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Mathematical Problems in Engineering
Volume 2012, Article ID 275239, 9 pages
Research Article

Single-Machine Group Scheduling Problems with Deterioration to Minimize the Sum of Completion Times

Yong He1 and Li Sun1,2

1School of Economics and Management, Southeast University, Nanjing 210096, China
2Foundation Department, Huaiyin Advanced Vocational and Technical Health School, Huaian 223300, China

Received 14 August 2012; Accepted 11 November 2012

Academic Editor: Gradimir Milovanovic

Copyright © 2012 Yong He and Li Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider two single-machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum of completion times minimization problems remains polynomially solvable under the agreeable conditions.