# A Survey on Variable Neighborhood Search for Sustainable Logistics
## 1 Introduction  
Logistics plays a crucial role in modern economies by facilitating the movement and storage of goods, services, and information from their point of origin to their point of consumption, with the primary goal of satisfying customer or business requirements. It involves the strategic planning, implementation, and control of various interconnected activities, such as transportation, warehousing, inventory management, and coordination of supply chains. These functions are essential to ensuring timely delivery, optimizing resource utilization, maintaining cost efficiency, and improving overall service levels. In recent years, the concept of sustainability has become increasingly integrated into logistics practices, driven by the need for businesses to meet the growing consumer demand for environmentally friendly products and services, as well as to comply with stricter environmental regulations worldwide. Sustainable logistics is a broader concept that refers to the management and optimization of supply chain processes in a way that minimizes environmental impact, promotes social responsibility, and ensures economic viability. The challenge lies in balancing these three pillars of sustainability--economic, environmental, and social--while maintaining high levels of service and efficiency. Sustainable logistics encompasses a range of initiatives aimed at reducing carbon emissions, implementing eco-friendly transportation methods, optimizing resource utilization, and minimizing waste, all while ensuring that businesses continue to thrive in an increasingly competitive market. The goal of sustainable logistics is to create a harmonious balance between economic growth, environmental stewardship, and social well-being. It requires careful consideration of immediate and long-term impacts on the environment, society, and economy. By optimizing logistics processes through sustainable practices, businesses can not only reduce their ecological footprint but also contribute to broader global sustainability goals. In the context of this study, the three key dimensions of sustainability are defined as follows:  
* Economic sustainability refers to the ability of an economic system to support long-term growth while ensuring the efficient use of resources and financial stability. It requires careful management to avoid negative impacts on social, environmental, or cultural factors. It emphasizes the efficient allocation of resources to ensure that industries, businesses, and economies can continue to function in a sustainable manner, while also providing opportunities for future generations to prosper. * Environmental sustainability focuses on managing and conserving natural resources in a responsible manner to prevent ecosystem degradation and ensure that these resources remain available for future generations. This dimension of sustainability involves reducing pollution, conserving biodiversity, minimizing waste, and promoting renewable energy sources and sustainable practices in industries such as transportation, manufacturing, and agriculture. The ultimate objective is to protect the health of the planet and maintain its ecological balance for the well-being of future generations. * Social sustainability is about creating and maintaining societies that promote social equity, justice, and well-being for all individuals. This pillar focuses on ensuring access to basic services such as education, healthcare, and employment opportunities, as well as fostering inclusive and resilient communities. Social sustainability emphasizes the importance of respecting human rights, cultural diversity, and social progress, ensuring that future generations inherit a world characterized by equality, fairness, and peace. These three pillars are deeply interconnected and often contradictory. For example, efforts to reduce environmental impacts might increase short-term costs, while focusing on social well-being may complicate economic efficiency.