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This paper aims at proposing a novel quadratic assignment-based mathematical model for designing an optimal facility layout in each period of the stochastic dynamic facility layout problem (SDFLP). Considering routing flexibility is the main assumption of this problem so that parts can pass through multiple routes. It is also assumed that product demands are independent, normally distributed random variables with known expected value and variance changing from period to period at random. In addition, to solve the proposed model, a new hybrid meta-heuristic algorithm is developed by combining simulated annealing (SA) and the CRAFT approaches. Finally, the proposed model and the hybrid algorithm are verified and validated using design of experiment, real case study and sensitivity analysis methods as well as solving some numerical examples.The results show that the hybrid algorithm has an outstanding performance from both solution quality and computational time perspectives. Moreover, the proposed model can be used to design the layout of facilities in both of the stochastic and deterministic environments of traditional and modern manufacturing systems.