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Assignment Problem Hungarian Method Baseball Umpiring

Baseball umpiring crews are currently in four cities where three game series are beginning. When these are finished, the crews are needed to work games in four different cities. The distance between each of the cities where the crews are currently working to the cities where the new games will begin are shown in the following table:

From Kansas City Chicago Detroit Toronto

Seattle 1500 1730 1940 2070
Arlington 460 810 1020 1270
Oakland 1500 1850 2080 X
Baltimore 960 610 400 330

The X indicates that the crew in Oakland cannot be sent to Toronto.

A. Is this a minimization or mazimization problem? Explain
B. What steps do you take to assure that the unacceptable route wont be chosen?
C. Using the Hungarian method, there are two optimal solutions to this problem (meaning there are assignment options that will give the same total miles traveled) First question: what is the total miles travelled in the optimal solution?
D. Which two crews have options as to where you can send them to maintain the same optimal miles travelled? Where are the two places they can be sent?
E. Where will you send the other two crews?

Solution Summary

This posting provides solution to assignment problem using Hungarian method for Baseball umpiring providing an optimal route between four different cities.