A hydro company operates a power plant in City 1 with a 30 million kilowatt-hours (kwh) supply capacity. Electricity is sent to Town 1, Town 2, and Town 3. Because of an anticipated increase in demand for electricity, the hydro company plans to increase capacity by constructing a new plant in one or more of the following cities: City 2, City 3, or City 4. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost (million dollars) Annual Capacity (million kwh) $375 $250 $275 City 2 City 3 City 4 Shipping costs and estimated demand for the electricity in each town are as follows: To Town 1 Town 2 Town 3 $10 $13 $16 $17 25 From City 1 City 2 City 3 $8 $9 $14 City 4 $15 Estimated demand 30 (million kwh) 45 40 35 $6 $12 $9 $10 35 The hydro company seeks to minimize the total cost (i.e., annual fixed cost and shipping costs) to meet the estimated demand for electricity in the three towns. For this purpose, the company attempts. to use an LP. a) Define the decision variables for the LP. b) Write the objective function of the LP. c) Write all the necessary constraints for the LP. d) Assume that a plant cannot be built in City 2 if a plant is built in City 3. What constraint(s) does one need to add to the original LP? e) Assume that a plant cannot be built in City 3 unless a plant is built in City 4. What constraint(s) does one need to add to the original LP?
A hydro company operates a power plant in City 1 with a 30 million kilowatt-hours (kwh) supply capacity. Electricity is sent to Town 1, Town 2, and Town 3. Because of an anticipated increase in demand for electricity, the hydro company plans to increase capacity by constructing a new plant in one or more of the following cities: City 2, City 3, or City 4. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost (million dollars) Annual Capacity (million kwh) $375 $250 $275 City 2 City 3 City 4 Shipping costs and estimated demand for the electricity in each town are as follows: To Town 1 Town 2 Town 3 $10 $13 $16 $17 25 From City 1 City 2 City 3 $8 $9 $14 City 4 $15 Estimated demand 30 (million kwh) 45 40 35 $6 $12 $9 $10 35 The hydro company seeks to minimize the total cost (i.e., annual fixed cost and shipping costs) to meet the estimated demand for electricity in the three towns. For this purpose, the company attempts. to use an LP. a) Define the decision variables for the LP. b) Write the objective function of the LP. c) Write all the necessary constraints for the LP. d) Assume that a plant cannot be built in City 2 if a plant is built in City 3. What constraint(s) does one need to add to the original LP? e) Assume that a plant cannot be built in City 3 unless a plant is built in City 4. What constraint(s) does one need to add to the original LP?
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter7: Transportation, Assignment, And Transshipment Problems
Section: Chapter Questions
Problem 26RP
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Transcribed Image Text:A hydro company operates a power plant in City 1 with a 30 million kilowatt-hours (kwh) supply
capacity. Electricity is sent to Town 1, Town 2, and Town 3.
Because of an anticipated increase in demand for electricity, the hydro company plans to increase
capacity by constructing a new plant in one or more of the following cities: City 2, City 3, or City 4.
The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows:
Proposed Plant Annual Fixed Cost (million dollars) Annual Capacity (million kwh)
City 2
City 3
City 4
$375
$250
$275
Shipping costs and estimated demand for the electricity in each town are as follows:
To
Town 2 Town 3
$6
$10
$12
$13
$9
$16
$10
$17
35
25
From
City 1
City 2
45
40
35
Town 1
$8
$9
City 3
$14
City 4
$15
Estimated demand 30
(million kwh)
The hydro company seeks to minimize the total cost (i.e., annual fixed cost and shipping costs) to
meet the estimated demand for electricity in the three towns. For this purpose, the company attempts
to use an LP.
a) Define the decision variables for the LP.
b) Write the objective function of the LP.
c) Write all the necessary constraints for the LP.
d) Assume that a plant cannot be built in City 2 if a plant is built in City 3. What constraint(s) does one
need to add to the original LP?
e) Assume that a plant cannot be built in City 3 unless a plant is built in City 4. What constraint(s)
does one need to add to the original LP?
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