# The Vehicle Routing Problem: State-of-the-Art Classification and Review
###### Abstract  
Transportation planning has been established as a key topic in the literature and social production practices. An increasing number of researchers are studying vehicle routing problems (VRPs) and their variants considering real-life applications and scenarios. Furthermore, with the rapid growth in the processing speed and memory capacity of computers, various algorithms can be used to solve increasingly complex instances of VRPs. In this study, we analyzed recent literature published between 2019 and August of 2021 using a taxonomic framework. We reviewed recent research according to models and solutions, and divided models into three categories of customer-related, vehicle-related, and depot-related models. We classified solution algorithms into exact, heuristic, and meta-heuristic algorithms. The main contribution of our study is a classification table that is available online as Appendix A. This classification table should enable future researchers to find relevant literature easily and provide readers with recent trends and solution methodologies in the field of VRPs and some well-known variants.  
vehicle routing problem; taxonomy; literature review; exact methods; heuristics; meta-heuristics +
Footnote †: journal: Applied  
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Footnote 1: email: {[[https://doi.org/10.3309/app112110295](https://doi.org/10.3309/app112110295)]([https://doi.org/10.3309/app112110295](https://doi.org/10.3309/app112110295))}  
[PERSON] et al. [4], the VRP represents an evolving field of operations research that has been growing exponentially at a rate of 6% per year, which makes it difficult to keep track of developments in the field and obtain a clear overview of which variants and solution methods are relatively novel.  
The VRP family can be considered as two combinatorial senses: (1) the number of possible solutions, which grow exponentially with computer science and algorithm design; and (2) the number of conceivable problem variants, which also grow exponentially with a variety of problem attributes [12]. This survey classifies the academic literature on VRPs from the perspective of solution methodologies, as well as the detailed characteristics of VRPs. Because we base our classification on the taxonomy presented in [4], we restrict our analysis to articles published between 2019 and August of 2021. Therefore, we do not intend to provide an exhaustive overview of VRP literature. To the best of our knowledge, this article provides the first structured classification of recent VRP literature based on solution and problem attributes.  
The main contribution of our paper is a classification table that is available online as Appendix A. This classification table should enable future researchers to find relevant literature easily by eliminating or selecting characteristics in the taxonomy, leaving only articles tailored to their interests. The main objective of this work is to provide readers with recent trends and solution methodologies in the field of VRPs and some well-known variants. This survey is expected to help future researchers identify a problem domain and promising topics for research.  
Section 2 defines the scope of this survey and Section 3 introduces the VRP and its variants. A comprehensive survey of state-of-the-art strategies currently used for solving VRPs is presented in Section 4. Section 5 summarizes our observations and conclusions.