This paper deals with two warehouse inventory model of determining the optimal replenishment policy for non-instantaneous deteriorating items partial backlogging and stock-dependent demand. In the model, shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. We discussed four special cases, the results for the models with instantaneous or non-instantaneous deterioration rate and with or without shortages are derived. Numerical example is presented to demonstrate the developed model. [ABSTRACT FROM AUTHOR]