Problem : A company has four factories F1,F2,F3,F4 and manufacturing the same product. Production an

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• Problem A company has four factories
  F1,F2,F3,F4 and manufacturing the same product.
  Production and raw material costs differ from
  factory to factory and are given in the following
  table in the first two rows. The transportation
  costs are from the factories to sales depots,
  S1,S2,S3,and S4are also given. The last two
  columns in the table give the sales price and the
  total requirement at each depot. The production
  capacity of each factory is given in the last
  row.

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• Determine the most profitable production and
  distribution schedule and the corresponding
  profit. The surplus production should be taken
  to yield zero profit.

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Assignment Problems

• Hungarian method

Step 1 Balance the problem if it is
unbalanced Place an M as the cost element if some
assignment is prohibited Convert into equivalent
min problem if it is a max problem In a given
matrix subtract the smallest element in each row
from every element of that row and do the same in
the column.
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• Step2 In the reduced matrix obtain from step 1,
  subtract the smallest element in each column from
  every element of that column
• Step 3 Make the assignment for the reduced matrix
  obtained from step 1 and step 2
• (all the zeros in rows/columns are either
  marked (?) or (x) and there is exactly one
  assignment in each row and each column. In such a
  case optimum assignment policy for the given
  problem is obtained.
• If there is row or column with out an assignment
  go to the next step.

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• Step 4 Draw the minimum number of vertical and
  horizontal lines necessary to cover all the
  zeros in the reduced matrix obtained from step 3
  by adopting the following procedure.
• (i) mark(v) all rows that do not have assignments
• (ii) Mark (v) all columns (not already marked)
  which have zeros in the marked rows
• (iii) Mark (v) all rows (not already marked) that
  have assignments in marked columns
• (iv) Draw straight lines through all unmarked
  rows and marked columns

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• Step 5 If the number of lines drawn are equal to
• the number of rows or columns, then it is an
  optimum solution ,otherwise go to step 6
• Step 6 Select the smallest element among all the
  uncovered elements. Subtract this smallest
  element from all the uncovered elements an add it
  to the element which lies at the intersection of
  two line. Thus we obtain another reduced matrix
  for fresh assignments.
• Step 7 go the step 3 and repeat the procedure
  until the umber of assignment become equal to the
  number of rows or columns. In such a case, we
  shall observe that row/column has an assignment.
  Thus, the current solution is an optimum solution.

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• Problem 1
• A company centre has got four expert
  programmers. The centre needs four application
  programmes to be developed. The head of the
  computer centre, after studying carefully the
  programmes to be developed, estimate the
  computer time in minutes required by the
  respective experts to develop the application
  programmes as follows.

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• Problem 2
• Suggest optimum solution to the following
  assignment problem and also the minimum cost

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