Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 7, Problem 10RP

Explanation of Solution

Optimal solution:

  • Using u-v method, the first step is to check whether the solution is optimal or not.
  • The table is shown below:
424
1284
  • The first step is to find the initial feasible solution.
  • It is found using Vogels App method.
  • In order to find the feasible solution, the first step is to find the difference between the two least cost cells which have not been allocated for both rows and columns.
  • The next step is to select the largest of the differences of both the rows and columns and if there is a tie, the one with the maximum quantity is considered.
  • The next step is to assign the largest quantity within the demand in that row or column where the cost is minimum.
  • Then the last step is to eliminate the entire row or column.
  • The cost value of cells is represented bycij.
  • Hence, c11 is 10, c12is 5, c22is 5 and c23 is 10.
  • In this method, the value uiand vj belongs to rows and columns respectively.
  • The formula to find ui and vj is as follows:

    ui+ vj= cij = m + n – 1 = 3 + 2 – 1 = 4

  • Here, mis the total number of rows and nis the total number of columns and cijis the cost value

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Operations Research : Applications and Algorithms
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ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole