Abstract
This paper considers the two-agent scheduling problems with linear deteriorating jobs to be processed on a single machine. By a deteriorating job we mean that the processing time of the job is a function of its starting time. Two agents compete for the usage of a common single machine and each agent has his own criterion to optimize. There are four objective functions: makespan, maximum lateness, maximum cost, and total completion time. Some basic properties of two different scheduling problems to minimize the objective function for one agent with a constraint on the other agent’s objective function are proved. Based on these properties, the optimal algorithms with polynomial time are presented for two different scheduling problems, respectively.
This work is supported by NSFC (Grant No. 70425003 and Grant No. 60674084), National 863 High-Tech Research and Development Program of China through approved No.2006AA04Z174 .
This is a preview of subscription content, access via your institution.
Buying options
Preview
Unable to display preview. Download preview PDF.
References
Agnetis, A., Mirchandani, P.B., Pacciarelli, D., Pacifici, A.: Scheduling Problems with Two Competing Agents. Operations Research 52, 229–242 (2004)
Agnetis, A., Pacciarelli, D., Pacifici, A.: Multi-agent Single Machine Scheduling. Annals of Operations Research 150, 3–15 (2007)
Alidaee, B., Womer, N.K.: Scheduling with Time Dependent Processing Times: Review and Extensions. Journal of the Operational Research Society 50, 711–720 (1999)
Baker, K.R., Smith, J.C.: A multiple-criterion Model for Machine Scheduling. Journal of Scheduling 6, 7–16 (2003)
Browne, S., Yechiali, U.: Scheduling Deteriorating Jobs on a Single Processor. Operations Research 38, 495–498 (1990)
Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A Concise Survey of Scheduling with Time-Dependent Processing Times. European Journal of Operational Research 152, 1–13 (2004)
Cheng, T.C.E., Ng, C.T., Yuan, J.J.: Multi-agent Scheduling on a Single Machine to Minimize Total Weighted Number of Tardy Jobs. Theoretical Computer Science 362, 273–281 (2006)
Cheng, T.C.E., Ng, C.T., Yuan, J.J.: Multi-agent Scheduling on a Single Machine with Max-Form Criteria. European Journal of Operational Research 188, 603–609 (2008)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and Approximation in Deterministic Sequencing and Scheduling Theory: a Survey. Annals of Discrete Mathematics 5, 287–326 (1979)
Gupta, J.N.D., Gupta, S.K.: Single Facility Scheduling with Nonlinear Processing Times. Computers and Industrial Engineering 14, 387–393 (1988)
Mosheiov, G.: Scheduling Jobs under Simple Linear Deterioration. Computers and Operations Research 21, 653–659 (1994)
Ng, C.T., Cheng, T.C.E., Bachman, A., Janiak, A.: Three Scheduling Problems with Deteriorating Jobs to Minimize the Total Completion Time. Information Processing Letters 81, 327–333 (2002)
Wu, C.C., Lee, W.C.: Scheduling Linear Deteriorating Jobs to Minimize Makespan with an Availability Constraint on a Single Machien. Information Processing Letters 87, 89–93 (2003)
Yuan, J.J., Shang, W.P., Feng, Q.: A Note on the Scheduling with Two Families of Jobs. Journal of Scheduling 8, 537–542 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, P., Tang, L. (2008). Two-Agent Scheduling with Linear Deteriorating Jobs on a Single Machine. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_63
Download citation
DOI: https://doi.org/10.1007/978-3-540-69733-6_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69732-9
Online ISBN: 978-3-540-69733-6
eBook Packages: Computer ScienceComputer Science (R0)