Optimizing Vehicle Routing: A Comprehensive Literature Review of Mixed Integer Linear Programming Solutions

Abstract

Combinatorial optimization is a sub-branch of mathematical optimization. In logistics and transportation, especially, the Vehicle Routing Problem (VRP) becomes prominent as an example for the combinatorial optimization problems with different implementations. Minimizing operational cost and satisfying resource utilization are very critical objectives for companies and decision makers in this field. It is proved in the literature that the Mixed Integer Linear Programming (MINLP) is very useful tool to solve VRPs efficiently due to its capability to handle complicated decision variables and constraints [1-3]. This study shows an extensive literature review that focuses on the implementation of MILP to the VRP. The study investigates the historical development of MILP-based approaches, underlying the evolution of mathematical formulations, solution ethodologies, and computational methods. It also examines the main outcomes and contributions from existing research studies in the area, categorizing them depending on problem types, constraints, and solution algorithms. In addition to that, the review searches the theoretical underpinnings of MILP in solving VRPs, discussing the benefits and limitations of this approach when compared to other optimization methods. It underlines the operational function of MILP in ensuring optimal or near-optimal solutions, allowing productive fleet management, and addressing real-world constraints such as time windows, capacity constraints, and heterogeneous fleets. Consequently, this literature review investigates the collective knowledge in the study area, providing precious insights into the state-of-the-art methods and challenges. It is aimed that the proposed study will be very useful guide for the decision makers working in the field.