: The natural and unnatural disasters are one of the main barriers for sustainable development of the countries, therefore not ready to confront such events make a lot of damages and losses. So in such cases the existence of a logistic system is essential to prepare disaster relief and supplyments for the injured people. This thesis at first presents a new mathematical model for multi-depot multi-compartment vehicle routing problem seeks to minimize the total cost of traortation. Then it presents a robust multi-depot multi-compartments location-routing problem with split delivery, by improving the first mathematical model. The objective function of the second model seeks to minimize the total travel distance and risk and also minimize the fixed cost of the establishment of the depots. In this type of problem, the cargo space of each vehicle has multiple compartments, and each compartment is dedicated to a single type of product. In the proposed model, split delivery for one given product is not allowed, therefore demand of a customer for a certain product must be fully delivered by a single vehicle; however, split delivery for a set of requested products is allowed, so different products can be delivered to a customer by different vehicles. In the case of stochastic demand this thesis consider the Mulvey scenario base method. Considering the Np-Hardness of the proposed problem, a hybrid algorithm composed of adaptive large neighborhood search and variable neighborhood search is developed to solve the large scale instances. Performance of the proposed algorithm is evaluated by comparing its results with the results of exact method, adaptive large neighborhood search algorithm and variable neighborhood search algorithm. The results demonstrate the good performance of the proposed hybrid algorithm.
