The bi-objective traveling purchaser problem with deliveries

In this work we introduce a variant of the well-known Traveling Purchaser Problem in which the purchased products must be delivered to a set of customers. The objective is to minimize the total cost (purchasing plus traveling costs) and the waiting time of the customers, simultaneously, while satisfying the total demand. This problem is called the bi-objective Traveling Purchaser Problem with Deliveries. In order to approximate Pareto fronts for this problem, a relinked variable neighborhood search is proposed and tested over a large set of artificial instances. Our results show that our algorithm is highly competitive compared to the ϵ-constraint method in small instances. On the other hand, experiments carried out over large instances show that our algorithm is able to find Pareto front approximations with more points in a shorter running time for uncapacitated instances than for capacitated ones. Also, computational results show that the performance of some local searches used in our algorithm depends on the characteristics of the instances, this underlines the importance of designing a metaheuristic based on multiple local searches.