This article proposes extensions of exact and heuristic dynamic programming algorithms for the traveling salesman problem with flexible time windows, which are a limited enlargement of the generally referred to as hard time windows. The service of a customer can be started before or after the hard time window at a penalty cost. The addressed problem thus requires the determination of a sequence of customers and their respective service start times in order to minimize the sum of traveling cost with earliness and lateness cost. Computational tests are conducted on a variety of symmetric and asymmetric instances proposed in the literature, and the advantages of flexible windows are stressed.

中文翻译：

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具有灵活时间窗的旅行商问题的精确启发式动态规划算法

本文提出了针对具有灵活时间窗的旅行商问题的精确和启发式动态规划算法的扩展，这是通常称为硬时间窗的有限扩展。可以在困难时段之前或之后启动客户服务，但要付出一定的代价。因此，所解决的问题需要确定顾客的顺序及其各自的服务开始时间，以使旅行成本与早期和迟到成本的总和最小化。对文献中提出的各种对称和非对称实例进行了计算测试，并强调了柔性窗的优势。