A great challenge in operational research is to apply time-efficient algorithms to find the optimal solutions to the travelling salesman problem (TSP) and its many variations. The TSP with time windows (TSPTW) arises due to intense pressure for business to improve customer service. As online shopping becomes more popular, customer satisfaction increases if customers can decide when their orders are delivered to them. Customers may choose a time window, which is defined by an earliest delivery time and a latest delivery time, during which the package is delivered. Delivering packages to multiple customers is a typical TSPTW. One main challenge for a delivery business is to determine the size of the time window (i.e., the difference between the latest and earliest delivery times), which affects delivery cost and customer satisfaction. Although many previous studies investigated the TSPTW, none of those focused on the size of time windows. This study is the first that experiments with different time window sizes and determines their impact on tour duration, customer satisfaction, and solution time of the optimal delivery routes. The experiment results show that increasing the size of the time window decreases tour duration and customer satisfaction and increases solution time. Decreasing the size of the time window increases tour duration and customer satisfaction and decreases solution time. A small solution time is necessary for the scheduling of deliveries to many customers. A large solution time prevents a delivery business from delivering packages using optimal routes, which increases delivery cost and decreases customer satisfaction. The results of this study indicate that a general guideline for business is to allow customers to choose a time window size that is within the cost limit but is sufficiently small to maximize customer satisfaction and optimize delivery routes.

运筹学中的一大挑战是应用高效的算法来找到旅行商问题（TSP）及其许多变化的最佳解决方案。具有时间窗口（TSPTW）的TSP是由于企业改善客户服务的巨大压力而产生的。随着在线购物变得越来越流行，如果客户可以决定何时将订单交付给他们，客户满意度就会提高。客户可以选择一个时间窗口，该时间窗口由最早的交付时间和最晚的交付时间定义，在此时间范围内，包裹将被交付。将包裹交付给多个客户是典型的TSPTW。交付业务的一个主要挑战是确定时间窗口的大小（即，最晚和最早的交付时间之间的差），这会影响交付成本和客户满意度。尽管以前的许多研究都对TSPTW进行了研究，但这些都没有关注时间窗口的大小。这项研究是首次进行不同时间窗口大小的实验，并确定它们对游览时间，客户满意度和最佳交付路线的解决时间的影响。实验结果表明，增加时间窗口的大小会减少游览时间和客户满意度，并增加解决时间。减小时间窗口的大小会增加游览时间和客户满意度，并减少解决时间。对于许多客户来说，安排交货时间只需要很小的解决方案时间。解决方案时间过长会阻止送货业务使用最佳路线运送包裹，从而增加送货成本并降低客户满意度。