A simple heuristic for maximizing service of carousel storage

We consider a system that stores cases of items. Items are removed from storage in groups. A group consists of a certain number of items of each type. The (integer maximization) problem is to determine how many cases of each type should be stored in order to maximize the number of groups of items that can be retrieved without re-loading. We give a simple heuristic that yields a feasible solution whose error can be bounded. Our method takes only linear time.