The 2-opt local search algorithm of the nearest neighbor heuristic in a vehicle routing problem with precedence customers was evaluated. A set of homogeneous vehicles are employed to deliver demand from a central depot to a set of customer location. The objective is to find the minimum traveling hours within a stipulated time constraint. In this study, customers can be registered as a precedence member, where the demand is at priority to be delivered first than the regular one. Vehicles with 10 kg carrying capacity are utilized in delivery accomplishment within 2.5 hours time constraint for 13 customer locations in Bandung City. The proposed algorithm was developed by incorporating Google Map application interface as its basis of traveling distances and duration within the customers and was applied for all possible combinations of precedence customers, where 8190 customer datasets are involved. Simulation results show that the presence of 1 to 12 number of precedence customers in the datasets increase the average traveling duration for vehicle routes up to 10.54% compared to the regular one.