Time analysis for planning a path in a time-window network

A systematic method is proposed to generate time information on the paths and nodes on a time-window network for planning and selecting a path under a constraint on the latest entering time at the destination node. Specifically, three algorithms are proposed to generate six basic time characteristics of the nodes, including the earliest and latest times of arriving at, entering, and departing from each node on the network. Using the basic time characteristics, we identify inaccessible nodes that cannot be included in a feasible path and evaluate the accessible nodes' flexibilities in the waiting and staying time. We also propose a method for measuring adverse effects of including an arc. Finally, based on the time characteristics and the proposed analyses, we develop an algorithm that can find the most flexible path in a time-window network.