Dynamic Scoring and Costing in the Orienteering Problem: A Model Based on Length of Stay

Abstract

In today's travel and tourism landscape, the role of travel agents has become increasingly complex as they are challenged to explore a variety of potential destinations. More specifically, the complicated task of planning itineraries that truly satisfy travellers puts travel agents in a crucial role, increasing the complexity of itinerary planning. This complexity is compounded not only by the multitude of possible destinations, but also by non-negotiable constraints such as cost and time. To address these challenges, the orienteering problem represents a fundamental mathematical model that provides a theoretical basis for understanding the nuanced difficulties faced by travel agents.This study ventures into a novel iteration of the orienteering problem, with a particular focus on optimizing travel satisfaction based on length of stay. A notable aspect of this variant is the inclusion of time and cost constraints in the route determination process. Using an integer programming model, the satisfaction scores for each location are described by a diminishing returns function linked to length of stay, while the costs associated with each location follow a linear function influenced by the same parameter. The application of this model is in a hypothetical scenario with 32 nodes, with the calculations facilitated by the FilMINT solver. A sensitivity analysis examines time and cost constraints and shows their decisive influence on the optimization of travel routes. The results of this research contribute significantly to a strategic framework and provide travel agencies with the opportunity to create itineraries that not only meet practical limits but, more importantly, increase traveller satisfaction.