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.