AbstractThe system to be controlled produces n products simultaneously in fixed proportions every time it is activated. Demands for the products in any period are components of an n dimensional vector random variable with known distribution function. Cases of excess demands backlogged and excess demands lost are considered. In the former the notion of k convexity can be generalized to guarantee relatively simple form for the optimal policy in an n decision problem. In the latter, this generalization was not successful although when there is no setup cost, a convexity argument can be used to show that the optimal policy has a simple form.