The time-window orientation problem under consideration belongs to the class of routing and scheduling problems arising from physical allocation. It considers a set of nodes (clients), each with associated profit and processing time (time window), and a set of edges, each characterized by a particular time. The goal of the problem is to construct an acyclic path starting at a given origin and ending at a given destination that maximizes total profit while meeting the time window constraints on all nodes and not exceeding a given time limit. The problem is classified as NP-hard, so an exact algorithm that executes in a reasonable time is unlikely to exist.