Online Scheduling on a Single Machine with Grouped Processing Times

Abstract EN

We consider the online scheduling problem on a single machine with the assumption that all jobs have their processing times in [ p , ( 1 + α ) p ] , where p > 0 and α = ( 5 - 1 ) / 2 .

All jobs arrive over time, and each job and its processing time become known at its arrival time.

The jobs should be first processed on a single machine and then delivered by a vehicle to some customer.

When the capacity of the vehicle is infinite, we provide an online algorithm with the best competitive ratio of ( 5 + 1 ) / 2 .

When the capacity of the vehicle is finite, that is, the vehicle can deliver at most c jobs at a time, we provide another best possible online algorithm with the competitive ratio of ( 5 + 1 ) / 2 .