REQUIRED: a) Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. b) Formulate an optimization model to solve this problem. (Set-up only the objective function and the Constrains do not solve) Question The Audio Company produces boombows However, management has decided to subcontract out the production of the speakers needed for the boombows. The vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers 1 2 > $22.700 In addition, each vendor would change a shipping cost Each shipment would go to one of the company's two warehouses. Each vendor has its own formula for calculating this shipping cost based on the mileage to the warehouse. These formulas and the mileage 1 Charge per shipment $300+0.40m

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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REQUIRED:
(a) Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes,
and demand nodes in this network.
(b) Formulate an optimization model to solve this problem. (Set-up only the objective function and the Constrains
do not solve)
1
Question
The Audiofile Company produces boomboxes. However, management has decided to
subcontract out the production of the speakers needed for the boomboxes. Three vendors
are available to supply the speakers. Their price for each shipment of 1,000 speakers is
shown below
Vendor
1
2
3
In addition, each vendor would charge a shipping cost. Each shipment would go to one of
the company's two warehouses. Each vendor has its own formula for calculating this
shipping cost based on the mileage to the warehouse. These formulas and the mileage
data are shown below
Vendor
1
2
3
Vendor
2
3
Warehouse 1
Price
$22,500
$22,700
$22,300
Charge per shipment
$300+0.40/m
$200+050/mle
$500+0.20/mile
1600 miles
500 miles
2,000 miles
Warehouse 1
Warehouse 2
Monthly demand
Warehouse 2
400 miles
600 miles
1,000 m
Whenever one of the company's two factories needs a shipment of speakers to assemble
into the boomboxes, the company hires a trucker to bring the shipment in from one of the
warehouses. The cost per shipment is given in the next column, along with the number of
shipments needed per month at each factory.
Unit Shipping Cost
Factory 1
$200
$400
10
Each vendor is able to supply as many as 10 shipments per month. However, because of
shipping limitations, each vendor is able to send a maximum of only & shipments per month
to each warehouse Similarly, each warehouse is able to send a maximum of only
shipments per month to each factory Management now wants to develop a plan for each
month regarding how many shipments if any) to order from each vandor, how many of
those shipments should go to each warehouse, and then how many shipments each
warehouse should send to each factory. The objective is to minimize the sum of the
purchase costs (including the shipping charge and the shipping costs from the warehouses
to the factories.
Unit Shipping Cost
Factory 2
$700
$500
4
Draw a network that depicts the company's supply network Identify the supply nodes.
transhipment nodes, and demand nodes in this network
(b) Formulate an optimization model to solve this problem (Set-up only the objective
function and the Constrains do not solve)
Transcribed Image Text:REQUIRED: (a) Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. (b) Formulate an optimization model to solve this problem. (Set-up only the objective function and the Constrains do not solve) 1 Question The Audiofile Company produces boomboxes. However, management has decided to subcontract out the production of the speakers needed for the boomboxes. Three vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers is shown below Vendor 1 2 3 In addition, each vendor would charge a shipping cost. Each shipment would go to one of the company's two warehouses. Each vendor has its own formula for calculating this shipping cost based on the mileage to the warehouse. These formulas and the mileage data are shown below Vendor 1 2 3 Vendor 2 3 Warehouse 1 Price $22,500 $22,700 $22,300 Charge per shipment $300+0.40/m $200+050/mle $500+0.20/mile 1600 miles 500 miles 2,000 miles Warehouse 1 Warehouse 2 Monthly demand Warehouse 2 400 miles 600 miles 1,000 m Whenever one of the company's two factories needs a shipment of speakers to assemble into the boomboxes, the company hires a trucker to bring the shipment in from one of the warehouses. The cost per shipment is given in the next column, along with the number of shipments needed per month at each factory. Unit Shipping Cost Factory 1 $200 $400 10 Each vendor is able to supply as many as 10 shipments per month. However, because of shipping limitations, each vendor is able to send a maximum of only & shipments per month to each warehouse Similarly, each warehouse is able to send a maximum of only shipments per month to each factory Management now wants to develop a plan for each month regarding how many shipments if any) to order from each vandor, how many of those shipments should go to each warehouse, and then how many shipments each warehouse should send to each factory. The objective is to minimize the sum of the purchase costs (including the shipping charge and the shipping costs from the warehouses to the factories. Unit Shipping Cost Factory 2 $700 $500 4 Draw a network that depicts the company's supply network Identify the supply nodes. transhipment nodes, and demand nodes in this network (b) Formulate an optimization model to solve this problem (Set-up only the objective function and the Constrains do not solve)
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