Two-machine open shop problem with controllable processing times

We consider a two-machine open shop problem in which the job processing times are controllable and can be compressed while incurring additional costs. We show that the problem of minimizing a linear compression cost function for a given upper bound on the makespan can be solved in O(n) time. For the bicriteria problem of minimizing the makespan and compression cost, we propose an O(nlogn) algorithm that finds all breakpoints of the efficient frontier.