APPLIED OPERATION RESEARCH
UNIT III
INTEGER PROGRAMMING AND GAME THEORY
Solution to pure and mixed integer programming problem by Branch and Bound and cutting
plane algorithms. Game Theory-Two person Zero sum games-Saddle point, Dominance Rule,
Convex Linear Combination (Averages), methods of matrices, graphical and LP solutions.
Contents
3.1 Integer Programming _____________________________________________________ 2
3.1.1 Branch and Bound algorithms _____________________________________________ 3
3.1.2 Geometry cutting plane __________________________________________________ 11
3.2 Game Theory ___________________________________________________________ 17
3.2.1 Two person Zero sum games-Saddle point __________________________________ 18
3.2.2 Dominance Rule ______________________________________________________ 20
3.2.3 Graphical solutions ____________________________________________________ 23
3.2.4 Methods of Matrices __________________________________________________ 28
3.2.5 Convex Linear Combination (Averages) ___________________________________ 30
3.2.6 LP solutions _________________________________________________________ 35
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