A new algorithm has been developed to calculate economic lot sizes for manufactured products. The algorithm allows for fluctuating and uncertain demand patterns which limit the effectiveness of the classical Wilson EOQ formula. In an environment of uncertain future demand, its performance is on a par with the Wagner-Whitin technique. Yet, the computations required are considerably less. For a single product the algorithm would produce results identical to the Part/Period formula of IBM. However, a new derivation is provided which parallels the derivation of the Silver and Meal formula. A new dimension is added when the algorithm is extended to the situation where there are limits on the combined production rate of all products. The algorithm prevents production from exceeding the limit. It therefore allows lot sizing to be implemented gradually, and it continues to protect the production line against sudden increases in demand after implementation. Finally, the dynamic lot sizing algorithm with capacity constraints is compatible with techniques which may be required to provide additional production smoothing.