Exact and Heuristic Optimization Methods for the Transportation of Radiopharmaceuticals

Abstract

This thesis addresses the optimization of radiopharmaceutical transportation for distribution by developing a comprehensive variant of the Vehicle Routing Problem (VRP). Radiopharmaceuticals are highly time-sensitive due to their short half-lives, making timely delivery crucial for maintaining clinical efficacy in PET scan imaging. The proposed model incorporates several realistic extensions to the classical (capacitated) VRP model, and these extensions are heterogeneous fleets, time windows, pickup and delivery, and split deliveries. The combination of these features within a single, healthcare-specific VRP model tailored to radiopharmaceutical delivery represents a meaningful and novel advancement not covered by existing literature.

An exact mixed-integer programming model is implemented using Gurobi to explore the scalability limits of exact methods. A series of computational experiments on randomly generated networks of increasing size reveals that exact methods quickly become infeasible beyond 17–18 nodes due to exponential runtime growth. To address this limitation, an Adaptive Large Neighborhood Search (ALNS) heuristic is developed and tested. A real-world case study involving 44 medical imaging facilities in the Metro-Detroit area is then used to evaluate heuristic performance at scale. Results show that the ALNS consistently produces high-quality solutions in an efficient manner, achieving up to a 21.5% improvement over an initial feasible solution. The most effective operator combination emerged as random removal followed by savings insertion, with the "adaptive" portion of the algorithm quickly learning to prioritize these heuristics. These findings underscore the potential of algorithmic approaches in improving delivery reliability for time-sensitive healthcare supply chains.