Project 5.2 − Small Production Planning Project
(Fixed Charge Problem via Network Flow with Side Constraints)
Jack Small Enterprises runs two factories in Ohio, one in Toledo and one in Centerville. His factories produce a variety of products. Two of his product lines are polished wood clocks which he adorns with a regional theme. Naturally, clocks popular in the southwest are not as popular in the northeast, and vice versa. Each plant makes both of the clocks. These clocks are shipped to St Louis for distribution to the southeast and western states and to Pittsburgh for distribution to the south and northeast.
Jack is considering streamlining his plants by removing certain production lines from certain plants. Among his options is potentially eliminating the clock production line at either the Toledo or the Centerville plant. Each plant carries a fixed operating cost for setting up the line and a unit production cost, both in terms of money and factory worker hours. This information is summarized in the table below.
Production Cost
Clocks Produced
per Clock
per Hour
Available
Plant
Fixed Cost for
Southwest
Northeast
Southwest
Northwest
Hours per
Line
Clock
Clock
Clock
Clock
Month
Toledo
$20,000
$10
$12
5
6
500
Centerville
$24,000
$9
$13
5.5
6.2
675

The Southwest clocks are sold for $23 each and the Northwest clocks are sold for $25 each. Demand rates used for production planning are 1875 Southwest clocks for sale out of the St Louis distribution center and 2000 Northeast clocks for sale out of the Pittsburgh distribution center. Assume all these units are sold. The per clock transportation costs from plant to distribution center is given in the following table. Develop a generalized network flow model for this problem and implement this model in solver. Use the model to answer the following questions.
a.
Should any of the production lines be shut down?
b.
How should worker hours be allocated to produce the clocks to meet the demand forecasts? Are there any excess hours, and if so how many?
c.
What is the expected monthly profit?
d.
If a plant is closed, what are the estimated monthly savings?

Question

Project 5.2 − Small Production Planning Project
(Fixed Charge Problem via Network Flow with Side Constraints)
Jack Small Enterprises runs two factories in Ohio, one in Toledo and one in Centerville. His factories produce a variety of products. Two of his product lines are polished wood clocks which he adorns with a regional theme. Naturally, clocks popular in the southwest are not as popular in the northeast, and vice versa. Each plant makes both of the clocks. These clocks are shipped to St Louis for distribution to the southeast and western states and to Pittsburgh for distribution to the south and northeast.
Jack is considering streamlining his plants by removing certain production lines from certain plants. Among his options is potentially eliminating the clock production line at either the Toledo or the Centerville plant. Each plant carries a fixed operating cost for setting up the line and a unit production cost, both in terms of money and factory worker hours. This information is summarized in the table below.
Production Cost
Clocks Produced
per Clock
per Hour
Available
Plant
Fixed Cost for
Southwest
Northeast
Southwest
Northwest
Hours per
Line
Clock
Clock
Clock
Clock
Month
Toledo
$20,000
$10
$12
5
6
500
Centerville
$24,000
$9
$13
5.5
6.2
675
​
The Southwest clocks are sold for $23 each and the Northwest clocks are sold for $25 each. Demand rates used for production planning are 1875 Southwest clocks for sale out of the St Louis distribution center and 2000 Northeast clocks for sale out of the Pittsburgh distribution center. Assume all these units are sold. The per clock transportation costs from plant to distribution center is given in the following table.  Develop a generalized network flow model for this problem and implement this model in solver. Use the model to answer the following questions. 
a.
Should any of the production lines be shut down?
b.
How should worker hours be allocated to produce the clocks to meet the demand forecasts? Are there any excess hours, and if so how many?
c.
What is the expected monthly profit?
d.
If a plant is closed, what are the estimated monthly savings?

Quizplus · Accepted Answer

The Answer of Project 5.2 − Small Production Planning Project
(Fixed Charge Problem via Network Flow with Side Constraints)
Jack Small Enterprises runs two factories in Ohio, one in Toledo and one in Centerville. His factories produce a variety of products. Two of his product lines are polished wood clocks which he adorns with a regional theme. Naturally, clocks popular in the southwest are not as popular in the northeast, and vice versa. Each plant makes both of the clocks. These clocks are shipped to St Louis for distribution to the southeast and western states and to Pittsburgh for distribution to the south and northeast.
Jack is considering streamlining his plants by removing certain production lines from certain plants. Among his options is potentially eliminating the clock production line at either the Toledo or the Centerville plant. Each plant carries a fixed operating cost for setting up the line and a unit production cost, both in terms of money and factory worker hours. This information is summarized in the table below.
Production Cost
Clocks Produced
per Clock
per Hour
Available
Plant
Fixed Cost for
Southwest
Northeast
Southwest
Northwest
Hours per
Line
Clock
Clock
Clock
Clock
Month
Toledo
$20,000
$10
$12
5
6
500
Centerville
$24,000
$9
$13
5.5
6.2
675
​
The Southwest clocks are sold for $23 each and the Northwest clocks are sold for $25 each. Demand rates used for production planning are 1875 Southwest clocks for sale out of the St Louis distribution center and 2000 Northeast clocks for sale out of the Pittsburgh distribution center. Assume all these units are sold. The per clock transportation costs from plant to distribution center is given in the following table.  Develop a generalized network flow model for this problem and implement this model in solver. Use the model to answer the following questions. 
a.
Should any of the production lines be shut down?
b.
How should worker hours be allocated to produce the clocks to meet the demand forecasts? Are there any excess hours, and if so how many?
c.
What is the expected monthly profit?
d.
If a plant is closed, what are the estimated monthly savings?