We present an efficient solution method - Direct Derivative Estimation (DDE
) - for computing optimal order-up-to levels for a discrete time non-statio
nary inventory control model. We generalize a number of non-stationary inve
ntory control models (which underlie larger models of supply chains) that i
nclude forecast updates, seasonality, information sharing, and exchange-rat
e 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 f
luctuations in the problem parameters. In our computational testing it was
found to be considerably faster than Dynamic Programming and Infinitesimal
Perturbation Analysis.