Annals of Operations Research

, Volume 21, Issue 1, pp 227–245 | Cite as

Constructing integer programming models by the predicate calculus

  • K. I. M. McKinnon
  • H. P. Williams
Article

Abstract

A modelling language for Integer Programming (IP) based on the Predicate Calculus is described. This is particularly suitable for building models with logical conditions. Using this language a model is specified in terms of predicates. This is then converted automatically by a series of transformation rules into a normal form from which an IP model can be created. There is also some discussion of alternative IP formulations which can be incorporated into the system as options. Further practical considerations are discussed briefly concerning implementation language and incorporation into practical Mathematical Programming Systems.

Keywords

Normal Form Programming Model Mathematical Program Integer Program Modelling Language 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A.L. Brearley, G. Mitra and H.P. Williams, Analysis of mathematical programming problems prior to applying the simplex algorithm, Mathematical Programming 8 (1975) 54–83.Google Scholar
  2. [2]
    W.F. Clocksin and C.S. Mellish,Programming in PROLOG (Springer-Verlag, New York, 1984).Google Scholar
  3. [3]
    R.E. Day and H.P. Williams, MAGIC: the design and use of an interactive modelling language for integer programming, IMA Journal of Mathematics in Management 1 (1986/87) 53–65.Google Scholar
  4. [4]
    A.M. Geoffrion and G.W. Graves, Multicommodity distribution system design by Benders decomposition, Management Science 20 (1974) 822–844.Google Scholar
  5. [5]
    R. Jeroslow, Representability in mixed integer programming, II: a lattice of relaxations, Georgia Institute of Technology, 1984.Google Scholar
  6. [6]
    R. Jeroslow and J.K. Lowe, Modelling with integer variables, Mathematical Programming Studies 22 (1984) 167–184.Google Scholar
  7. [7]
    R. Jeroslow and J.K. Lowe, Experimental results with the new techniques for integer programming formulation, Journal of the Operational Research Society 36 (1985) 393–403.Google Scholar
  8. [8]
    R. Jeroslow, Representability in mixed integer programming, I: characterization results, Discrete Applied Mathematics 17 (1987) 223–243.Google Scholar
  9. [9]
    M.H. Karwan et al. (eds.),Redundancy in Mathematical Programming: A State of the Art Survey (Springer Verlag, New York, 1983).Google Scholar
  10. [10]
    E. Mendelson,Introduction to Mathematical Logic (Van Nostrand, Princeton, 1964).Google Scholar
  11. [11]
    H.P. Williams, Logical problems and integer programming, Bulletin of the Institute of Mathematics and its Applications 13 (1977) 18–20.Google Scholar
  12. [12]
    H.P. Williams, Experiments in the formulation of integer programming problems, Mathematical Programming Studies 2 (1974) 180–197.Google Scholar
  13. [13]
    H.P. Williams, The reformulation of two mixed integer programming problems, Mathematical Programming 14 (1978) 325–331.Google Scholar
  14. [14]
    H.P. Williams,Model Building in Mathematical Programming (Wiley, Chichester, 1985).Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1989

Authors and Affiliations

  • K. I. M. McKinnon
    • 1
  • H. P. Williams
    • 2
  1. 1.University of EdinburghUK
  2. 2.University of SouthamptonUK

Personalised recommendations