Location-routing-inventory problem (LRIP) involves the decisions of three key problems in optimizing a logistics system, i.e. facility location-allocation, vehicle routing, and inventory control. In this paper, a model for the multi-period, multi-depot LRIP with stochastic customer demand in logistics distribution systems Is developed. And a mixed genetic algorithm is proposed to solve the model. Finally, the validity of the model and algorithm are demonstrated by a numerical example,