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We present an efficient solution method -- Direct Derivative Estimation (DDE) -- for computing optimal order-up-to levels for a discrete time non-stationary inventory control model. We generalize a number of non-stationary inventory control models (which underlie larger models of supply chains) that include forecast updates. seasonality, information sharing, and exchange-rate fluctuations. This procedure is different from the existing ones in that it computes, in a recursive manner, the derivative of the cost function and not the cost function itself. It can also handle a much wider variety of fluctuations in the problem parameters. In our computational testing it was found to be considerably faster than Dynamic Programming and Infinitesimal Perturbation Analysis. [ABSTRACT FROM AUTHOR]