Improved algorithm for maximizing service of carousel storage

We consider a problem of maximizing the service of a carousel storage system from which items are removed in groups, where each group consists of a certain given number of items of each type. Kim (Comput. Oper. Res., forthcoming) has developed an algorithm for solving this problem with a running time of O(j2). In this article, we present an algorithm with an improved complexity of O(j log j).