Generating the best K sequences in relocation problems

There is a set J of h jobs to be processed. For every i, job Ji demands ni units of resources and returns ai units after completion. The problem is to find the best K schedules whose resource requirements are minimum along all h! ones. In this paper, the authors present some important structural properties and then propose an O(hlogh+hKlogK) time algorithm, which runs in polynomial time if K is fixed.