Evolutionary Multi-Objective Optimization for the Vendor-Managed Inventory Routing Problem

The class of inventory routing problems (IRPs) is present in several areas, including automotive industry and cash management for ATM networks. In the specific case of vendor-managed IRPs, in which the supplier is responsible for managing the product inventory in each client and for properly providing replenishments, the challenge is to determine which retailers should be served, the amount of product that should be delivered to each of these retailers, and which routes the distribution vehicles should follow, so that the associated costs are minimized. Although this is clearly a multi-objective optimization problem, in the literature it has been generally modeled as a single-objective problem, which limits the scope of the obtained results. Therefore, this work presents a multi-objective approach to solve one version of the IRP usually found in the scientific literature, by simultaneously minimizing both the inventory and transportation costs. The method proposed in this work is based on the well-known SPEA2 (Strength Pareto Evolutionary Algorithm) and includes innovative aspects mainly associated with the representation of candidate solutions, genetic operators and local search. The experiments were performed on a set of known benchmark IRPs from the literature, so that the obtained results could be properly compared to the best solution found for the single-objective version of each problem.