article

Scheduling a single server in a two-machine flow shop

Authors:

T. C. E. Cheng,

M. Y. KovalyovAuthors Info & Claims

Computing, Volume 70, Issue 2

Pages 167 - 180

https://doi.org/10.1007/s00607-002-1467-8

Published: 01 April 2003 Publication History

Abstract

We study the problem of scheduling a single server that processes n jobs in a two-machine flow shop environment. A machine dependent setup time is needed whenever the server switches from one machine to the other. The problem with a given job sequence is shown to be reducible to a single machine batching problem. This result enables several cases of the server scheduling problem to be solved in O(n log n) by known algorithms, namely, finding a schedule feasible with respect to a given set of deadlines, minimizing the maximum lateness and, if the job processing times are agreeable, minimizing the total completion time. Minimizing the total weighted completion time is shown to be NP-hard in the strong sense. Two pseudopolynomial dynamic programming algorithms are presented for minimizing the weighted number of late jobs. Minimizing the number of late jobs is proved to be NP-hard even if setup times are equal and there are two ditstinct due dates. This problem is solved in O(n³) time when all job processing times on the first machine are equal, and it is solved in O(n⁴) time when all processing times on the second machine are equal.

References

[1]

{1} Albers, S., Brucker, P.: The complexity of one-machine batching problems. Discrete Appl. Math. 47, 87-107 (1993).

Digital Library

[2]

{2} Allahverdi, A., Gupta, J. N. D., Aldowaisan, T.: A review of scheduling research involving setup considerations. Omega 27, 219-239 (1999).

[3]

{3} Baker, K. R.: Introduction to sequencing and scheduling. New York: Wiley 1974.

[4]

{4} Blazewicz, J., Ecker, K., Pesch, E., Schmidt, G., Weglarz, J.: Scheduling computer and manufacturing processes. Heidelberg: Springer 1996.

[5]

{5} Brucker, P.: Scheduling algorithms. Heidelberg: Springer 1995.

[6]

{6} Brucker, P., Dhaenens-Flipo, C., Knust, S., Kravchenko, S. A., Werner, F.: Complexity results for parallel machine problems with a single server. In: Extended Abstracts of Seventh International Workshop on Project Management and Scheduling, Osnabruck, Germany, April 17-19, 2000, pp 82-84.

[7]

{7} Brucker, P., Gladky, A., Hoogeveen, J. A., Kovalyov, M. Y., Potts, C. N., Tautenhahn, T., van de Velde, S. L.: Scheduling a batching machine. Journal of Scheduling 1, 31-54 (1998).

[8]

{8} Brucker, P., Knust, S., Wang, G.: Complexity results for flow-shop problems with a single server. In: Proc. 5th Int. Conf. on Optimization: Techniques and Applications, Li, D. (ed.), 153-167 (2001).

[9]

{9} Brucker, P., Kovalyov, M. Y.: Single machine batch scheduling to minimize the weighted number of late jobs. Math. Methods Oper. Res. 43, 1-8 (1996).

[10]

{10} Cheng, T. C. E., Wang, G., Sriskandarajah, C.: One-operator-two-machine flowshop scheduling problems with setup and dismounting times. Computers Oper. Res. 26, 715-730 (1999).

Digital Library

[11]

{11} Coffman, Jr. E. G., (ed.): Computer and job-shop scheduling theory. New York: Wiley 1976.

[12]

{12} Coffman, Jr. E. G., Yannakakis, M., Magazine, M. J., Santos, C.: Batch sizing and job sequencing on a single machine. Ann. Oper. Res. 26, 135-147 (1990).

Digital Library

[13]

{13} Conway, R. W., Maxwell, W. L., Miller, L. W.: Theory of scheduling. Addison Wesley, Reading 1967.

[14]

{14} Garey, M. R., Johnson, D. S.: Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and Co., San Francisco 1979.

[15]

{15} Glass, C., Shafransky, Y. M., Strusevich, V, A.: Scheduling for parallel dedicated machines with a single server. Naval Res. Logistics 47, 304-328 (1999).

[16]

{16} Hall, N. G., Potts, C. N., Sriskandarajah, C.: Parallel machine scheduling with a common server. Discr. Appl. Math. 102, 223-243 (2000).

Digital Library

[17]

{17} Hochbaum, D. S., Landy, D.: Scheduling with batching: minimizing the weighted number of tardy jobs. Oper. Res. Lett. 16, 79-86 (1994).

Digital Library

[18]

{18} Kravchenko, S. A., Werner, F.: Parallel machine scheduling problems with a single server. Math. Comp. Modelling 26, 1-11 (1997).

Digital Library

[19]

{19} Koulamas, C. P.: Scheduling on two parallel machines for minimizing machine interference. Working paper. Department of Decision Sciences and Information Systems. Florida International University 1993.

[20]

{20} Kovalyov, M. Y.: A rounding technique to construct approximation algorithms for knapsack and partition type problems. Appl. Math. Comp. Sci. 6, 101-113 (1996).

[21]

{21} Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., Shmoys, D. B.: Sequencing and scheduling: algorithms and complexity. In: Logistics of Production and Inventory, Handbooks in Operations Research and Management Science, Graves, S. C., Zipkin, P. H., Rinnooy Kan, A. H. G. (eds.), vol. 4, North-Holland, Amsterdam, 445-522 (1993).

[22]

{22} Moore, J. M.: An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 15, 102-109 (1968).

[23]

{23} Pinedo, M., Chao, X.: Operation scheduling with applications in manufacturing and services. New York: Irwin/McGraw-Hill, 1999.

[24]

{24} Potts, C. N., Kovalyov, M. Y.: Scheduling with batching: a review. Eur. J. Oper. Res. 120, 228-249 (2000).

[25]

{25} 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).

[26]

{26} Sahni, S.: General techniques for combinatorial approximation. Oper. Res. 25, 920-936 (1977).

Digital Library

[27]

{27} Tanaev, V. S., Gordon, V. S., Shafransky, Y. M.: Scheduling theory. Single-stage systems. Kluwer Academic Publishers, Dordrecht Boston/London 1994.

[28]

{28} Webster, S. T., Baker, K. R.: Scheduling groups of jobs on a single machine. Oper. Res. 43, 692-703 (1995).

Digital Library

[29]

{29} Wagelmans, A. P. M., Gerodimos, A. E.: Improved dynamic programs for some batching problems involving the maximum lateness criterion. Oper. Res. Lett. 27, 109-118 (2000).

Digital Library

Cited By

Yang DXie ZLiu QYu X(2023)A signal-driven based flexible integrated scheduling algorithm with bidirectional coordination mechanismMultimedia Tools and Applications10.1007/s11042-023-14544-582:22(34029-34051)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1007/s11042-023-14544-5
Zhang AWang HChen YChen G(2016)Scheduling jobs with equal processing times and a single server on parallel identical machinesDiscrete Applied Mathematics10.1016/j.dam.2016.05.014213:C(196-206)Online publication date: 20-Nov-2016
https://dl.acm.org/doi/10.1016/j.dam.2016.05.014
Jiang YZhang QHu JDong JJi M(2015)Single-server parallel-machine scheduling with loading and unloading timesJournal of Combinatorial Optimization10.1007/s10878-014-9727-z30:2(201-213)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1007/s10878-014-9727-z

Index Terms

Scheduling a single server in a two-machine flow shop

Recommendations

Batching and scheduling in a multi-machine flow shop

We study the problem of batching and scheduling n jobs in a flow shop comprising m , m 2, machines. Each job has to be processed on machines 1, , m in this order. Batches are formed on each machine. A machine dependent setup time precedes the ...
Single machine batch scheduling problem with family setup times and release dates to minimize makespan

In this paper we consider the single machine batch scheduling problem with family setup times and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an $$O(n (\frac{n}{m}+1)^m)$$ time dynamic programming algorithm and an $$O(mk^{k}P^{2k-1})$$ time dynamic ...
Single machine batch scheduling with deadlines and resource dependent processing times

We consider the problem of scheduling n jobs on a single machine where each job has a deadline and a processing time that is a linear decreasing function of the amount of a common discrete resource allocated to the job. Jobs may be combined to form ...

Comments

Information & Contributors

Information

Published In

cover image Computing

Computing Volume 70, Issue 2

April 2003

91 pages

ISSN:0010-485X

Issue’s Table of Contents

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 April 2003

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Yang DXie ZLiu QYu X(2023)A signal-driven based flexible integrated scheduling algorithm with bidirectional coordination mechanismMultimedia Tools and Applications10.1007/s11042-023-14544-582:22(34029-34051)Online publication date: 1-Sep-2023
https://dl.acm.org/doi/10.1007/s11042-023-14544-5
Zhang AWang HChen YChen G(2016)Scheduling jobs with equal processing times and a single server on parallel identical machinesDiscrete Applied Mathematics10.1016/j.dam.2016.05.014213:C(196-206)Online publication date: 20-Nov-2016
https://dl.acm.org/doi/10.1016/j.dam.2016.05.014
Jiang YZhang QHu JDong JJi M(2015)Single-server parallel-machine scheduling with loading and unloading timesJournal of Combinatorial Optimization10.1007/s10878-014-9727-z30:2(201-213)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1007/s10878-014-9727-z

View Options

View options

Figures

Tables

Media

View Issue’s Table of Contents