Solution approaches for the green vehicle routing problem with time window and simultaneous pickup and delivery

The vehicle routing problem is an integrated optimization problem in which the shortest distribution route is determined for the distribution to be made from a central depot to customers located at different coordinates, with vehicles with a certain capacity. Increasing environmental awareness and constraints such as time, simultaneous pickup and delivery, route length, multiple depots, load division, fuel consumption, and carbon emissions have been added to the problem. New variants have been introduced to make the problem more suitable for real life. In this study, the green vehicle routing problem, in which environmental sensitivity is at the forefront, and the simultaneous pickup and delivery vehicle routing problems with time windows are discussed in an integrated manner. At this point, environmental factors are also considered important factors to ensure sustainability during collection and distribution demands, delivery times of orders, and distribution. Within the scope of the study, a new mixed integer nonlinear mathematical model was proposed for the green and simultaneous pickup and delivery vehicle routing problem with time window (GSPDVRP-TW), and a solution was sought with different methods by linearizing the model under certain conditions. For the solution of GSPDVRP-TW, the metaheuristic search algorithms Genetic Algorithm (GA) and Weighted Superposition Attraction Algorithm (WSA) were used, and test data were created by integrating the relevant data in the literature. As a result of the experimental studies, better results were obtained with GA in terms of solution fitness value and solution time, and WSA integrated with the or-opt heuristic gave satisfactory results close to the results obtained with GA.