APPLIED OPERATION RESEARCH
UNIT II
LINEAR PROGRAMMING EXTENSIONS
Transportation Models (Minimising and Maximising Problems) – Balanced and unbalanced
Problems – Initial Basic feasible solution by N-W Corner Rule, Least cost and Vogel’s
approximation methods. Check for optimality. Solution by MODI / Stepping Stone method.
Case of Degeneracy. Transhipment Models. Assignment Models (Minimising and
Maximising Problems) – Balanced and Unbalanced Problems. Solution by Hungarian and
Branch and Bound Algorithms. Travelling Salesman problem. Crew Assignment Models.
Contents
2.1 Transportation Models _______________________________________ 2
2.1.1 Minimising problems ________________________________________ 2
2.1.2 N-W Corner Rule ___________________________________________ 4
2.1.3 Least cost method __________________________________________ 7
2.1.4 VAM method ______________________________________________ 15
2.1.5 Check for optimality ________________________________________ 15
2.1.6 Maximising problems ________________________________________ 19
2.1.7 Transhipment models ________________________________________ 24
2.2 Assignment models _________________________________________ 28
2.2.1 Hungarian Method __________________________________________ 29
2.2.2 Crew assignment ___________________________________________ 52
2.2.3 Unbalanced ________________________________________________ 56
2.2.4 Travelling salesman _________________________________________ 61
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