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The TamuTamu products company ltd is considering an expansion into five new sales districts. The company has been able to hire four new experienced salespersons. Upon...

      

The TamuTamu products company ltd is considering an expansion into five new sales districts. The
company has been able to hire four new experienced salespersons. Upon analysing the new
salesperson's past experience in combination with a personality test which was given to them, the
company assigned a rating to each of the salespersons for each of the districts .These ratings are as follows:
tamutamu1412019930.png
The company knows that with four salespersons, only four of the five potential districts can be covered.
Required:
i) The four districts that the salespersons should be assigned to in order to maximize the total of the
ratings
ii) Maximum total rating.

  

Answers


Mutiso
This is a case of assignment problem.
Assignment problems usually require that the number of sources equal the number of supply. Here there
are 5 districts and only 4 salespersons. A dummy salesperson E is introduced with zero ratings.
tamutamu1412019930i.png
By following the Hungarian
method: Firstly:
For each row, the lowest rating is reduced from each rating in the particular row. This results to a row
reduced rating table. Then all the zeroes are to be crossed by the least number of vertical and horizontal
lines. If the number of lines equal the number of rows (or columns = 5 in this case) then the final
assignment has been determined. Otherwise the following steps are followed.
tamutamu1412019930ii.png
Secondly, for each column, the lowest rating is reduced from every rating in the particular column. In
this case the table will remain the same since the dummy salesperson has ratings of zero for every
district.
Thirdly a revision of the opportunity-rating table is done.
The smallest rating in the table not covered by the lines is taken (in this case it is one). This is reduced from all the uncrossed ratings and added to the ratings at the intersection of the crossings. Then all the zeroes are to be crossed by the least number of vertical and horizontal lines. If the number of lines equal the number of rows (or columns = 5 in this case) then the final assignment has been determined.
tamutamu1412019930iii.png
Mutiso answered the question on January 14, 2019 at 18:37


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