Affiliation:
1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
2. School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China
Abstract
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], wherep>0andα=(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 mostcjobs at a time, we provide another best possible online algorithm with the competitive ratio of(5+1)/2.
Funder
Jiangxi University of Finance and Economics