I'm trying to look up this problem but I don't know what it's called. The premise is this:
Given m machines and j jobs, where each job can only be assigned to machines i through j, I need to assign the jobs to machines so that I maximize busy machines at one time. I am only concerned with how they are assigned at time 0. I am not concerned with how I would schedule remaining jobs after a job is completed.
Once a job and a machine are assigned to each other, no other job or machine can act on either member.