Skip to main content

Abstract

In this chapter we provide the reader with basic notions used throughout the book. After a short introduction into sets and relations, decision problems, optimization problems and the encoding of problem instances are discussed. The way algorithms will be represented, and problem membership of complexity classes are other issues that are essential because algorithms for scheduling problems and their properties will be discussed from the complexity point of view. Afterwards graphs, especially certain types such as precedence graphs and networks that are important for scheduling problems, are presented. The last two sections deal with algorithmic methods used in scheduling such as enumerative algorithms (e. g. dynamic programming and branch and bound) and heuristic approaches (e. g. tabu search, simulated annealing, ejection chains, and genetic algorithms).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Agin, Optimum seeking with branch and bound, Management Sci. 13, 1966, B176–185.

    Article  Google Scholar 

  2. E. J. Anderson, C. A. Glass, C. N. Potts, Local search in combinatorial optimization: applications in machine scheduling, Working paper, University of Southampton, 1995.

    Google Scholar 

  3. A. V. Aho, J. E. Hopcroft, J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.

    Google Scholar 

  4. E. H. L. Aarts, J. Korst, Simulated Annealing and Boltzmann Machines, J. Wiley, Chichester, 1989.

    Google Scholar 

  5. R. K. Ahuja, T. L. Magnanti, J. B. Orlin, Network Flows, Prentice Hall, Englewood Cliffs, N.J., 1993

    Google Scholar 

  6. K. Baker, Introduction to Sequencing and Scheduling, J. Wiley, New York, 1974.

    Google Scholar 

  7. R. Bellman, S. E. Dreyfus, Applied Dynamic Programming, Princeton University Press, Princeton, N.J., 1962.

    Google Scholar 

  8. R. Bellman, Dynamic Programming, Princeton University Press, Princeton, N.J., 1957.

    Google Scholar 

  9. C. Berge, Theory of Graphs and its Applications, Methuen, London, 1962.

    Google Scholar 

  10. C. Berge, Graphs and Hypergraphs, North Holland, Amsterdam, 1973.

    Google Scholar 

  11. N. E. Collins, R. W. Eglese, B. L. Golden, Simulated annealing — an annotated bibliography, American J. Math. Management Sci. 8, 1988, 209–307.

    Google Scholar 

  12. V. Cerny, Thermodynamical approach to the traveling salesman problem; an efficient simulation algorithm, J. Optimization Theory and Applications 45, 1985, 41–51.

    Article  Google Scholar 

  13. B. V. Cherkasskij, Algoritm postrojenija maksimalnogo potoka w sieti so sloznostju O(V2E1/2) operacij, Matematiczeskije Metody Reszenija Ekonomiczeskich Problem 7, 1977, 117–125.

    Google Scholar 

  14. T.-Y. Cheung, Computational comparison of eight methods for the maximum network flow problem, ACM Trans. Math. Software 6, 1980, 1–16.

    Article  Google Scholar 

  15. M. Chams, A. Hertz, D. de Werra, Some experiments with simulated annealing for colouring graphs, European J. Oper. Res. 32, 1987, 260–266.

    Article  Google Scholar 

  16. Y. Crama, A. Kolen, E. Pesch, Local search in combinatorial optimization, Lecture Notes in Computer Science 931, 1995, 157–174.

    Article  Google Scholar 

  17. E. G. Coffman Jr. (ed.), Scheduling in Computer and Job Shop Systems, J. Wiley, New York, 1976.

    Google Scholar 

  18. S. A. Cook, The complexity of theorem proving procedures, Proc. 3rd ACM Symposium on Theory of Computing, 1971, 151–158.

    Google Scholar 

  19. E. V. Denardo, Dynamic Programming: Models and Applications, Prentice-Hall, Englewood Cliffs, N.J., 1982.

    Google Scholar 

  20. E. A. Dinic, Algoritm reszenija zadaczi o maksimalnom potokie w sieti so stepennoj ocenkoj, Dokl. Akad. Nauk SSSR 194, 1970, 1277–1280.

    Google Scholar 

  21. S. E. Dreyfus, A. M. Law, The Art and Theory of Dynamic Programming, Academic Press, New York, 1979.

    Google Scholar 

  22. U. Dorndorf, E. Pesch, Fast clustering algorithms, ORSA J. Comput. 6, 1994, 141–153.

    Article  Google Scholar 

  23. U. Dorndorf, E. Pesch, Evolution based learning in a job shop scheduling environment, Computers and Oper. Res. 22, 1995, 25–40.

    Article  Google Scholar 

  24. G. Dueck, T. Scheuer, Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing, J. Comp. Physics 90, 1990, 161–175.

    Article  Google Scholar 

  25. A. E. Eiben, E. H. L. Aarts, K. H. van Hee, Global convergence of genetic algorithms: A Markov Chain analysis, Lecture Notes in Computer Science 496, 1991, 4–9.

    Article  Google Scholar 

  26. J. Edmonds, Paths, trees and flowers, Canadian J. Math. 17, 1965, 449–467.

    Article  Google Scholar 

  27. J. Edmonds, R. M. Karp, Theoretical improvement in algorithmic efficiency for network flow problem, J. Assoc. Comput. Mach. 19, 1972, 248–264.

    Article  Google Scholar 

  28. S. Even, Graph Algorithms, Computer Science Press Inc., New York, 1979.

    Google Scholar 

  29. L. R. Ford Jr., D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, N.J., 1962.

    Google Scholar 

  30. M. R. Garey, D. S. Johnson, Strong NP-completeness results: motivation, examples, and implications, J. Assoc. Comput. Mach. 25, 1978, 499–508.

    Article  Google Scholar 

  31. M. R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco, 1979.

    Google Scholar 

  32. F. Glover, Heuristic for integer programming using surrogate constraints, Decision Sciences 8, 1977, 156–160.

    Article  Google Scholar 

  33. F. Glover, Future paths for integer programming and links to artificial intelligence, Computers and Oper. Res. 13, 1986, 533–549.

    Article  Google Scholar 

  34. F. Glover, Tabu-search — Part I, ORSA J. Comput. 1, 1989, 190–206.

    Article  Google Scholar 

  35. F. Glover, Tabu Search — Part II, ORSA J. Comput. 2, 1990, 4–32.

    Article  Google Scholar 

  36. F. Glover, Tabu search: a tutorial, Interfaces 20(4), 1990, 74–94.

    Article  Google Scholar 

  37. F. Glover, Multilevel tabu search and embedded search neighborhoods for the traveling salesman problem, Working paper, University of Colorado, Boulder, 1991.

    Google Scholar 

  38. F. Glover, Ejection chains, reference structures and alternating path methods for traveling salesman problems, Working paper, University of Colorado, Boulder, 1992.

    Google Scholar 

  39. F. Glover, Scatter search and star-paths: Beyond the genetic metaphor, OR Spektrum 17, 1995, 125–137.

    Article  Google Scholar 

  40. F. Glover, H. J. Greenberg, New approaches for heuristic search: A bilateral linkage with artificial intelligence, European J. Oper. Res. 13, 1989, 563–573.

    Google Scholar 

  41. F. Glover, M. Laguna, E. Taillard, D. de Werra (eds.), Tabu Search, Annals of Operations Research 41, Baltzer, Basel, 1993.

    Google Scholar 

  42. F. Glover, C. McMillan, The general employee scheduling problem: An integration of MS and AI, Computers and Oper. Res. 13, 1986, 563–573.

    Article  Google Scholar 

  43. F. Glover, E. Pesch, TSP ejection chains, Discrete Appl. Math., 1996, to appear.

    Google Scholar 

  44. GP96b F. Glover, E. Pesch, Ejection chain applications, Working paper, University of Bonn, 1996.

    Google Scholar 

  45. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, Mass., 1989.

    Google Scholar 

  46. P. Hansen, B. Jaumard, Algorithms for the maximum satisfiability problem, Computing 44, 1990, 279–303.

    Article  Google Scholar 

  47. J. H. Holland, Adaptation in Natural and Artificial Systems, The University of Michigan Press, Ann Arbor, 1975.

    Google Scholar 

  48. R. A. Howard, Dynamic Programming and Markov Processes, MIT Press, Cambridge, Mass., 1969.

    Google Scholar 

  49. A. Hertz, D. de Werra, The tabu search metaheuristic: How we use it, Ann. Math. Artif. Intell. 1, 1990, 111–121.

    Article  Google Scholar 

  50. D. S. Johnson, C. R. Aragon, L. A. McGeoch, C. Schevon, Optimization by simulated annealing: An experimental evaluation; Part I, Graph partitioning, Oper. Res. 37, 1989, 865–892.

    Article  Google Scholar 

  51. D. S. Johnson, C. R. Aragon, L. A. McGeoch, C. Schevon, Optimization by simulated annealing: An experimental evaluation; Part H, Graph coloring and number partitioning, Oper. Res. 39, 1991, 378–406.

    Article  Google Scholar 

  52. D. S. Johnson, A Catalog of Complexity Classes, in: J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Elsevier, New York, 1990, Ch.2.

    Google Scholar 

  53. D. S. Johnson, Local optimization and the traveling salesman problem, Lecture Notes in Computer Science 443, 1990, 446–461.

    Article  Google Scholar 

  54. K. de Jong, Genetic-algorithm-based learning, in: Y. Kodratoff, R. Michalski (eds.) Machine Learning, Vol. III, Morgan Kaufmann, San Mateo, 1990, 611–638.

    Google Scholar 

  55. D. S. Johnson, C. H. Papadimitriou, M. Yannakakis, How easy is local search? J. Computer System Sci. 37, 1988, 79–100.

    Article  Google Scholar 

  56. R. M. Karp, Reducibility among combinatorial problems, in: R. E. Miller, J. W. Thatcher (eds.), Complexity of Computer Computation, Plenum Press, New York, 1972, 85–104.

    Chapter  Google Scholar 

  57. A. W. Karzanov, Nachozdenije maksimalnogo potoka w sieti metodom predpotokow, Dokl. Akad. Nauk SSSR 215, 1974, 434–437.

    Google Scholar 

  58. S. Kirkpatrick, C. D. Gelatt Jr., M. P. Vecchi, Optimization by simulated annealing, Science 220, 1983, 671–680.

    Article  Google Scholar 

  59. A. Kolen, E. Pesch, Genetic local search in combinatorial optimization, Discrete Appl. Math. 48, 1994, 273–284.

    Article  Google Scholar 

  60. M. Kubale, The complexity of scheduling independent two-processor tasks on dedicated processors, Inform. Process. Lett. 24, 1987, 141–147.

    Article  Google Scholar 

  61. P. J. M. van Laarhoven, E. H. L. Aarts, Simulated Annealing: Theory and Applications, Reider, Dordrecht, 1987.

    Book  Google Scholar 

  62. E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, New York, 1976.

    Google Scholar 

  63. V. J. Leon, R. Balakrishnan, Strength and adaptability of problem-space based neigborhoods for resource constrained scheduling, OR Spektrum 17, 1995, 173–182.

    Article  Google Scholar 

  64. J. K. Lenstra, Sequencing by Enumerative Methods, Mathematical Centre Tracts 69, Amsterdam, 1977.

    Google Scholar 

  65. S. Lin, B. W. Kernighan, An effective heuristic algorithm for the traveling salesman problem, Oper. Res. 21, 1973, 498–516.

    Article  Google Scholar 

  66. J. K. Lenstra, A. H. G. Rinnooy Kan, P. Brucker, Complexity of machine scheduling problems, Ann. Discrete Math. 1, 1977, 343–362.

    Article  Google Scholar 

  67. E. L. Lawler, D. E. Wood, Branch and bound methods: a survey, Oper. Res. 14, 1966, 699–719.

    Article  Google Scholar 

  68. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, 1992.

    Google Scholar 

  69. L. G. Mitten, Branch-and-bound methods: general formulation and properties, Oper. Res. 18, 1970, 24–34.

    Article  Google Scholar 

  70. M. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, Equation of state calculations by fast computing machines, J. Chemical Physics 21, 1953, 1087–1092.

    Article  Google Scholar 

  71. I. H. Osman, J. P. Kelly, Meta-Heuristics: Theory and Applications, Kluwer, Dordrecht, 1996.

    Book  Google Scholar 

  72. C. H. Papadimitriou, Computational Complexity, Addison-Wesley, Reading, Mass., 1994.

    Google Scholar 

  73. C. H. Papadimitriou, K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, N.J., 1982.

    Google Scholar 

  74. E. Pesch, Learning in Automated Manufacturing, Physica, Heidelberg, 1994.

    Book  Google Scholar 

  75. E. Pesch, S. Voß (eds.), Applied Local Search, OR Spektrum 17, 1995.

    Google Scholar 

  76. I. Rechenberg, Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Problemata, Frommann-Holzboog, 1973.

    Google Scholar 

  77. C. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Problems, Blackwell Scientific Publishing, 1993.

    Google Scholar 

  78. A. H. G. Rinnooy Kan, Machine Scheduling Problems: Classification, Complexity and Computations, Martinus Nijhoff, The Hague, 1976.

    Google Scholar 

  79. A. H. G. Rinnooy Kan, Probabilistic analysis of approximation algorithms, Ann. Discrete Math. 31, 1987, 365–384.

    Google Scholar 

  80. C. Rego, C. Roucairol, An efficient implementation of ejection chain procedures for the vehicle routing problem, Research Report RR-94/44, PRISM Laboratory, University of Versailles, 1994.

    Google Scholar 

  81. H.-P. Schwefel, Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie, Birkhäuser, Basel, 1977.

    Google Scholar 

  82. E. A. Silver, R. V. Vidal, D. de Werra, A tutorial on heuristic methods, European J. Oper. Res. 5, 1980, 153–162.

    Article  Google Scholar 

  83. N. L. J. Ulder, E. H. L. Aarts, H.-J. Bandelt, P. J. M. van Laarhoven, E. Pesch, Genetic local search algorithms for the traveling salesman problem, Lecture Notes in Computer Science 496, 1991, 109–116.

    Article  Google Scholar 

  84. R. J. M. Vaessens, E. H. L. Aarts, J. K. Lenstra, Job shop scheduling by local search, Working paper, University of Technology, Eindhoven, 1995.

    Google Scholar 

  85. S. Voss, Intelligent Search, Springer, Berlin, 1996, to appear.

    Google Scholar 

  86. J. Valdes, R. E. Tarjan, E. L. Lawler, The recognition of series parallel digraphs, SIAM J. Comput. 11, 1982, 298–313.

    Article  Google Scholar 

  87. D. de Werra, A. Hertz, Tabu search techniques: a tutorial and an application to neural networks, OR Spektrum 11, 1989, 131–141.

    Article  Google Scholar 

  88. M. Yannakakis, The analysis of local search problems and their heuristics, Lecture Notes in Computer Science 415, 1990, 298–311.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Błażewicz, J., Ecker, K.H., Pesch, E., Schmidt, G., Węglarz, J. (1996). Basics. In: Scheduling Computer and Manufacturing Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03217-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03217-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03219-0

  • Online ISBN: 978-3-662-03217-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics