Single machine hierarchical scheduling with customer orders and multiple job classes

In this paper, we consider single machine bi-criteria scheduling problems where jobs are from multiple job classes and there are customer orders such that each customer order consists of at least one job from each of the job classes. A set-up time is needed whenever the machine is changed over from a job in one class to a job in another class. One objective is to minimize the makespan which is equivalent to minimizing the total set-up time. The other objective is to minimize total carrying costs of the customer orders. The carrying cost of a customer order is measured by the length of the time interval between the completion times of the first job and the last job in the customer order. We propose constructive polynomial time algorithms for the two hierarchical scheduling problems with these two objectives, i.e. the two scheduling problems in which one objective is to be optimized while holding the other objective fixed at its optimal value.