# PREEMPTIVE SCHEDULING IN A TWO-STAGE MULTIPROCESSOR FLOWSHOP WITH RESOURCE CONSTRAINTS

### Ewa Figielska

#### Abstract

A heuristic combining the column generation technique and a genetic algorithm is proposed for solving the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines and renewable resources at the first stage and a single machine at the second stage. The objective is to minimize the makespan. The lower bound on the optimal makespan is derived to be used in the performance analysis of the heuristic. The performance of the heuristic is analyzed by a computational experiment. The results show that the heuristic is able to find near-optimal solutions in reasonable computation time.

#### References

- Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., and Vance, P. (1998). Branch and price: column generation for solving huge integer problems. Oper. Res., 46:316-329.
- Brah, S. A. and Loo, L. L. (1999). Heuristics for scheduling in a flow shop with multiple processors. Europ. J. of Opernl Res., 113:113-112.
- Chen, B. (1995). Analysis of classes of heuristics for scheduling a two-stage flow shop with parallel machines at one stage. J. of Opernl Res. Soc., 46:234- 244.
- Chen, Z.-L. and Lee, C.-Y. (2002). Parallel machine scheduling with a common due window. Europ. J. of Opernl Res., 136:512-527.
- Dantzig, G. B. and Wolfe, P. (1960). Decomposition principle for linear programs. Oper. Res., 8:101-111.
- Figielska, E. (1999). Preemptive scheduling with changeovers: using column generation technique and genetic algorithm. Comp. and Ind. Engin., 37:63-66.
- Gilmore, P. C. and Gomory, R. E. (1961). A linear programming approach to the cutting-stock problem. Oper. Res., 9:849-859.
- Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley.
- Gupta, J. N. D. (1988). Two stage hybrid flowshop scheduling problem. J. of Opernl Res. Soc., 39:359-364.
- Haouari, M. and M'Hallah, R. (1997). Heuristic algorithms for the two-stage hybrid flowshop problem. Oper. Res. Let., 21:43-53.
- Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI.
- Hoogeveen, J. A., Lenstra, J. K., and Veltman, B. (1996). Preemptive scheduling in a two-stage multiprocessor flow shop is np-hard. Europ. J. of Opernl Res., 89:172-175.
- Linn, R. and Zhang, W. (1999). Hybrid flow shop scheduling: a survey. Comp. and Ind. Engin., 37:57-61.
- Oguz, C., Ercan, M. F., Cheng, T. C. E., and Fung, Y. F. (2003). Heuristic algorithms for multiprocessor task scheduling in a two-stage hybrid flow shop. Europ. J. of Opernl Res., 149:390-403.
- Ruiz, R. and Maroto, C. (2006). A genetic algorithm for hybrid flowshops with sequence dependent setup times and machine eligibility. Europ. J. of Opernl Res., 169:781-800.
- Santos, D. L., Hunsucker, J. L., and Deal, D. E. (1995). Global lower bounds for flow shop with multiple processors. Europ. J. of Opernl Res., 80:112-120.
- Slowinski, R. (1980). Two aproaches to problems of resource allocation among project activities - a comparative study. J. Opl Res. Soc., 31:711-723.
- Suresh, V. (1997). A note on scheduling of two-stage flow shop with multiple processors. Int. J. of Prod. Econ., 49:77-82.

#### Paper Citation

#### in Harvard Style

Figielska E. (2006). **PREEMPTIVE SCHEDULING IN A TWO-STAGE MULTIPROCESSOR FLOWSHOP WITH RESOURCE CONSTRAINTS** . In *Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-972-8865-59-7, pages 130-135. DOI: 10.5220/0001220101300135

#### in Bibtex Style

@conference{icinco06,

author={Ewa Figielska},

title={PREEMPTIVE SCHEDULING IN A TWO-STAGE MULTIPROCESSOR FLOWSHOP WITH RESOURCE CONSTRAINTS},

booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2006},

pages={130-135},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001220101300135},

isbn={978-972-8865-59-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - PREEMPTIVE SCHEDULING IN A TWO-STAGE MULTIPROCESSOR FLOWSHOP WITH RESOURCE CONSTRAINTS

SN - 978-972-8865-59-7

AU - Figielska E.

PY - 2006

SP - 130

EP - 135

DO - 10.5220/0001220101300135