Transportation model

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Transportation model

  1. 1. GYAN GANGA INSTITUTE OF <br />TECHNOLOGY AND MANAGEMENT, BHOPAL<br />Transportation Problem<br />Presented by:<br /><ul><li>Aditya Khare
  2. 2. Dhruvnanada Singh Gour
  3. 3. Mohd. Muqeem Mansoori
  4. 4. Rahul Jain</li></ul>Guided by:<br />Prof. Lokesh Payasi<br />
  5. 5. Definition<br /><ul><li>It deals with problems concerning as to what happens to the effectiveness function when we associate each of a number of origins with each of a possibly different number of destination.</li></li></ul><li>History<br /><ul><li>“The Distribution of a Product from Several Sources of Numerous Localities”</li></ul> Study by: F.L. Hitchcock(1941)<br /><ul><li>“Optimum Utilization of the Transportation System”</li></ul> Study by: T.C. Koopmans(1947)<br /> These two contribution are mainly responsible for the development of Transportation Model.<br />
  6. 6. Application of Transportation Problem<br /><ul><li>Minimize shipping costs
  7. 7. Determine low cost location
  8. 8. Find minimum cost production schedule
  9. 9. Military distribution system</li></li></ul><li>Process<br /><ul><li>Standardization of problem
  10. 10. Check the nature of the problem
  11. 11. Check prohibited cell
  12. 12. Check balancing problem</li></li></ul><li>Methods<br /><ul><li>North West Corner Rule (NWCR)
  13. 13. Row Minima Method
  14. 14. Column Minima Method
  15. 15. Least Cost Method
  16. 16. Vogle Approximation Method (VAM)</li></li></ul><li>North West Corner Rule (NWCR)<br /><ul><li>This method consists in allocating in the north-west corner of the matrix.</li></ul>Supply<br />North-west Corner<br />6<br />Demand<br />/1<br />
  17. 17. Row Minima Method<br /><ul><li>This method consists in allocating as much as possible lowest cost cell of the first row.</li></ul>Supply<br />Minimum cost in the Row<br />Demand<br />
  18. 18. Column Minima Method<br /><ul><li>This method consists in allocating as much as possible lowest cost cell of the first column.</li></ul>Supply<br />Minimum cost in the Column<br />Demand<br />
  19. 19. Least Cost Method<br /><ul><li>This method consists in allocating as much as possible lowest cost cell of the table.</li></ul>Supply<br />Minimum cost in the Table<br />Demand<br />
  20. 20. Vogle’s Approximation Method<br /><ul><li>Step 1: Compute the penalties.
  21. 21. Step 2: Identify the largest penalty and assign the highest possible value to </li></ul>the variable.<br /><ul><li>Step 3: Identify the largest penalty and assign the highest possible value to </li></ul>the variable.<br /><ul><li>Step 4: Identify the largest penalty and assign the highest possible value to </li></ul>the variable.<br />
  22. 22. Vogel’s Method <br />Transportation-12<br />
  23. 23. AssignmentProblem<br />
  24. 24. Introduction<br /><ul><li>It concern to assign a number of resources (origin) to equal number </li></ul>of jobs (destination) on to one basis so as to minimize total costs of performing the tasks at hand or maximize total profit of allocation.<br />
  25. 25. Applications<br /><ul><li>Assign vehicles to routes.
  26. 26. Assign salesmen to sales territories.
  27. 27. Assign accountant to clients accounts.
  28. 28. Assign development engineers to several construction sites.
  29. 29. Assign contracts to bidders through systematic evaluation of bids from competing suppliers.
  30. 30. Schedule teachers to classes, etc.</li></li></ul><li>Few important Points<br /><ul><li>Balanced Assignment Problem.
  31. 31. Unbalanced Assignment Problem.
  32. 32. Dummy Job/Facility
  33. 33. An Infeasible Assignment.</li></li></ul><li>Solution<br />Minimum Value of the column<br />New Matrix after subtracting the minimum value<br />
  34. 34. Thank You<br />

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