King Finance Corporation, headquartered in New York, wants to assign three recently hired college graduates, Julie Jones, Al Smith, and Pat Wilson, to regional offices. However, the firm also has an opening in New York and would send one of the three there if it were more economical than a move to

Question

King Finance Corporation, headquartered in New York, wants to assign three recently hired college graduates, Julie Jones, Al Smith, and Pat Wilson, to regional offices. However, the firm also has an opening in New York and would send one of the three there if it were more economical than a move to Omaha, Dallas, or Miami. It will cost $1,000 to relocate Jones to New York, $800 to relocate Smith there, and $1,500 to move Wilson. What is the optimal assignment of personnel to offices?

HIREE	OFFICE
	OMAHA	MIAMI	DALLAS
Jones	$800	$1,100	$1,200
Smith	$500	$1,600	$1,300
Wilson	$500	$1,000	$2,300

Accepted Answer

a) The cost table has a fourth column to represent New York. To “balance” the problem, we add a “dummy” row (person) with a zero relocation cost to each city.

HIREE	OFFICE
	OMAHA	MIAMI	DALLAS
Jones	$800	$1,100	$1,200
Smith	$500	$1,600	$1,300
Wilson	$500	$1,000	$2,300

b) Subtract the smallest number in each row and cover all zeros (column subtraction of each column’s zero will give the same numbers and therefore is not necessary). See Figure 15.SP.1a.

c) Only 2 lines cover, so subtract the smallest uncovered number (200) from all uncovered numbers, and add it to each square where two lines intersect. Then cover all zeros. See Figure 15.SP.1b.

d) Only 3 lines cover, so subtract the smallest uncovered number (100) from all uncovered numbers, and add it to each square where two lines intersect. Then cover all zeros. See Figure 15.SP.1c.

e) Still only 3 lines cover, so subtract the smallest uncovered number (100) from all uncovered numbers, add it to squares where two lines intersect, and cover all zeros. See Figure 15.SP.1d.

f) Because it takes four lines to cover all zeros, an optimal assignment can be made at zero squares. We assign:
Wilson to Omaha
Jones to Miami
Dummy (no one) to Dallas
Smith to New York
Cost = $500 + $1,100 + $0 + $800
= $2,400

Question 15.SP.1: King Finance Corporation, headquartered in New York, wants t...

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