An Algorithm for the Traveling Salesperson Problem with Time Windows and Lateness Costs

This paper presents a model and dynamic programming based algorithm for the Traveling Salesperson Problem with Time Windows (TSPTW). The main difference of our model compared with the previous ones lies in that the time windows we are concerned are far more flexible and realistic. In the typical TSPTW, the service at a node must begin within the time grid called the time window that is defined by the earliest and the latest time to start the service at the node. But, in real business practices, a lateness cost is usually penalized rather than the service is prohibited at all when a vehicle arrives after the latest time. Considering this situation, we propose a model with a new time window that allows an arrival after the latest time and penalizes the late arrival by charging a lateness cost. An algorithm introduced for the model is extensively tested to verify the accuracy and efficiency.