Solving a bi-objective medicine distribution problem considering delivery to waste center using a hybrid clustering, mathematical modeling and NSGA-II approach

Proper transportation and distribution of commodities plays a pivotal role in the expenditures of supply chains. In this paper, a clustered vehicle routing problem with pick-up and delivery is studied. A fleet of distinct vehicles is concurrently responsible for distribution of medicines and collection of their wastes. Collected wastes should be sent to a waste center. To solve the problem, a bi-objective mathematical model is presented. Fairness of travelled distances among drivers and transportation expenses are two objective functions considered in the model. Since the proposed problem is NP-hard, a three-step hybrid approach is developed to solve the problem. First, K-medoids clustering algorithm allocates customers to subsets based on their coordinates. Second, a mathematical model is used for routing vehicles within each cluster. Third, NSGA-II is used to produce final result using the outcome of step 2. Extensive numerical results indicate the superiority of the proposed approach against the NSGA-II.