforts that entail more efficient route scenarios to incorporate adaptation to temporal and spatial heterogeneity in travel demand. However, such motivations are usually hindered by ubiquitous arrival unpunctuality resulting from traffic congestion. To resolve this problem, we suggest a time-dependent bus route planning methodology that explicitly considers path flexibility between nodes to be visited. First, we establish a mixed-integer programming model to formulate the problem, where decision-making considerations in bus route planning, path choice between nodes, and passenger assignment are concurrently integrated. Then, we develop a hybrid metaheuristic (combining tabu search and variable neighborhood search) to solve the model, in which satisfactory performance is observed from the numerical test in a small-sized example. Finally, the problem and methodology are addressed in a city-scale instance, where the effects of time-window features and traffic congestion, as well as the benefits from path flexibility inclusion in terms of cost, travel time, and distance are investigated.
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