Abstract
In this note, we study a single-machine scheduling problem with deteriorating jobs whose processing times are an increasing function of their start times. The objective is to determine the optimal due-date and schedule simultaneously to minimize the total of due-date, earliness and tardiness penalties. We give a concise analysis of the problem and provide a polynomial time algorithm to solve the problem. Moreover, the algorithm can be easily applied to the ‘mirror’ scheduling problem in which the actual processing time of a job is a decreasing function of its starting time.
Similar content being viewed by others
References
Bachman A and Janiak A (2000). Minimizing maximum lateness under linear deterioration. Eur J Opl Res 126: 557–566.
Bachman A, Janiak A and Kovalyov MY (2002). Minimizing the total weighted completion time of deteriorating jobs. Inform Process Lett 81: 81–84.
Browne S and Yechiali U (1990). Scheduling deteriorating jobs on a single processor. Opns Res 38: 495–498.
Cheng TCE, Kang L and Ng CT (2004). Due-date assignment and single machine scheduling with deteriorating jobs. Opl Res Soc 55: 198–203.
Cheng TCE, Kang L and Ng CT (2005). Single machine due-date scheduling of jobs with decreasing start-time dependent processing times. Int Trans Opns Res 12: 355–366.
Graham RL, Lawler EL, Lenstra JK and Rinnooy Kan AHG (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann Discrete Math 5: 287–326.
Hardy GH, Littlewood JE and Polya G (1967). Inequalities. Cambridge University Press: London p. 261.
Kunnathur AS and Gupta SK (1990). Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. Eur J Opnl Res 47: 56–64.
Mosheiov G (1991). V-shaped policies for scheduling deteriorating jobs. Opns Res 39: 979–991.
Mosheiov G (1994). Scheduling jobs under simple linear deterioration. Comput Opns Res 21: 653–659.
Mosheiov G (1995). Scheduling jobs with step-deterioration: Minimizing makespan on a single- and multi-machine. Comput Indust Eng 28: 869–879.
Mosheiov G (1996). Λ-shaped policies to schedule deteriorating jobs. Opnl Res Soc 47: 1184–1191.
Panwalkar SS, Smith ML and Seidmann A (1982). Common due date assignment to minimize total penalty for the one machine scheduling problem. Opns Res 30: 391–399.
Zhao CL and Tang HY (2005). Single machine scheduling problems with deteriorating jobs. Appl Math Comput 161: 865–874.
Acknowledgements
We are grateful to two anonymous referees for their helpful comments on an earlier version of the paper. This research is supported in part by the National Science Council of Taiwan, Republic of China, under grant number NSC-94-2213-E-150-016.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kuo, WH., Yang, DL. A note on due-date assignment and single-machine scheduling with deteriorating jobs. J Oper Res Soc 59, 857–859 (2008). https://doi.org/10.1057/palgrave.jors.2602396
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1057/palgrave.jors.2602396