7. Integer Programming: Logical Constraints

  1. Kenneth R. Baker

Published Online: 7 MAR 2011

DOI: 10.1002/9780470949108.ch7

Optimization Modeling with Spreadsheets, Second Edition

Optimization Modeling with Spreadsheets, Second Edition

How to Cite

Baker, K. R. (2011) Integer Programming: Logical Constraints, in Optimization Modeling with Spreadsheets, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470949108.ch7

Author Information

  1. Tuck School of Business, Dartmouth College, Hanover, NH, USA

Publication History

  1. Published Online: 7 MAR 2011
  2. Published Print: 4 APR 2011

ISBN Information

Print ISBN: 9780470928639

Online ISBN: 9780470949108



  • binary variables;
  • integer programming;
  • linear objective functions;
  • logical constraints;
  • transportation problem;
  • traveling salesperson problem (TSP)


This chapter expands the use of binary variables in connection with relationships that are called as logical constraints; the constraints restrict consideration to certain combinations of variables. Linear objective functions assume strict proportionality: In particular, the cost incurred by an activity is proportional to the activity level. The integer programming model itself represents a variation on the incorporation of fixed costs and the use of linking constraints. The facility location model can be thought of as the strategic version of the transportation problem, in the sense that the warehouse or distribution center (DC) locations are treated as given in the transportation problem but as choices in the facility location problem. Applications of the traveling salesperson problem (TSP) occur frequently in manufacturing and logistics, and some very powerful solution methods, tailored to the TSP, have been developed for repeated use or for tackling especially large versions.

Controlled Vocabulary Terms

Facility location problem; integer programming; Travelling salesman problem