Lagrangian rRelaxation for Green Vehicle Routing Problem with Time Windows and Speed Limitations: A Case Study

As a relatively emerging topic in optimization, green routing could reduce the fixed and variable costs induced by different parts of a routing and transportation system and the costs imposed by pollution. This study proposes green transportation routing with a time window under confirmed stable conditions that consider transportation capacity restrictions, speed and time of delivery, and allocation of authorized drivers. This being the case, the goals of selecting the shortest route to goods transfer with the lowest costs caused by pollution, overdue fines, and maintenance of costs could be attained. Accordingly, the Lagrangian relaxation algorithm was employed, and the mathematical model of mixed-integer was developed to address the problem. Lagrange coefficient takes advantage of subgradient methods and closed methods. Lagrangian relaxation is applied separately to address two restrictions. The algorithm saves time by immediate problem solving than the Baron approach. These papers seek to simultaneously use complex restrictions close to actual incidents and could be more similar to natural conditions than other developed models.