SunNet is a residential Internet Service Provider (ISP) in the central Florida a
ID: 3687315 • Letter: S
Question
SunNet is a residential Internet Service Provider (ISP) in the central Florida area. Presently, the company operates one centralized facility that all of its clients call into for Internet access. To improve service, the company is planning to open three satellite offices in the cities of Pine Hills, Eustis, and Sanford. The company has identified five different regions to be serviced by these three offices. The following table summarizes the number of customers in each region, the service capacity at each office, and the average monthly per customer cost of providing service to each region from each office. Table entries of n.a. indicate infeasible region-to-service-center combinations. SunNet would like to determine how many customers from each region to assign to each service center to minimize cost.
a. Draw a network flow model to represent this problem.
b. Implement your model in Excel and solve it.
c. What is the optimalsolution?
Explanation / Answer
SunNet is a residential Internet Service Provider (ISP) in the central Florida area. Presently, the company operates one centralized facility that all of its clients call into for Internet access. To improve service, the company is planning to open three satellite offices in the cities of Pine Hills, Eustis, and Sanford. The company has identified five different regions to be serviced by these three offices. The following table summarizes the number of customers in each region, the service capacity at each office, and the average monthly per customer cost of providing service to each region from each office. Table entries of n.a. indicate infeasible region-to-service-center combinations. SunNet would like to determine how many customers from each region to assign to each service center to minimize cost.
Region
Pine Hills
Eustis
Sanford
Customers
1
2
3
4
5
Capacity
$6.50
$7.00
$8.25
n.a
n.a.
60,000
$7.50
$8.00
$7.25
$7.75
$7.50
70,000
n.a
n.a
$6.75
$7.00
$6.75
40,000
30,000
40,000
25,000
35,000
33,000
Subject to: X11+X12+X13 = 30,000
X21+X22+X23 = 40,000
X31+X32+X33 = 25,000
X41+X42+X43 = 35,000
X51+X52+X53 = 33,000
-X11 -X21 -X31 -X41 -X51 = 60,000
-X12 -X22 -X32 -X42 -X52 = 70,000
-X13 -X23 -X33 -X43 -X53 = 40,000
What is optimal solution?
Alternative or approach that best fits the situation, employs resources in a most effective and efficient manner, and yields the highest possible return under the circumstances. Any tinkering with an optimum decision makes it only worse. Very few optimal solutions can be found by statistical analysis or formulae, most require cut-and-try (experimental) approach.
The Excel Solution on progress.
Region
Pine Hills
Eustis
Sanford
Customers
1
2
3
4
5
Capacity
$6.50
$7.00
$8.25
n.a
n.a.
60,000
$7.50
$8.00
$7.25
$7.75
$7.50
70,000
n.a
n.a
$6.75
$7.00
$6.75
40,000
30,000
40,000
25,000
35,000
33,000
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