using a tuning parameter to compromise computation time and shipping cost in an mdvrp

Vehicle routing in last-mile delivery plays a decisive role in the new world of people’s lifestyles. at present, a growing number of people order their needs online, and this forces companies  to employ innovative delivery logistics to reduce their last-mile shipping costs. the goal is to minimize the cost of travel that depends on the euclidean distance between customers. companies require solving vehicle routing problems (vrp) in a reasonable time. in this paper, a new approach is introduced that solves the multi-depot vehicle routing problem (mdvrp) in real-time. we propose a new method by clustering and decomposing the main problem into smaller ones using a tuning parameter α . this approach could reduce the solution time noticeably (up to 95%) while the shipping cost is still reasonable.