Fifty Years of Integer Programming: A Review of the Solution Approaches 

Santosh Kumar1, Monga K. Luhandjula2, Elias Munapo3 and Brian C. Jones4

1Department of Mathematics and Statistics, University of Melbourne, Parkville, Melbourne, Australia.
2&3Department of Decision Sciences, University of South Africa,  PO Box 392, UNISA 0003, Pretoria, South Africa.
4Department of Applied Mathematics, National University of Science and Technology, PO Box AC 939, Ascot, Bulawayo, Zimbabwe.

Many scientific, industrial engineering and economic problems may be cast into an integer-programming model. This paper attempts to review various approaches that have been developed for solving this model, emphasizing on the methodological view. For the sake of space, we restrict ourselves mainly to the pure integer-programming problem. The paper is expository in nature and it includes many references to give credit to essential results in the field and help readers obtain more detailed information on issues of interest.

Keywords: Integer Programmes, Cutting Plane Approaches, Corner Polyhedron, Branch and Bound, Additive Algorithms, Branch and Cut, Branch and Price, Interior Point Hybrids, Lagrange Relaxation, Random Search, Descending Hyper-Plane, Heuristics, Stochastic Integer Programs, Fuzzy Logic.