article

The Single Machine Early/Tardy Problem

Authors:

Thomas E. MortonAuthors Info & Claims

Management Science, Volume 35, Issue 2

Pages 177 - 191

https://doi.org/10.1287/mnsc.35.2.177

Published: 01 February 1989 Publication History

Abstract

We examine the problem of scheduling a given set of jobs on a single machine to minimize total early and tardy costs. Two dispatch priority rules are proposed and tested for this NP-complete problem. These were found to perform far better than known heuristics that ignored early costs. For situations where the potential cost savings are sufficiently high to justify more sophisticated techniques, we propose a variation of the Beam Search method developed by researchers in artificial intelligence. This variant, called Filtered Beam Search, is able to use priority functions to search a number of solution paths in parallel. A computational study showed that this search method was not only efficient but also consistent in providing near-optimal solutions with a relatively small search tree. The study also includes an investigation of the impacts of Beam Search parameters on three variations of Beam Search for this problem.

References

[1]

BAKER, K. R., Introduction to Sequencing and Scheduling. John Wiley and Sons, New York, 1974.

[2]

BAKER, K. R. AND J. B. MARTIN, "An Experimental Comparison of Solution Algorithms for the Single-Machine Tardiness Problem," Naval Res. Logist. Quart., 21, 1 (January 1974), 187-199.

[3]

BARR, A. AND E. A. FEIGENBAUM, The Handbook of Artificial Intelligence. Vol. 1, Heuris Tech Press, Stanford, CA, 1981.

[4]

CONWAY, R. W., W. L. MAXWELL AND L. W. MILLER, Theory of Scheduling, Addison-Wesley, Reading, MA, 1967.

[5]

EMMONS, HAMILTON, "One-Machine Sequencing to Minimize Certain Functions of Job Tardiness," Oper. Res., 17 (1969), 701-715.

Digital Library

[6]

Fox, M. S., "Constraint-Directed Search: A Case Study of Job-Shop Scheduling," Ph.D. Dissertation, Carnegie-Mellon University, 1983.

[7]

KANET, J. K., "Minimizing the Average Deviation of Job Completion Times About a Common Duedate," Naval Res. Logist. Quart., 28, 4 (1981), 643-651.

[8]

KARP, R. M., "Reducibility among Combinatorial Problems," In Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, (Eds.), Plenum Press, New York, 1972, 83-103.

[9]

LAKSHMINARAYAN, SANKARAN, RAM LAKSHMANAN, ROBERT L. PAPINEAU AND RENE ROCHETTE, "Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties," Oper. Res., 26, 6 (November-December 1978), 1079-1082.

Digital Library

[10]

LAWLER, E. L., "A "Pseudopolynomial" Algorithm for Sequencing Jobs to Minimize Total Tardiness," Ann. Discrete Math., 1 (1977), 331-342.

[11]

LAWLER, E. L. AND D. E. WOODS, "Branch-and-Bound Methods: A Survey," Oper. Res., 14, 4 (July-August 1966), 699-719.

Digital Library

[12]

LOWERRE, B. T., "The HARPY Speech Recognition System," Ph.D. Dissertation, Carnegie-Mellon University, April 1976.

[13]

MONTAGNE, E. R., JR., "Sequencing with Time Delay Costs," Arizona State University, Industrial Eng., January 1969.

[14]

MORTON, T. E., R. M. RACHAMADUGU AND A. VEPSALEINEN, "Accurate Myopic Heuristics for Tardiness Scheduling," Working Paper W.P. 36-83-84, Carnegie-Mellon University, February 1984.

[15]

NILSSON, NILS J., Principles of Artificial Intelligence, Tioga Publishing, Palo Alto, CA, 1980.

[16]

Ow, PENG SI, "Heuristic Knowledge and Search for Scheduling," Ph.D. Dissertation, Graduate School of Industrial Administration, Carnegie-Mellon University, 1984.

[17]

Ow, PENG SI AND STEPHEN F. SMITH, "Viewing Scheduling as an Opportunistic Problem-Solving Process," To appear in Annals of Operations Research, Intelligent Approaches to Decision Support, R. Jeroslow, (Ed.).

[18]

PANWALKAR, S. S., M. L. SMITH AND A. SEIDMANN, "Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem," Oper. Res., 30, 2 (March-April 1982), 391-399.

Digital Library

[19]

RUBIN, S., "The ARGOS Image Understanding System," Ph.D. Dissertation, Carnegie-Mellon University, April 1978.

[20]

SEIDMANN, A., S. S. PANWALKER AND M. L. SMITH, "Optimal Assignment of Due-Dates for a Single Processor Scheduling Problem," Internal. Production Res., 19, 4 (May 1981), 393-399.

[21]

SIDNEY, JEFFREY, "Optimal Single-Machine Scheduling with Earliness and Tardiness Penalties," Oper. Res., 25, I (January-February 1977), 62-69.

[22]

SRINIVASAN, V., "A Hybrid Algorithm for the One Machine Sequencing Problem to Minimize Total Tardiness," Naval Res. Logist. Quart., 18 (September 1971), 317-327.

[23]

SUNDARARAGHAVAN, P. S. AND M. U. AHMED, "Minimizing the Sum of Absolute Lateness in Single-Machine and Multimachine Scheduling," Naval Res. Logist. Quart., 31, 2 (1984), 325-333.

[24]

WILKERSON, L. J. AND J. D. IRWIN, "An Improved Method for Scheduling Independent Tasks," AIIE Trans., 3, 5 (September 1971), 239-245.

Cited By

Hudaifah HAndriansyah AAl-Shareef KDarghouth MSaleh H(2024)Genetic algorithm with normal boundary intersection for multi-objective early/tardy scheduling problem with carbon-emission consideration: a Pareto-optimum solutionNeural Computing and Applications10.1007/s00521-023-09146-z36:5(2493-2506)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s00521-023-09146-z
Hooker J(2019)Improved Job Sequencing Bounds from Decision DiagramsPrinciples and Practice of Constraint Programming10.1007/978-3-030-30048-7_16(268-283)Online publication date: 30-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-30048-7_16
Jiang XXu YZhou CChew ELee L(2018)Frame Trolley Dispatching Algorithm for the Frame Bridge Based Automated Container TerminalTransportation Science10.1287/trsc.2017.081552:3(722-737)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1287/trsc.2017.0815
Show More Cited By

Index Terms

The Single Machine Early/Tardy Problem
1. Computing methodologies
  1. Artificial intelligence
    1. Search methodologies
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Scheduling algorithms
    2. Online algorithms
      1. Online learning algorithms
        Scheduling algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

Recommendations

Stochastic Single Machine Scheduling with Quadratic Early-Tardy Penalties

<P>We address the problem of scheduling n jobs on a single machine, which is subject to random breakdowns, to minimize an expected sum of nonregular penalty functions. A simple recourse model is considered when the penalty function is the squared ...
Scheduling with Multiple Performance Measures: The One-Machine Case

<P>Most scheduling research has considered optimizing a single performance measure (criterion). In this paper we consider the problem of scheduling jobs on a single machine when the desirability of a schedule is evaluated using more than one performance ...
Scheduling with Multiple Performance Measures: The One-Machine Case

Most scheduling research has considered optimizing a single performance measure criterion. In this paper we consider the problem of scheduling jobs on a single machine when the desirability of a schedule is evaluated using more than one performance ...

Comments

Information & Contributors

Information

Published In

cover image Management Science

Management Science Volume 35, Issue 2

February 1989

131 pages

ISSN:0025-1909

Issue’s Table of Contents

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 February 1989

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

38
Total Citations
View Citations
0
Total Downloads

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

Reflects downloads up to 26 Jul 2024

Other Metrics

View Author Metrics

Citations

Cited By

Hudaifah HAndriansyah AAl-Shareef KDarghouth MSaleh H(2024)Genetic algorithm with normal boundary intersection for multi-objective early/tardy scheduling problem with carbon-emission consideration: a Pareto-optimum solutionNeural Computing and Applications10.1007/s00521-023-09146-z36:5(2493-2506)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s00521-023-09146-z
Hooker J(2019)Improved Job Sequencing Bounds from Decision DiagramsPrinciples and Practice of Constraint Programming10.1007/978-3-030-30048-7_16(268-283)Online publication date: 30-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-30048-7_16
Jiang XXu YZhou CChew ELee L(2018)Frame Trolley Dispatching Algorithm for the Frame Bridge Based Automated Container TerminalTransportation Science10.1287/trsc.2017.081552:3(722-737)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1287/trsc.2017.0815
Yuce BFruggiero FPackianather MPham DMastrocinque ELambiase AFera M(2017)Hybrid Genetic Bees Algorithm applied to single machine scheduling with earliness and tardiness penaltiesComputers and Industrial Engineering10.1016/j.cie.2017.07.018113:C(842-858)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.cie.2017.07.018
Gonçalves TValente JSchaller J(2016)Metaheuristics for the single machine weighted quadratic tardiness scheduling problemComputers and Operations Research10.1016/j.cor.2016.01.00470:C(115-126)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1016/j.cor.2016.01.004
Vilí MPereira J(2013)Exact and heuristic procedures for single machine scheduling with quadratic earliness and tardiness penaltiesComputers and Operations Research10.1016/j.cor.2013.01.01940:7(1819-1828)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1016/j.cor.2013.01.019
Rebai MKacem IAdjallah K(2012)Earliness---tardiness minimization on a single machine to schedule preventive maintenance tasksJournal of Intelligent Manufacturing10.1007/s10845-010-0425-023:4(1207-1224)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1007/s10845-010-0425-0
Chen SChen MChang PZhang QChen Y(2010)Guidelines for developing effective Estimation of Distribution Algorithms in solving single machine scheduling problemsExpert Systems with Applications: An International Journal10.1016/j.eswa.2010.02.07337:9(6441-6451)Online publication date: 1-Sep-2010
https://dl.acm.org/doi/10.1016/j.eswa.2010.02.073
Sharaf MChrysanthis PLabrinidis AAmza CÇetintemel UZdonik SKossmann D(2009)Optimizing i/o-intensive transactions in highly interactive applicationsProceedings of the 2009 ACM SIGMOD International Conference on Management of data10.1145/1559845.1559927(785-798)Online publication date: 29-Jun-2009
https://dl.acm.org/doi/10.1145/1559845.1559927
Chen SChang PChan CMani V(2009)A Hybrid Electromagnetism-Like Algorithm for Single Machine Scheduling ProblemProceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence10.1007/978-3-540-74205-0_59(543-552)Online publication date: 17-Nov-2009
https://dl.acm.org/doi/10.1007/978-3-540-74205-0_59
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents