The time dependent vehicle routing problem with time windows: Benchmark problems, an efficient solution algorithm, and solution characteristics

► New replicable problems for time-dependent routing problems with hard time-windows. ► New algorithm for time dependent routing problems with hard or soft time-windows. ► Algorithm computational time is proportional to the number of customers squared. ► Efficient, simple and fast solution algorithm well suited for dynamic problems. ► Solution quality, computational time, and problem perturbation results are analyzed. An algorithm that can tackle time dependent vehicle routing problems with hard or soft time windows without any alteration in its structure is presented. Analytical and experimental results indicate that average computational time increases proportionally to the number of customers squared. New replicable test problems that capture the typical speed variations of congested urban settings are proposed. Solution quality, time window perturbations, and computational time results are discussed as well as a method to study the impact of perturbations by problem type. The algorithm efficiency and simplicity is well suited for urban areas where fast running times may be required.