Abstract
This paper investigates the online scheduling problem on parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels. Hence each job and machine are labelled with the GoS levels, and each job can be processed by a particular machine only when the GoS level of the job is not less than that of the machine. The goal is to minimize the makespan. In this paper, we consider the problem with two GoS levels. It assumes that the GoS levels of the first k machines and the last m – k machines are 1 and 2, respectively, and every job has a GoS level of 1 alternatively or 2. We first prove the lower bound of the problem under consideration is at least 2. Then we discuss the performance of algorithm AW presented in [2] for the problem and show it has a tight bound of 4 – 1/m. Finally, We present an approximation algorithm with a competitive ratio of \(\frac{12+4\sqrt{2}}{7}\approx 2.522\).
Research supported by National Natural Science Foundation of China (10271110)and Natural Science Foundation of Zhejiang Province (Y605316).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hwang, H., Chang, S., Lee, K.: Parallel machine scheduling under a grade of service provision. Computer & Operations Research 31, 2055–2061 (2004)
Azar, Y., Naor, J., Rom, R.: The competitiveness of on-line assignments. Journal of Algorithms 18, 221–237 (1995)
Lenstra, J.K., Shmoys, D.B., Tardos, N.E.: Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming 46, 259–271 (1990)
Jiang, Y.W., He, Y., Tang, C.M.: Optimal online algorithms for scheduling on two identical machines under a grade of service. Journal of Zhejiang University SCIENCE 7(3), 309–314 (2005)
Zhou, P., He, Y., Jiang, Y.W.: Parallel machines scheduling with two GoS levels, Technical Report, Zhejiang University (2005) (in Chinese)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiang, Y. (2006). Online Scheduling on Parallel Machines with Two GoS Levels. In: Cheng, SW., Poon, C.K. (eds) Algorithmic Aspects in Information and Management. AAIM 2006. Lecture Notes in Computer Science, vol 4041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11775096_3
Download citation
DOI: https://doi.org/10.1007/11775096_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35157-3
Online ISBN: 978-3-540-35158-0
eBook Packages: Computer ScienceComputer Science (R0)