Heuristics for minimizing the number of tardy jobs on a single machine with release time

 

 

E. O. Oyetunji^I; A. E. Oluleye^II

^IDepartment of Industrial and Production Engineering, University of Ibadan, Nigeria eoyetunji@yahoo.com
^IIDepartment of Industrial and Production Engineering, University of Ibadan, Nigeria ayodeii.oluleye@mail.ui.edu.ng

 

 

---

ABSTRACT

This paper considers the problem of minimizing the number of tardy jobs with release time on a single machine. Given that the problem has been classified as strongly NP-Hard, three heuristics (EOO, HR2, and HR3) are proposed for this problem. They are compared with a heuristic by Dauzere-Perez (selected from the literature). Randomly-generated problems ranging from 3 to 500 jobs are solved. Experimental results show that one of the proposed heuristics (EOO) outperforms other heuristics, both in terms of quality of solution (effectiveness) and speed of execution (efficiency).

---

OPSOMMING

Die navorsing behandel die ministering van voltooiingstyd van die aantal draaltake by 'n enkele werktuig. As aanvaar word dat die problem geklassifiseer word as hoofsaaklike NP-hard, word voorgestel dat die vraagstuk bestudeer word deur gebruik te maak van drie heuristiese metodes (EOO, HR2, HR3). Die metodes word vergelyk ten opsigte van vertoning met die Dauzere-Perez-metode. Toevalsgegenereerde probleme wat strek vanaf 3 tot 500 draaltake word behandel. Die eksperimentele werk lewer bewys dat die EOO-metode ander metodes die loef afsteek ten opsigte van oplossingsgoedheid en -snelheid.

---

 

 

“Full text available only in PDF format” 

 

 

REFERENCES

[1] Baptiste, P., Laurent, P. and Eric, P. 2003. A branch and bound to minimize the number of late jobs on a single machine with release time constraints, European Journal of Operational Research, 144(1), pp. 1-11.         [ Links ]

[2] Carlier, J. 1981. Probleme a une machine et algorithms polynomiaux, Questio 5.         [ Links ]

[3] Carlier, J. 1982. The one-machine sequencing problem, European Journal of Operational Research, 11(1), pp. 42-47.         [ Links ]

[4] Dauzere-Perez, S. 1995. Minimizing late jobs in the general one-machine scheduling problem, European Journal of Operational Research, 81(1), pp. 134-142.         [ Links ]

[5] Dauzere-Perez, S. and Sevaux, M. 1998. An efficient formulation for minimizing the number of late jobs in single-machine scheduling, Technical Report 98/9/Auto, Ecole des Mines de Nantes.         [ Links ]

[6] Dauzere-Perez, S. and Sevaux, M. 2003. Using lagrangean relaxation to minimize the weighted number of late jobs, Naval Research Logistics, 50, pp. 273-288.         [ Links ]

[7] Dauzere-Perez, S. and Sevaux, M. 2004. An exact method to minimize the number of tardy jobs in single machine scheduling, Journal of Scheduling, 7, pp. 405-420.         [ Links ]

[8] Edwin, C.T.C., Milhail, Y.K. and Alexander, V.T. 1996. Single machine group scheduling with two ordered criteria, Journal of Operational Research, 47, pp. 315-320.         [ Links ]

[9] French, S. 1982. Sequencing and scheduling. Ellis Horwood Limited.         [ Links ]

[10] Graham, R.L., Lawler, E.L., Lenstra, J.K. and Rinnooy Kan, A.H.G. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey, Annals of Discrete Mathematics, 5, pp. 287-326.         [ Links ]

[11] Hallah, R.M. and Bulfin, R. L. 2003. Minimizing the weighted number of tardy jobs on a single machine, European Journal of Operational Research, 145(1), pp. 45-56.         [ Links ]

[12] Hatice, Ucar and Fatih Tasgetiren, M. 2006. A particle swarm optimization algorithm for permutation flow shop sequencing problem with the number of tardy jobs criterion, IMS 2006: 5th International Symposium on intelligent manufacturing systems: Agents and virtual worlds, May 29-31, 2006, Sakarya, Turkey.         [ Links ]

[13] Kise, H., Ibaraki, T. and Mine, H. 1978. A solvable case of the one-machine scheduling problem with ready and due times, Operations Research, 26, pp. 121-126.         [ Links ]

[14] Lambrechts, O., Demeulemeester, E.L. and Herroelen, W.S. 2007. Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities, Journal of Scheduling (in press).         [ Links ]

[15] Lawler, E.L. 1990. A dynamic programming algorithm for the preemptive scheduling of a single machine to minimize the number of late jobs, Annals of Operations Research, 26, pp. 125-133.         [ Links ]

[16] Lawler, E.L. and Moore, J.M. 1969. A functional equation and its application to resource allocation and sequencing problems, Management Science, 16, pp. 77-84.         [ Links ]

[17] Moore, J.M. 1968. A n job, one machine sequencing algorithm for minimizing the number of late jobs, Management Science, 15, pp. 102-109.         [ Links ]

[18] Oluleye, A.E. and Oyetunji, E.O. 1999. Performance of some static flowshop scheduling heuristics, Directions in Mathematics, pp. 315-327.         [ Links ]

[19] Uthaisombut, P. 2000. New directions in machine scheduling. PhD thesis, Michigan State University.         [ Links ]

[20] Phojanamongkolkij, N., Grabenstetter, D. and Ghrayeb, O. 2003. Scheduling jobs to improve weighted on-time performance of a single machine, Journal of Manufacturing Systems, 22, pp. 148-156.         [ Links ]

[21] Potts. C.N. and Wassenhove, L. N. 1988. Algorithms for scheduling a single machine to minimize the weighted number of late jobs, Management Science, 34, pp. 843-858.         [ Links ]

[22] Sevaux, M. and Sorensen, K. 2004. A genetic algorithm for robust schedules in a just-in-time environment with ready times and due dates, 4OR - Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 2, pp. 129-147.         [ Links ]

[23] Sevaux, M. and Dauzere-Perez, S. 2003. Genetic algorithms to minimize the weighted number of late jobs on a single machine, European Journal of Operational Research, 151(2), pp. 296-306.         [ Links ]

[24] Sevaux, M. and Thomin, P. 2001. Heuristics and metaheuristics for parallel machine scheduling: A computational evaluation, in Proceedings of 4th Metaheuristics International Conference, MIC 2001, pp. 411-415, Porto, Portugal, 16-20 July 2001.         [ Links ]

[25] Van den Akker, J.M. and Hoogeveen, J.A. 2004. Minimizing the number of tardy jobs in cases of stochastic processing times with minimum success probabilities, Institute of Information and Computing Sciences, Utrecht University Technical Report UU-CS-2004-067.         [ Links ]