Hungarian method: a useful tool for managers

By   January 27, 2016

There is a method which can be quite useful for decision makers and managers. Hungarian method is helpful in decision making process choosing from different alternatives. You can read Dr. Attila Benko’s article: “Hungarian method: a useful tool for managers” which was published on Linkedin Pulse.

Background

The following algorithm was developed by Harold Kuhn (1955), based on the previous work of two famous Hungarian mathematicians: Dénes Kőnig andJenő Egerváry.

The problem:

Let we assume that we have three software developers: Alan, Bob and Chloe. One of them has to create the documentations, another has to implement software and the third has to test programs, but they each demand different time to complete these tasks. The problem is to find an optimal assignment for all of the jobs.

  • Alan would create the documentation for 250 engineerig hours; he would implement the software for 400 hours and he would test programs for 350 hours.
  • Bob would work on these tasks for 400; 600 and 350 hours.
  • Chloe would work on these tasks for 200; 400 and 250 hours.

Create the cost assignment matrix:

Substract the smallest element in each row from all elements in its row:

Substract the smallest element in each column from all elements in its column:

Cross out all zero elements with minimum number of horizontal or vertical lines:

Determine the optimal assignment:

We choose an optimal assignment (the total cost for this assignment is zero) from the zeroes (here: one zero per column) so we got the following solution on the original matrix:

[It would be my pleasure if you would be so kind as to contact me in case of you would like to share your valuable comment regarding the discussed topic.]

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