On-line scheduling with setup costs

This paper deals with an on-line scheduling problem where tasks belong to a given set of c task types and are to be assigned to one of the m machines in order to minimize the maximum completion time. If a task of a certain type is assigned to a machine that has just completed the execution of a task of the same type, then it can be processed immediately. Otherwise, there is a setup time associated with switching the machine to a different task type. A suitable version of the classical List Scheduling algorithm is analyzed. A new algorithm is also proposed and an upper bound on its competitive ratio is introduced. Finally, lower bound on the competitive ratio for any on-line algorithm is derived.