Solving a New Multi-objective Inventory-Routing Problem by a Non-dominated Sorting Genetic Algorithm

This paper considers a multi-period, multi-product inventory-routing problem in a two-level supply chain consisting of a distributor and a set of customers. This problem is modeled with the aim of minimizing bi-objectives, namely the total system cost (including startup, distribution and maintenance costs) and risk-based transportation. Products are delivered to customers by some heterogeneous vehicles with specific capacities through a direct delivery strategy. Additionally, storage capacities are considered limited and the shortage is assumed to be impermissible. To validate this new bi-objective model, the e-constraint method is used for solving problems. The e-constraint method is an exact method for solving multi-objective problems, which offers Pareto's solutions, such as meta-heuristic algorithms. Since problems without distribution planning are very complex to solve optimally, the problem considered in this paper also belongs to a class of NP-hard ones. Therefore, a non-dominated sorting genetic algorithm (NSGA-II) as a well-known multi-objective evolutionary algorithm is used and developed to solve a number of test problems. In this paper, 20 sample problems with the e-constraint method and NSGA-II are solved and compared in different dimensions based on Pareto's solutions and the time of resolution. Furthermore, the computational results showed the better performance of the NSGA-II.