Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n, m and k and computes a solution with an approximation factor that can be made arbitrarily close to 3 2.
We address the problem of sequential single machine scheduling of jobs with release times, where jobs are classified into types, and the machine must be properly configured to handle jobs of a given type. The objective is to minimize the maximum flow time (time from release until completion) of any job. We consider this problem under the assumptions of sequence independent set-up times and item availability with the objective of minimizing the maximum flow time. We present an online algorithm that is O(1)-competitive, that is, always gets within a constant factor of optimal. We also show that exact offline optimization of maximum flow time is NP-hard.