Design of a robust production facility layout with minimum handling cost (MHC) presents an appropriate approach to tackle facility layout problems in a dynamic volatile environment,in which product demands randomly change in each planning period.The objective of the design is to find the robust facility layout with minimum total material handling cost over the entire multiperiod planning horizon.This paper proposes a new mathematical model for designing robust machine layout in the stochastic dynamic environment of manufacturing systems using quadratic assignment problem (QAP) formulation.In this investigation,product demands are assumed to be normally distributed random variables with known expected value,variance,and covariance that randomly change from period to period.The proposed model was verified and validated using randomly generated numerical data and benchmark examples.The effect of dependent product demands and varying interest rate on the total cost function of the proposed model has also been investigated.Sensitivity analysis on the proposed model has been performed.Dynamic programming and simulated annealing optimization algorithms were used in solving the modeled example problems.