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Operation research unit 3 Transportation problem

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Dr. L K Bhagi
Dr. L K Bhagi

Formulation of Transportation Problem, Initial Feasible Solution Methods, Degeneracy in Transport Problem and Optimality Test (Modi Method and stepping stone Method)

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OPERATION RESEARCH UNIT – III (Transportation and Assignment) Dr. Loveleen Kumar Bhagi Associate Professor School of Mechanical Engineering LPU Formulation of Transportation Problem, Initial Feasible Solution Methods, Optimality Test, Degeneracy in TP, Assignment Problem, Hungerian Method,Traveling Salesman Problem Commodities areTRANSPORTED while peopleTRAVEL
Transportation Model The transportation model deals with a special class of linear programming problem in which the objective is to transport a homogeneous commodity from various origins or factories or supply centers to different destinations or markets or demand centers at a total minimum cost. Dr. L K Bhagi, School of Mechanical Engineering, LPU 2
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 3
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 4
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 5
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 6
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 7
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 8
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 9
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 10
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 11
Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 12
Dr. L K Bhagi, School of Mechanical Engineering, LPU 13
Dr. L K Bhagi, School of Mechanical Engineering, LPU 14
Dr. L K Bhagi, School of Mechanical Engineering, LPU 15
Dr. L K Bhagi, School of Mechanical Engineering, LPU 16
Dr. L K Bhagi, School of Mechanical Engineering, LPU 17
Vogel’s Approximation Method (VAM) Dr. L K Bhagi, School of Mechanical Engineering, LPU 18
Dr. L K Bhagi, School of Mechanical Engineering, LPU 19 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2 6 1 10 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 20 VAM Destinations/Demand Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2 6 1 10 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 21 VAM Destinations/Demand Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2/1 6 1/0 10 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 22 VAM Destinations/Demand Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2/1 6 1/0 10 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 23 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2/1 6 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 24 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5/0 3 2/1 6/1 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 25 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5/0 3 2/1 6/1 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 26 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7 5/0 3 2/1 6/1 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 27 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6 5/0 3 2/1 6/1/0 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 28 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6 5/0 3 2/1 6/1/0 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4
Dr. L K Bhagi, School of Mechanical Engineering, LPU 29 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1
Dr. L K Bhagi, School of Mechanical Engineering, LPU 30 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1
Dr. L K Bhagi, School of Mechanical Engineering, LPU 31 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1 𝑇𝐶 = 2 × 1 + 3 ×5+1×1+5×6+15×3+9× 1 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 32 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1 𝑇𝐶 = 2 × 1 + 3 ×5+1×1+5×6+15×3+9× 1 = 𝑅𝑠. 102
Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 33
Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 34
Dr. L K Bhagi, School of Mechanical Engineering, LPU 35 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 5 1 6 3 1 𝑇𝐶 = 2 × 1 + 3 ×5+1×1+5×6+15×3+9× 1 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 36 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 37 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 38 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 39 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 40 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 41 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 42 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 43 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 44 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 45 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 46 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 47 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 48 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 49 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
Dr. L K Bhagi, School of Mechanical Engineering, LPU 50
Dr. L K Bhagi, School of Mechanical Engineering, LPU 51
Dr. L K Bhagi, School of Mechanical Engineering, LPU 52
Dr. L K Bhagi, School of Mechanical Engineering, LPU 53
Dr. L K Bhagi, School of Mechanical Engineering, LPU 54
Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 55
Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 56
Dr. L K Bhagi, School of Mechanical Engineering, LPU 57
Dr. L K Bhagi, School of Mechanical Engineering, LPU 58
Dr. L K Bhagi, School of Mechanical Engineering, LPU 59 Modi method helps in comparing the relative advantage of alternative allocations for all the unoccupied cells simultaneously. The Modified-distribution (MODI) method (also called u-v method or method of multipliers) is used to calculate opportunity cost associated with each unoccupied cell and then improving the current solution leading to an optimal solution.
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 60
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 61
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 62
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 63
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 64
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 65
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 66
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 67
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 68
Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 69
Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 70
Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 71
Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 72
Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 73
Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 74
Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 75

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Operation research unit 3 Transportation problem

  • 1. OPERATION RESEARCH UNIT – III (Transportation and Assignment) Dr. Loveleen Kumar Bhagi Associate Professor School of Mechanical Engineering LPU Formulation of Transportation Problem, Initial Feasible Solution Methods, Optimality Test, Degeneracy in TP, Assignment Problem, Hungerian Method,Traveling Salesman Problem Commodities areTRANSPORTED while peopleTRAVEL
  • 2. Transportation Model The transportation model deals with a special class of linear programming problem in which the objective is to transport a homogeneous commodity from various origins or factories or supply centers to different destinations or markets or demand centers at a total minimum cost. Dr. L K Bhagi, School of Mechanical Engineering, LPU 2
  • 3. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 3
  • 4. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 4
  • 5. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 5
  • 6. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 6
  • 7. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 7
  • 8. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 8
  • 9. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 9
  • 10. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 10
  • 11. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 11
  • 12. Transportation Problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 12
  • 13. Dr. L K Bhagi, School of Mechanical Engineering, LPU 13
  • 14. Dr. L K Bhagi, School of Mechanical Engineering, LPU 14
  • 15. Dr. L K Bhagi, School of Mechanical Engineering, LPU 15
  • 16. Dr. L K Bhagi, School of Mechanical Engineering, LPU 16
  • 17. Dr. L K Bhagi, School of Mechanical Engineering, LPU 17
  • 18. Vogel’s Approximation Method (VAM) Dr. L K Bhagi, School of Mechanical Engineering, LPU 18
  • 19. Dr. L K Bhagi, School of Mechanical Engineering, LPU 19 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2 6 1 10 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 20. Dr. L K Bhagi, School of Mechanical Engineering, LPU 20 VAM Destinations/Demand Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2 6 1 10 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 21. Dr. L K Bhagi, School of Mechanical Engineering, LPU 21 VAM Destinations/Demand Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2/1 6 1/0 10 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 22. Dr. L K Bhagi, School of Mechanical Engineering, LPU 22 VAM Destinations/Demand Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2/1 6 1/0 10 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 23. Dr. L K Bhagi, School of Mechanical Engineering, LPU 23 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5 3 2/1 6 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 24. Dr. L K Bhagi, School of Mechanical Engineering, LPU 24 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5/0 3 2/1 6/1 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 25. Dr. L K Bhagi, School of Mechanical Engineering, LPU 25 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 7 5/0 3 2/1 6/1 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X 3 3 4
  • 26. Dr. L K Bhagi, School of Mechanical Engineering, LPU 26 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7 5/0 3 2/1 6/1 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4
  • 27. Dr. L K Bhagi, School of Mechanical Engineering, LPU 27 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6 5/0 3 2/1 6/1/0 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4
  • 28. Dr. L K Bhagi, School of Mechanical Engineering, LPU 28 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6 5/0 3 2/1 6/1/0 1/0 10 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4
  • 29. Dr. L K Bhagi, School of Mechanical Engineering, LPU 29 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1
  • 30. Dr. L K Bhagi, School of Mechanical Engineering, LPU 30 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1
  • 31. Dr. L K Bhagi, School of Mechanical Engineering, LPU 31 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1 𝑇𝐶 = 2 × 1 + 3 ×5+1×1+5×6+15×3+9× 1 = 𝑅𝑠. 102
  • 32. Dr. L K Bhagi, School of Mechanical Engineering, LPU 32 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 7/6/0 5/0 3/0 2/1/0 6/1/0 1/0 10/0 5 1 1 3 5 6 3 5 4 2 3 X 4 2 1 1 5 1 X X 3 3 4 6 3 1 𝑇𝐶 = 2 × 1 + 3 ×5+1×1+5×6+15×3+9× 1 = 𝑅𝑠. 102
  • 33. Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 33
  • 34. Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 34
  • 35. Dr. L K Bhagi, School of Mechanical Engineering, LPU 35 VAM Destinations Sources or Supply Centres P Q R S A 2 3 11 7 B 1 0 6 1 C 5 8 15 9 1 5 1 6 3 1 𝑇𝐶 = 2 × 1 + 3 ×5+1×1+5×6+15×3+9× 1 = 𝑅𝑠. 102
  • 36. Dr. L K Bhagi, School of Mechanical Engineering, LPU 36 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 37. Dr. L K Bhagi, School of Mechanical Engineering, LPU 37 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 38. Dr. L K Bhagi, School of Mechanical Engineering, LPU 38 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 39. Dr. L K Bhagi, School of Mechanical Engineering, LPU 39 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 40. Dr. L K Bhagi, School of Mechanical Engineering, LPU 40 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 41. Dr. L K Bhagi, School of Mechanical Engineering, LPU 41 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 42. Dr. L K Bhagi, School of Mechanical Engineering, LPU 42 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 43. Dr. L K Bhagi, School of Mechanical Engineering, LPU 43 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 44. Dr. L K Bhagi, School of Mechanical Engineering, LPU 44 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 45. Dr. L K Bhagi, School of Mechanical Engineering, LPU 45 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 46. Dr. L K Bhagi, School of Mechanical Engineering, LPU 46 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 47. Dr. L K Bhagi, School of Mechanical Engineering, LPU 47 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 48. Dr. L K Bhagi, School of Mechanical Engineering, LPU 48 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 49. Dr. L K Bhagi, School of Mechanical Engineering, LPU 49 VAM Destinations Sources or Supply Centres P Q R S A 2 3 B 1 C 5 15 9 𝑇𝐶 = 𝑅𝑠. 102
  • 50. Dr. L K Bhagi, School of Mechanical Engineering, LPU 50
  • 51. Dr. L K Bhagi, School of Mechanical Engineering, LPU 51
  • 52. Dr. L K Bhagi, School of Mechanical Engineering, LPU 52
  • 53. Dr. L K Bhagi, School of Mechanical Engineering, LPU 53
  • 54. Dr. L K Bhagi, School of Mechanical Engineering, LPU 54
  • 55. Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 55
  • 56. Test For Optimality Dr. L K Bhagi, School of Mechanical Engineering, LPU 56
  • 57. Dr. L K Bhagi, School of Mechanical Engineering, LPU 57
  • 58. Dr. L K Bhagi, School of Mechanical Engineering, LPU 58
  • 59. Dr. L K Bhagi, School of Mechanical Engineering, LPU 59 Modi method helps in comparing the relative advantage of alternative allocations for all the unoccupied cells simultaneously. The Modified-distribution (MODI) method (also called u-v method or method of multipliers) is used to calculate opportunity cost associated with each unoccupied cell and then improving the current solution leading to an optimal solution.
  • 60. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 60
  • 61. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 61
  • 62. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 62
  • 63. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 63
  • 64. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 64
  • 65. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 65
  • 66. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 66
  • 67. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 67
  • 68. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 68
  • 69. Test For Optimality > Stepping Stone Method Dr. L K Bhagi, School of Mechanical Engineering, LPU 69
  • 70. Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 70
  • 71. Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 71
  • 72. Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 72
  • 73. Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 73
  • 74. Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 74
  • 75. Degeneracy in Transportation problem Dr. L K Bhagi, School of Mechanical Engineering, LPU 75