The relief logistics and humanitarian supply chain in academic literature refer to the process of planning‎, ‎execution‎, ‎and effective controlling of the flow of costs and information and storage of necessary goods and materials from the point of origin to consumption with the primary purpose of reducing and relieving the affected people suffer. This paper discusses a multi-objective model for multi-period location-distribution-routing problems considering the evacuation of casualties and homeless people and fuzzy paths in relief logistics‎. ‎Firstly‎, ‎an uncertain multi-objective model of the problem was developed based on uncertain parameters of demand‎, ‎time‎, ‎and transport capacity‎, ‎and then‎, ‎using the fuzzy programming method‎, ‎uncertain parameters of the problem were controlled‎. ‎As the problem is NP-hard and GAMS software has not able to solve the model in larger sizes‎, meta-heuristic algorithms of NSGA-II and MOPSO were used to solve the problem.