×

Single machine quadratic penalty function scheduling with deteriorating jobs and group technology. (English) Zbl 1201.90090

Summary: This paper considers single machine scheduling problems with group technology (GT) and deteriorating jobs. We consider the case of jobs whose processing times are a simple linear function of their starting time. The two objectives of scheduling problems are to minimize the weighted sum of squared completion times and the weighted sum of squared waiting times, respectively. We also provide polynomial time algorithms to solve these problems.

MSC:

90B35 Deterministic scheduling theory in operations research
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alidaee, B.; Womer, N. K., Scheduling with time dependent processing times: review and extensions, J. Oper. Res. Soc., 50, 711-720 (1999) · Zbl 1054.90542
[2] Cheng, T. C.E.; Ding, Q.; Lin, B. M.T., A concise survey of scheduling with time dependent processing times, Eur. J. Oper. Res., 152, 1-13 (2004) · Zbl 1030.90023
[3] Gawiejnowicz, S., Time-dependent Scheduling (2008), Springer: Springer Berlin, ISBN 978-3-540-69445-8 · Zbl 1155.90004
[4] Browne, S.; Yechiali, U., Scheduling deteriorating jobs on a single processor, Oper. Res., 38, 495-498 (1990) · Zbl 0703.90051
[5] Mosheiov, G., V-shaped policies for scheduling deteriorating jobs, Oper. Res., 39, 979-991 (1991) · Zbl 0748.90033
[6] Mosheiov, G., Scheduling jobs under simple linear deterioration, Comput. Oper. Res., 21, 653-659 (1994) · Zbl 0810.90074
[7] Sundararaghavan, P. S.; Kunnathur, A. S., Single machine scheduling with start time dependent processing times: some solvable cases, Eur. J. Oper. Res., 78, 394-403 (1994) · Zbl 0816.90088
[8] Wang, J.-B.; Xia, Z.-Q., Scheduling jobs under decreasing linear deterioration, Inform. Process. Lett., 94, 63-69 (2005) · Zbl 1182.68359
[9] Chen, Z.-L., Parallel machine scheduling with time dependent processing times, Discrete Appl. Math., 70, 81-94 (1996) · Zbl 0855.68032
[10] Hsieh, Y. C.; Bricker, D. L., Scheduling linearly deteriorating jobs on multiple machines, Comput. Ind. Eng., 32, 727-734 (1997)
[11] Mosheiov, G., Multi-machine scheduling with linear deterioration, INFOR, 36, 205-214 (1998) · Zbl 07677568
[12] Mosheiov, G., Complexity analysis of job-shop scheduling with deteriorating jobs, Discrete Appl. Math., 117, 195-209 (2002) · Zbl 1004.68031
[13] Kononov, A.; Gawiejnowicz, S., NP-hard cases in scheduling deteriorating jobs on dedicated machines, J. Oper. Res. Soc., 52, 708-717 (2001) · Zbl 1181.90120
[14] Wang, J.-B.; Xia, Z.-Q., Flow shop scheduling with deteriorating jobs under dominating machines, Omega, 34, 327-336 (2006) · Zbl 1090.90095
[15] Wang, J.-B.; Xia, Z.-Q., Flow shop scheduling problems with deteriorating jobs under dominating machines, J. Oper. Res. Soc., 57, 220-226 (2006) · Zbl 1090.90095
[16] Wang, J.-B., Flow shop scheduling problems with decreasing linear deterioration under dominant machines, Comput. Oper. Res., 34, 2043-2058 (2007) · Zbl 1193.90116
[17] Mitrofanov, S. P., Scientific Principles of Group Technology (1966), National Lending Library: National Lending Library London, UK
[18] Potts, C. N.; Van Wassenhove, L. N., Integrating scheduling with batching and lot-sizing: a review of algorithms and complexity, J. Oper. Res. Soc., 43, 395-406 (1992) · Zbl 0756.90050
[19] Ng, C. T.; Cheng, T. C.E.; Janiak, A.; Kovalyov, M. Y., Group scheduling with controllable setup and processing times: minimizing total weighted completion time, Ann. Oper. Res., 133, 147-163 (2005) · Zbl 1119.90020
[20] Wu, C.-C.; Shiau, Y.-R.; Lee, W.-C., Single machine group scheduling problems with deterioration consideration, Comput. Oper. Res., 35, 1652-1659 (2008) · Zbl 1211.90094
[21] Wu, C.-C.; Lee, W.-C., Single machine group scheduling problems with deteriorating setup times and job processing times, Int. J. Prod. Econ., 115, 128-133 (2008)
[22] Wang, J.-B.; Lin, L.; Shan, F., Single machine group scheduling problems with deteriorating jobs, Int. J. Adv. Manuf. Technol., 39, 808-812 (2008)
[23] Wang, J.-B.; Gao, W.-J.; Wang, L.-Y.; Wang, D., Single machine group scheduling with general linear deterioration to minimize the makespan, Int. J. Adv. Manuf. Technol., 43, 146-150 (2009)
[24] Graham, R. L.; Lawler, E. L.; Lenstra, J. K.; Rinnooy Kan, A. H.G., Optimization and approximation in deterministic sequencing and scheduling: a survey, Ann. Discrete Math., 5, 287-326 (1979) · Zbl 0411.90044
[25] Townsend, W., The single machine problem with quadratic penalty function of completion times: a branch-and-bound solution, Manag. Sci., 24, 530-534 (1978) · Zbl 0371.90065
[26] Szwarc, W.; Posner, M. E.; Liu, J. J., The single machine problem with a quadratic cost function of completion times, Manag. Sci., 34, 1480-1488 (1988) · Zbl 0663.90042
[27] Szwarc, W.; Mukhopadhyay, S. K., Minimizing a quadratic cost function of waiting times in single machine scheduling, J. Oper. Res. Soc., 46, 753-761 (1995) · Zbl 0833.90072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.