Question

Save Homework: HW 7B - Binary Optimization Score: 0 of 1 pt X 14.2.9 1 of 1 (1 complete) HW Score: 0%, 0 of 1 pt Question Help Hatch Financial, which recently absorbed another firm, is now downsizing and must relocate five information systems analysts from recently closed locations. Unfortunately, there are only three positions available for five people. Salaries are fairly uniform among this group (those with higher pay were already given the opportunity to begin anew). Moving expenses will be used as the means of determining who will be sent where. Estimated moving expenses are in the accompanying table. Model this as an integer optimization model to minimize cost and determine which analysts to relocate to the three locations. Click the icon to view the estimated moving expenses for each analyst to each city. To minimize the costs, should relocate to Gary, should relocate to Salt Lake City, and should relocate to Fresno. Estimated Moving Expenses - X e Analyst Arlene Bobby Charlene Douglas Emory Gary $6,000 $12,000 $5,000 $3,500 $6,500 Moving Cost To Salt Lake City $8,000 $18,500 $13,000 $18,500 $4,000 Fresno $5,500 $18,500 $8,000 $8,000 $4,500 Print Done Click to select your answer(s) and then click Check Answer.

Answer 1

Answer:

To minimize the costs Douglas should relocate to Gary, Emory should relocate to Salt Lake City and Ariene should relocate to Fresno.

The minimized cost will be $13,000.

Calculations and explanations:

Let the binary variables (i.e. can be either 0 or 1) associated with analysts and locations be as shown below:

Analyst	Gary	Salt Lake City	Fresno
Ariene	a1	a2	a3
Bobby	b1	b2	b3
Charlene	c1	c2	c3
Douglas	d1	d2	d3
Emory	e1	e2	e3

Objective function =  6000a1 + 8000a2 + 5500a3 + 12000b1 + 18500b2 + 18500b3 + 5000c1 + 13000c2 + 8000c3 + 3500d1 + 18500d2 + 8000d3 + 6500e1 + 4000e2 + 4500 e3

This has to be minimized.

Constraints:

The 1st five constraints show that each analyst can move to a single location.

(i): a1+a2+a3<=1

(ii): b1+b2+b3<=1

(iii): c1+c2+c3<=1

(iv): d1+d2+d3<=1

(v): e1+e2+e3<=1

The next 3 constraints show that each location will have 1 analyst each. So:

(vi) a1+b1+c1+d1+e1 =1

(vii) a2+b2+c2+d2+e2 = 1

(viii) a3+b3+c3+d3+e3 = 1

Lastly as opening is there for only 3 analysts sum of all variables = 3

So (ix): a1+a2+a3+b1+b2+b3+......e1+e2+e3 = 3

Solving this in excel's solver we get the following:

Analyst	Gary	Salt Lake City	Fresno
Ariene	-	-	1
Bobby	-	-	-
Charlene	-	-	-
Douglas	1	-	-
Emory	-	1	-
Objective function	13,000
Constraints
1	<=	1
-	<=	1
-	<=	1
1	<=	1
1	<=	1
1	=	1
1	=	1
1	=	1
3	=	3