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This paper puts forward a dynamic capacitated location-routing problem with fuzzy demands (DCLRP-FD). It is given on input a set of identical vehicles (each having a capacity, a fixed cost and availability level), a set of depots with restricted capacities and opening costs, a set of customers with fuzzy demands, and a planning horizon with multiple periods. The problem consists of determining the depots to be opened only in the first period of the planning horizon, the customers and the vehicles to be assigned to each opened depot, and performing the routes that may be changed in each time period due to fuzzy demands. A fuzzy chance-constrained programming (FCCP) model has been designed using credibility theory and a hybrid heuristic algorithm with four phases is presented in order to solve the problem. To obtain the best value of the fuzzy parameters of the model and show the influence of the availability level of vehicles on final solution, some computational experiments are carried out. The validity of the model is then evaluated in contrast with CLRP-FD's models in the literature. The results indicate that the model and the proposed algorithm are robust and could be used in real world problems.