Scheduling Resources for Executing a Partial Set of Jobs

In this paper, the authors consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined by its start-time and end-time; moreover, every resource has a capacity and a cost associated with it. They consider two versions of this problem. In the partial covering version, they are also given as input a number k, specifying the number of jobs that must be performed.