@article { author = {Arab, R and Ghaderi, S.F and Tavakkoli-Moghaddam, R}, title = {Solving a New Multi-objective Inventory-Routing Problem by a Non-dominated Sorting Genetic Algorithm}, journal = {International Journal of Engineering}, volume = {31}, number = {4}, pages = {588-596}, year = {2018}, publisher = {Materials and Energy Research Center}, issn = {1025-2495}, eissn = {1735-9244}, doi = {}, abstract = {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 ε-constraint method is used for solving problems. The ε-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.}, keywords = {Inventory,Routing problem,multi,objective optimization,ε,constraint Method,Non,dominated sorting genetic algorithm}, url = {https://www.ije.ir/article_73156.html}, eprint = {https://www.ije.ir/article_73156_7124f4427ba5213028bedc5bb91ee999.pdf} }