article

Single machine batch scheduling with release times and delivery costs

Authors:

Esaignani Selvarajah,

George Steiner,

Rui ZhangAuthors Info & Claims

Journal of Scheduling, Volume 16, Issue 1

Pages 69 - 79

https://doi.org/10.1007/s10951-011-0255-8

Published: 01 February 2013 Publication History

Abstract

We study single machine batch scheduling with release times. Our goal is to minimize the sum of weighted flow times (or completion times) and delivery costs. Since the problem is strongly $\mathcal{NP}$ -hard even with no delivery cost and identical weights for all jobs, an approximation algorithm is presented for the problem with identical weights. This uses the polynomial time solution we give for the preemptive version of the problem. We also present an evolutionary metaheuristic algorithm for the general case. Computational results show very small gaps between the results of the metaheuristic and the lower bound.

References

[1]

Afrati, F., Bampis, E., Chekuri, C., Karger, D., Kenyon, C., Khanna, S., Milis, I., Queyranne, M., Skutella, M., Stein, C., & Sviridenko (1999). Approximation schemes for minimizing average weighted completion time with release dates. In Proc. 40th annual symposium on foundations of computer science .

[2]

Albers, S., & Brucker, P. (1993). The complexity of one-machine batching problems. Discrete Applied Mathematics, 47 , 87-107.

Digital Library

[3]

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

[4]

Allahverdi, A., Ng, C. T., Cheng, T. C. E., & Kovalyov, M. Y. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187 , 985-1032.

[5]

Bean, J. C. (1994). Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing, 6 , 154-160.

[6]

Chekuri, C., Motwani, R., Natarajan, B., & Stein, C. (2001). Approximation techniques for average completion time scheduling. SIAM Journal on Computing, 31 , 146-166.

Digital Library

[7]

Chu, C. (1992a). Efficient heuristics to minimize total flow time with release dates. Operations Research Letters, 12 , 321-330.

Digital Library

[8]

Chu, C. (1992b). A branch-and-bound algorithm to minimize total flow time with unequal release dates. Naval Research Logistics, 39 , 859-875.

[9]

Coffman, E. G., Yannakakis, M., Magazine, M. J., & Santos, C. (1990). Batch sizing and job sequencing on a single machine. Naval Research Logistics, 26 , 135-147.

[10]

Dyer, M. E., & Wolsey, L. A. (1990). Formulating the single machine sequencing problem with release dates as a mixed integer program. Discrete Applied Mathematics, 26 , 255-270.

Digital Library

[11]

Gfeller, B., Peeters, L., Weber, B., & Widmayer, P. (2009). Single machine batch scheduling with release times. Journal of Combinatorial Optimization, 17 , 323-338.

[12]

Goemans, M. X., Wein, J. M., & Williamson, D. P. (2000). A 1.47-approximation algorithm for a preemptive single-machine scheduling problem. Operations Research Letters, 26 , 149-154.

Digital Library

[13]

Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 4 , 287-326.

[14]

Hall, N. G., & Potts, C. N. (2003). Supply chain scheduling: Batching and delivery. Operations Research, 51 , 566-584.

[15]

Hariri, A. M. A., & Potts, C. N. (1983). An algorithm for single machine sequencing with release times to minimize total weighted completion time. Discrete Applied Mathematics, 5 , 99-109.

[16]

Kellerer, H., Tautenhahn, T., & Woeginger, G. J. (1999). Approximability and nonapproximability results for minimizing total flow time on single machine. SIAM Journal on Computing, 28 , 1155- 1166.

Digital Library

[17]

Labetoulle, J., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1984). Preemptive scheduling of uniform machines subject to release dates. InW. R. Pulleyblank (Ed.), Progress in combinatorial optimization (pp. 245-261). New York: Academic Press.

[18]

Lee, I. S., & Yoon, S. H. (2010). Coordinated scheduling of production and delivery stages with stage-dependent inventory holding costs. Omega, 38 , 509-521.

[19]

Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Operations Research, 1 , 343-362.

[20]

Mazdeh, M. M., Sarhadi, M., & Hindi, K. S. (2008). A branch-and-bound algorithm for single-machine scheduling with batch delivery and job release times. Computers & Operations Research, 35 , 1099-1111.

[21]

Potts, C. N., & Kovalyov, Y. M. (2000). Scheduling with batching: a review. European Journal of Operational Research, 120 , 228- 249.

[22]

Schrage, L. (1968). A proof of the shortest remaining processing time processing discipline. Operations Research, 16 , 687-690.

[23]

Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics, 3 , 59-66.

[24]

Steiner, G., & Stephenson, P. (2000). Subset-restricted interchange for dynamic min-max scheduling problems. SIAM Journal on Discrete Mathematics, 13 , 419-435.

Digital Library

Cited By

Mahmud SChakrabortty RAbbasi ARyan M(2022)Swarm intelligent based metaheuristics for a bi-objective flexible job shop integrated supply chain scheduling problemsApplied Soft Computing10.1016/j.asoc.2022.108794121:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.asoc.2022.108794
Xu SWang J(2018)An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic AlgorithmInternational Journal of Strategic Decision Sciences10.4018/IJSDS.20180101019:1(1-17)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.4018/IJSDS.2018010101
Gharaei AJolai F(2018)A multi-agent approach to the integrated production scheduling and distribution problem in multi-factory supply chainApplied Soft Computing10.1016/j.asoc.2018.02.00265:C(577-589)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1016/j.asoc.2018.02.002
Show More Cited By

Single machine batch scheduling with release times and delivery costs
1. Computing methodologies
  1. Artificial intelligence
    1. Search methodologies
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
    2. Online algorithms
      1. Online learning algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning

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Information

Published In

cover image Journal of Scheduling

Journal of Scheduling Volume 16, Issue 1

February 2013

143 pages

ISSN:1094-6136

Issue’s Table of Contents

Copyright © Copyright © 2013 Springer Science+Business Media New York.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 February 2013

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Cited By

Mahmud SChakrabortty RAbbasi ARyan M(2022)Swarm intelligent based metaheuristics for a bi-objective flexible job shop integrated supply chain scheduling problemsApplied Soft Computing10.1016/j.asoc.2022.108794121:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.asoc.2022.108794
Xu SWang J(2018)An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic AlgorithmInternational Journal of Strategic Decision Sciences10.4018/IJSDS.20180101019:1(1-17)Online publication date: 1-Jan-2018
https://dl.acm.org/doi/10.4018/IJSDS.2018010101
Gharaei AJolai F(2018)A multi-agent approach to the integrated production scheduling and distribution problem in multi-factory supply chainApplied Soft Computing10.1016/j.asoc.2018.02.00265:C(577-589)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1016/j.asoc.2018.02.002
Fu LAloulou MArtigues C(2018)Integrated production and outbound distribution scheduling problems with job release dates and deadlinesJournal of Scheduling10.1007/s10951-017-0542-021:4(443-460)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s10951-017-0542-0
Shen JZhu Y(2016)Scheduling in a two-stage supply chain with uncertain parametersJournal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology10.3233/IFS-16209130:6(3439-3449)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.3233/IFS-162091

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