The generalized team orienteering problem with time windows

The Orienteering Problem (OP) is an optimization problem in which a subset of nodes must be selected to form a route that starts and ends at predefined points, aiming to maximize the total collected reward under a limited time budget. When multiple travellers are involved, the problem is extended to the Team Orienteering Problem (TOP). If the nodes are grouped into clusters, TOP becomes the Generalized Team Orienteering Problem (GTOP). When time constraints are added—specifically, time windows within which visits must occur—the problem evolves into the Time-Windowed Generalized Team Orienteering Problem (GTOP-TW). GTOP-TW is a highly complex optimization problem that combines both cluster constraints and time windows, making it particularly relevant in real-world applications such as logistics, route planning, and task allocation. Despite its practical importance, no prior study in the literature has directly addressed GTOP-TW. This thesis aims to introduce the GTOP-TW to the academic community by proposing a set of novel mathematical models tailored to solve it. First, a general mathematical model for GTOP-TW is formulated. Then, based on this general structure, eight alternative model variants are proposed. These models incorporate various strategies involving node and cluster-level sequencing, flow constraints, and time-window limitations. Each model is tested under different scenarios, and their performance is analysed comparatively. This thesis represents one of the first systematic efforts to address the GTOP-TW and fills an important gap in the literature. It also lays the groundwork for future research involving heuristic and metaheuristic solution approaches for this newly defined problem type.