Operational research on Assignment ppt


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Operational research on Assignment ppt

  3. 3. OPERATIONAL RESEARCH (O.R) O.R is developed “to ensure reduction in costs.  O.R is a scientific approach to problem solving.  For executive decision making which requires formulation of mathematical, economic and statistical models for decision making and controlling. 
  4. 4. O.R IS USED FOR Personal management  Production management  Financial management  Marketing management 
  5. 5. APPLICATION IN PUBLIC SECTOR In Airways  In Hospitals  In Government  In Banks  In Railways  In Highways 
  6. 6. CHARACTERISTICS OF O.R Uses mixed team approach to find optimal solution.  Uses scientific methods to achieve at optimal solution.  Emphasis on overall approach to the system.  Optimizes the total output by maximizing profit and minimizing cost. 
  7. 7. LIMITATION OF O.R Involves the use of mathematical and complex method.  Ignores intangible factors such as better customer satisfaction, skill attitude of worker, initiative of management etc.  Usually associated with high cost.  Overuse of assumptions to simplify mathematical models may not represent a true situation. 
  8. 8. ASSIGNMENT  Assignment is a technique to find out lowest possible allocable cost of the project by assigning the best possible least costs to the jobs and workers.
  9. 9. ASSIGNMENT IS USED In assigning machines to factory orders.  In assigning sales/marketing people to sales territories.  In assigning contracts to bidders by systematic bid-evaluation.  In assigning teachers to classes.  In assigning accountants to accounts of the clients. 
  10. 10. STEPS : 1. Ensure that the sum is in the matrix form 2. The matrix form is used only in minimization technique. if it is not a minimization sum then we have to convert it into minimization sum 3. Number of rows should be equal to number of columns if number of row is not equal to number of column then we have to introduce a “Dummy” column or row to make it balance.
  11. 11. CONTINUE . . . 4. Row Minima  In this step we have to choose the lowest element in the row and deduct it from all element. 5. Column Minima  In this step we choose the lowest element and deduct it from other numbers in the column.
  12. 12. CONTINUE. . . 6. Now try to cover maximum zeros using minimum lines. if the lines are equal to order of matrix the optimal solution is reached.
  13. 13. ASSIGNING THE JOBS First select the row or column which has only one zero  encircle that zero that means that the assignment is made and all zeros, if any, in that row or column will be cancelled.  If there are more than one zero in a row or column then allocate zero from top-bottom or left-right .  It is better to select the row or column with minimum zero. 
  14. 14. OPTIMALITY IS NOT REACHED If in Step 3. the number of lines is not equal to order of matrix then the optimal solution is not reached:  In such matrix there are three elements:  The uncovered elements which are not on any lines.  The elements covered by the lines and are on point of intersection.  Covered elements but not on point of intersection. 
  15. 15. CONTINUE. . . Now find the minimum element from the uncovered elements :  Deduct that element from all uncovered elements.  Add that element to the elements on the point of intersection.  The other elements should be kept as it is. 
  16. 16. CONTINUE . . . Now new matrix is formed.  And again we have follow the steps.  Now if the number of lines is equal to order of matrix than optimality is reached or else again follow the steps. 
  17. 17. MAXIMIZATION MATRIX If the matrix is in the form of maximization matrix then we have to convert it into the minimization matrix.  To convert the maximization matrix into the minimization we have to select the highest element in the matrix and deduct that element from the other elements.  Thus new matrix formed is minimization matrix all other step remains same. 
  18. 18. IF NQ APPEARS NQ is means Not Assignable.  If NQ appears we have to put “M”.  “M” represents highest possible number.  If any number deducted form “M” than also it will remain “M”. 
  19. 19. CONCLUSION Assignment is used to assign the jobs on one-on-one basis.  It is used to maximize the profit and minimize the cost.  If all the steps followed in the proper way the optimality reached will be effectively useful. 
  20. 20. THANK YOU