A New Model for Green Location- Routing- Inventory Problem under Uncertainty

The most studies carried out in the logistics have had the same attitude towards inventory control components such as the optimal order quantity, order frequency and the amount of safety stock of inventory storage centers. For instance, they consider the number of inventory orders for all inventory storage centers as the same during the whole period of planning while according to customers of each distribution center, it may vary. In addition, we may determine the safety stock from different scenarios in each center. The present study offers a new model for location-routing-inventory under uncertainty with regard to environmental considerations. This model simultaneously determines the number and location of distribution centers, allocation of retailers to distribution centers and active routes and the order of visiting the retailers in each route, optimal order quantities, and optimal number of ordering times for each distribution center as well as the level of safety stock for each distribution center. Another aim of the study is minimizing the annual expected cost and the amount of carbon emissions from transport fleet during the delivery process in the entire network.
Since the proposed model is NP-hard problem, we recommend meta-heuristic approaches to obtain optimal solutions. Therefore, Non-dominated sorting genetic algorithm II (NSGA- II), multi-objective particle swarm optimization (MOPSO) and strength Pareto evolutionary algorithm II (SPEA-II) have been developed to solve the problem. Finally, we compare the performance of the proposed algorithms using standard measures. The results show the MOPSO is more efficient than both NSGA-II and SPEA-II.