zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The strong NP-hardness of the maximum lateness minimization scheduling problem with the processing-time based aging effect. (English) Zbl 1237.90096
Summary: We analyse the single machine maximum lateness minimization scheduling problem with the processing time based aging effect, where the processing time of each job is described by a non-decreasing function dependent on the sum of the normal processing times of preceded jobs. The computational complexity of this problem was not determined. However, we show it is strongly NP-hard by proving the strong NP-hardness of the single machine maximum completion time minimization problem with this aging model and job deadlines. Furthermore, we determine the boundary between polynomially solvable and NP-hard cases.
90B35Scheduling theory, deterministic
68Q25Analysis of algorithms and problem complexity
[1]Dababneh, A. J.; Swanson, N.; Shell, R. L.: Impact of added rest breaks on the productivity and well being of workers, Ergonomics 44, 164-174 (2001)
[2]Eilon, S.: On a mechanistic approach to fatigue and rest periods, Int. J. Prod. res. 3, 327-332 (1964)
[3]Mandich, N. V.: Overview of surface preparation of metals prior to finishing: part 2, Met. finish. 101, 33-58 (2003)
[4]Mcmullen, P. R.; Clark, M.; Albritton, D.; Bell, J.: A correlation and heuristic approach for obtaining production sequences requiring a minimum of tool replacements, Comput. oper. Res. 30, 443-462 (2003) · Zbl 1029.90026 · doi:10.1016/S0305-0548(01)00110-1
[5]Stanford, M.; Lister, P. M.: Investigation into the relationship between tool-wear and cutting environments when turning EN 32 steel, Ind. lubr. Tribol. 56, 114-121 (2004)
[6]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 · doi:10.1016/S0377-2217(02)00909-8
[7]Xingong, Z.; Guangle, Y.: Single-machine group scheduling problems with deteriorated and learning effect, Appl. math. Comput. 216, 1259-1266 (2010) · Zbl 1187.90147 · doi:10.1016/j.amc.2010.02.018
[8]Yang, S. -H.; Wang, J. -B.: Minimizing total weighted completion time in a two-machine flow shop scheduling under simple linear deterioration, Appl. math. Comput. 217, 4819-4826 (2011) · Zbl 1230.90104 · doi:10.1016/j.amc.2010.11.037
[9]Cheng, T. C. E.; Lee, W. -C.; Wu, C. -C.: Single-machine scheduling with deteriorating functions for job processing times, Appl. math. Model. 34, 4171-4178 (2010) · Zbl 1201.90073 · doi:10.1016/j.apm.2010.04.014
[10]Janiak, A.; Rudek, R.: Scheduling jobs under an aging effect, J. oper. Res. soc. 61, 1041-1048 (2010) · Zbl 1196.90048 · doi:10.1057/jors.2009.30
[11]Lai, P. -J.; Lee, W. -C.: Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects, Omega 39, 467-471 (2011)
[12]Yang, S. -J.; Yang, D. -L.; Cheng, T. C. E.: Single-machine due-window assignment and scheduling with job-dependent aging effects and deteriorating maintenance, Comput. oper. Res. 37, 1510-1514 (2010) · Zbl 1183.90203 · doi:10.1016/j.cor.2009.11.007
[13]Cheng, T. C. E.; Wu, W. -H.; Cheng, S. -R.; Wu, C. -C.: Two-agent scheduling with position-based deteriorating jobs and learning effects, Appl. math. Comput. 217, 8804-8824 (2011) · Zbl 1231.90182 · doi:10.1016/j.amc.2011.04.005
[14]Gawiejnowicz, S.: A note on scheduling on a single processor with speed dependent on a number of executed jobs, Inf. process. Lett. 57, 297-300 (1996) · Zbl 0875.68080 · doi:10.1016/0020-0190(96)00021-X
[15]Kuo, W. -H.; Yang, D. -L.: Minimizing the makespan in a single-machine scheduling problem with the cyclic process of an aging effect, J. oper. Res. soc. 59, 416-420 (2008) · Zbl 1145.90387 · doi:10.1057/palgrave.jors.2602363
[16]Mosheiov, G.: A note on scheduling deteriorating jobs, Math. comput. Model. 41, 883-886 (2005) · Zbl 1082.90038 · doi:10.1016/j.mcm.2004.09.004
[17]Yang, S. -J.: Single-machine scheduling problems with both start-time dependent learning and position dependent aging effects under deteriorating maintenance consideration, Appl. math. Comput. 217, 3321-3329 (2010) · Zbl 1202.90149 · doi:10.1016/j.amc.2010.08.064
[18]Yang, S. -J.; Yang, D. -L.: Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities, Omega 38, 528-533 (2010)
[19]Zhao, C. -L.; Tang, H. -Y.: Single machine scheduling with general job-dependent aging effect and maintenance activities to minimize makespan, Appl. math. Model. 34, 837-841 (2010) · Zbl 1185.90106 · doi:10.1016/j.apm.2009.07.002
[20]Gordon, V. S.; Potts, C. N.; Strusevich, V. A.; Whitehead, J. D.: Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation, J. sched. 11, 357-370 (2008) · Zbl 1168.90441 · doi:10.1007/s10951-008-0064-x
[21]Lai, P. -J.; Lee, W. -C.: Single-machine scheduling with a nonlinear deterioration function, Inf. process. Lett. 110, 455-459 (2010) · Zbl 1229.90062
[22]Lai, P. -J.; Lee, W. -C.; Chen, H. -H.: Scheduling with deteriorating jobs and past-sequence-dependent setup times, Int. J. Adv. manuf. Technol. 54, 737-741 (2011)
[23]Wang, J. -B.; Wang, L. -Y.; Wang, D.; Wang, X. -Y.: Single-machine scheduling with a time-dependent deterioration, Int. J. Adv. manuf. Technol. 43, 805-809 (2009)
[24]Kuo, W. -H.; Yang, D. -L.: Single-machine group scheduling with a time-dependent learning effect, Comput. oper. Res. 33, 2099-2112 (2006) · Zbl 1086.90025 · doi:10.1016/j.cor.2004.11.024
[25]Sun, L.: Single-machine scheduling problems with deteriorating jobs and learning effects, Comput. ind. Eng. 57, 843-846 (2009)
[26]Huang, X.; Wang, J. -B.; Wang, L. -Y.; Gao, W. -J.; Wang, X. -R.: Single machine scheduling with time-dependent deterioration and exponential learning effect, Comput. ind. Eng. 58, 58-63 (2010)
[27]Lee, W. -C.; Wu, C. -C.; Liu, H. -C.: A note on single-machine makespan problem with general deteriorating function, Int. J. Adv. manuf. Technol. 40, 1053-1056 (2009)
[28]Wang, J. -B.; Wang, L. -Y.; Wang, D.; Huang, X.; Wang, X. -R.: A note on single-machine total completion time problem with general deteriorating function, Int. J. Adv. manuf. Technol. 44, 1213-1218 (2009)
[29]Lee, W. -C.; Lai, P. -J.: Scheduling problems with general effects of deterioration and learning, Inf. sci. 181, 1164-1170 (2011) · Zbl 1208.90072 · doi:10.1016/j.ins.2010.11.026
[30]Lee, W. -C.; Lai, P. -J.; Wu, C. -C.: Some single-machine and flowshop scheduling problems with a non-linear deterioration function, Comput. math. Appl. 62, 2487-2496 (2011) · Zbl 1231.90205 · doi:10.1016/j.camwa.2011.07.037
[31]R. Rudek, Some single-machine scheduling problems with the extended sum-of-processing-time based aging effect, Int. J. Adv. Manuf. Technol., doi:10.1007/s00170-011-3481-5 (in press).
[32]Yang, S. -J.; Yang, D. -L.: Minimizing the total completion time in single-machine scheduling with aging/deteriorating effects and deteriorating maintenance activities, Comput. math. Appl. 60, 2161-2169 (2010) · Zbl 1205.90141 · doi:10.1016/j.camwa.2010.08.003
[33]R. Rudek, Minimising maximum lateness in a single machine scheduling problem with processing time based aging effects, Eur. J. Ind. Eng., in press.
[34]Graham, R. L.; Lawler, E. L.; Lenstra, J. K.; Kan, A. H. G. Rinnooy: Optimization and approximation in deterministic sequencing and scheduling: a survey, Ann. discrete math. 5, 287-326 (1979) · Zbl 0411.90044
[35]Garey, M. R.; Johnson, D. S.: Computers and intractability: A guide to the theory of NP-completeness, (1979)
[36]Yang, S. -J.; Yang, D. -L.: Single-machine scheduling problems with aging/deteriorating effect under an optional maintenance activity consideration, Infor 48, 171-179 (2010)
[37]S.-J. Yang, C.-J. Hsu, D.-L. Yang, Single-machine scheduling and slack due-date assignment with aging effect and deteriorating maintenance, Optim. Lett., in press, doi:10.1007/s11590-011-0382-3.