Optimizing Vehicle Routing with Soft Time Windows Using a Hybrid Genetic Algorithm

Determining delivery routes thatminimize total cost is a key issue in goodsdistribution. This study focuses on a bottleddrinking water (AMDK) company in City X thatdistributes its products to multiple retail outlets withdifferent service time requirements. Such conditionsfall within the scope of the Vehicle Routing Problemwith Time Windows (VRPTW). In this study, a softtime windows approach is adopted, allowing vehiclesto serve retailers beyond their specified time limitsat the expense of penalty costs. The main objective isto identify optimal delivery routes under the softtime windows policy while minimizing total cost. Theresults demonstrate that the Hybrid GeneticAlgorithm outperforms the initial solution in termsof total cost reduction. The initial routes aregenerated using the Nearest Insertion Heuristic andsubsequently refined through mutation processeswithin the genetic algorithm framework.