A simple heuristic for maximizing service of carousel storage

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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. Scope and purpose Performance of an automated storage and retrieval system such as a carousel depends greatly upon the way it is loaded. Commonly a carousel will be loaded with cases of items that will be retrieved in groups. A group is a certain number of items of each type. For example, a group might constitute the parts needed to manufacture one instance of a product. Typically the carousel operator wants to retrieve as many groups as possible without running out of items of any type. We present a simple heuristic that prescribes how many cases of each item type should be loaded. The number of groups supplied by our solution is close to optimal. The solution is given by explicit equations, and can be computed in time linear in the number of item types.