# A Survey on Variable Neighborhood Search for Sustainable Logistics
## 4 Results and Findings
### Sustainability Analysis
#### 4.5.1 Economic Criteria  
As previously mentioned, cost is a critical factor that is considered either directly or indirectly in all selected papers. Regardless of the specific optimization problem, cost minimization plays a central role in determining the efficiency and feasibility of the proposed solutions.  
In the context of location problems, costs often encompass a variety of factors. These typically include the expenses associated with the installation of new facilities and the distances between demand points and their nearest service locations [54; 99; 100; 101]. Minimizing these distances is crucial, as it directly impacts transportation costs, which are a major component of overall operational expenses in logistics networks. In some cases, other factors such as land acquisition and facility setup costs are also considered [71], especially when multiple locations are involved in the optimization process.  
When it comes to vehicle routing problems, costs are generally reduced by minimizing travel time or total travel distance, as shorter routes result in lower fuel consumption and fewer operational expenses. In some papers, the cost model is further expanded to account for emissions and fuel costs, particularly in cases where sustainable logistics practices are a focus [35; 57; 102; 103; 104]. Additionally, penalties are sometimes incurred for specific operational inefficiencies, such as early or late arrivals (earliness or tardiness) and unscheduled stops or visits [105; 106; 107]. These penalties can significantly increase overall costs and are important to consider in routing scenarios where time windows or service guarantees are critical. The number of vehicles used is another potential cost factor, although it is less frequently considered [108; 109]. However, when included, the size of the fleet directly impacts both capital expenditure and ongoing operational costs, such as driver wages and vehicle maintenance.  
In scheduling problems, cost reduction is often linked to the minimization of the makespan--the total time required to complete all tasks or jobs. By reducing the makespan, companies can optimize resource allocation, increase throughput, and lower operational expenses such as labor and machine costs. In some cases, scheduling papers also factor in other costs related to delays or downtime, which can impact overall productivity [30; 78].  
Network design problems, on the other hand, tend to involve the most complex cost structures due to the multitude of elements involved in the optimization process. These problems typically integrate a wide range of costs, combining transportation expenses between different facilities, the costs associated with opening and operating facilities at different levels, and penalties related to tardiness in meeting delivery deadlines [62; 63; 34]. Furthermore, network design models often have to account for the fixed and variable costs of maintaining facilities over time, as well as any logistics costs associated with managing inventory, handling products, and maintaining service levels across the network [17; 64; 110].  
In many cases, these cost components are interrelated, and the trade-offs between them must be carefully considered in the optimization process. For example, opening additional facilities may reduce transportation costs by shortening delivery routes, but it also increases fixed facility costs. As a result, papers addressing network design often present highly sophisticated cost models that balance these competing factors to find the most cost-effective solution for complex supply chain and logistics problems.