Comparative review of algorithms in vehicle routing and rail container service scheduling problem

This paper presents a comparative analysis in network structure, delivery units and customer interaction in Vehicle Routing Problem (VRP) and the Rail Container Scheduling Problem (RCSSP), two critical challenges in transportation logistics. While both VRP and RCSSP are NPhard optimization problems, they operate in distinct environments—VRP in dynamic road networks emphasizing real-time adaptability and RCSSP in fixed scheduled robust rail systems—leading to divergent algorithmic approaches. Different recent algorithms from 2018 used in VRP and RCSSP is discussed here. Exact methods such as Branch-and-Bound algorithms, dynamic modeling, Mixed-Integer Programming (MIP) and Mixed-Integer Linear Programming model (MILP) are discussed for their precision but limited scalability. Heuristic, metaheuristics algorithm, modern algorithms (such as Deep Reinforcement Learning, and Large Language models), and hybrid algorithms are explored as practical solutions for handling large-scale instances and combination of problems within vehicle and train networks. The paper also discusses the recent trends of algorithms and suggests future directions on cross-domain applications, such as integrating VRP-inspired methods into multi-modal rail scheduling, offering innovative approaches to improving logistics efficiency across both road and rail systems.