Textbook Problem. Practical Management Science. 6Th Edition78. In the original RedBrand problem (Example 5.4), suppose that the company could add up to 100 tons of capacity, in increments of 10 tons, to any singleplant. Use SolverTable to determine the yearly savings in cost from having extra capacity at the various plants. Assume that the capacity will cost $28,000 per ton right now. Also, assume that the annual cost savings from having the extra capacity will extend over 10 years and that the total 10-year savings will be discounted at an annual 10% interest rate. How much extra capacity should the company purchase, and which plant should be expanded? (Hint: Use the PV function to find the present value of the total cost saving over the 10-year period. You can assume that the costs occur at the ends of the respective years.) Figure 5.21 Logistics ModelACEFH.K1 RedBrand shipping model3 Inputs4 Common arc capacity2006 Network structure, flows, and arc capacity constraintsUnit CostNode balance constraints7OriginDestinationFlowArc CapacityPlant constraints8120.200NodePlant net outflowPlant capacityく=9133.180く=2001180く=2001014く=200300く=3001115く=2003100く=100121620く=2001317200.200Warehouse constraintsく=1419.200NodeWarehouse net outflowRequiredく=1529.0.く=200%3D161120く=200%3D1710.く=200188.180く=200Customer constraints197150.く=200NodeCustomer net inflowCustomer demand2010.40.<=2006.400>=4002128.0.く=20071801802234180く=200Range names usedArc_CapacityCustomer demandCustomer_net_inflowDestination230.5200く=200=Model!$F$8:$F$33|=Model!$K$20:$K$21=Model!$I$20:$I$21=Model!$B$8:$B$33|=Model!$D$8:$D$33=Model!$A$8:$A$33=Model!$K$9:$K$11=Model!$I$9:$I$11=Model!$B$36=Model!$C$8:$C$33=Model!$I$15:$I$16243100.く=2002537120.く=2002641.20.く=2002746200く=2002847120.く=200FlowOriginPlant_capacityPlant_net_outflowTotal_cost2940.80.<3=20030200く=200317120.く=2003271180く=200Unit_CostWarehouse_net_outflow33770.く=2003435 Objective to minimize36 Total cost$3,260 Table 5.5 Shipping Costs for RedBrand Example (in $1000s)To nodeFrom node123456.75.03.05.05.020.020.09.09.01.01.08.015.00.48.01.00.510.012.041.22.012.00.82.012.01.07.0123t567

Analyze the case when a company adds 100 tons of extra capacity in increments of 10 tons to any…

Answered: In the original RedBrand problem…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Textbook Problem. Practical Management Science. 6Th Edition

78. In the original RedBrand problem (Example 5.4), suppose that the company could add up to 100 tons of capacity, in increments of 10 tons, to any singleplant. Use SolverTable to determine the yearly savings in cost from having extra capacity at the various plants. Assume that the capacity will cost $28,000 per ton right now. Also, assume that the annual cost savings from having the extra capacity will extend over 10 years and that the total 10-year savings will be discounted at an annual 10% interest rate. How much extra capacity should the company purchase, and which plant should be expanded? (Hint: Use the PV function to find the present value of the total cost saving over the 10-year period. You can assume that the costs occur at the ends of the respective years.)

Figure 5.21 Logistics Model
A
C
E
F
H.
K
1 RedBrand shipping model
3 Inputs
4 Common arc capacity
200
6 Network structure, flows, and arc capacity constraints
Unit Cost
Node balance constraints
7
Origin
Destination
Flow
Arc Capacity
Plant constraints
8
1
2
0.
200
Node
Plant net outflow
Plant capacity
く=
9
1
3
3.
180
く=
200
1
180
く=
200
10
1
4
く=
200
300
く=
300
11
1
5
く=
200
3
100
く=
100
12
1
6
20
く=
200
13
1
7
20
0.
200
Warehouse constraints
く=
14
1
9.
200
Node
Warehouse net outflow
Required
く=
15
2
9.
0.
く=
200
%3D
16
1
120
く=
200
%3D
17
1
0.
く=
200
18
8.
180
く=
200
Customer constraints
19
7
15
0.
く=
200
Node
Customer net inflow
Customer demand
20
1
0.4
0.
<=
200
6.
400
>=
400
21
2
8.
0.
く=
200
7
180
180
22
3
4
1
80
く=
200
Range names used
Arc_Capacity
Customer demand
Customer_net_inflow
Destination
23
0.5
200
く=
200
=Model!$F$8:$F$33
|=Model!$K$20:$K$21
=Model!$I$20:$I$21
=Model!$B$8:$B$33
|=Model!$D$8:$D$33
=Model!$A$8:$A$33
=Model!$K$9:$K$11
=Model!$I$9:$I$11
=Model!$B$36
=Model!$C$8:$C$33
=Model!$I$15:$I$16
24
3
10
0.
く=
200
25
3
7
12
0.
く=
200
26
4
1.2
0.
く=
200
27
4
6
200
く=
200
28
4
7
12
0.
く=
200
Flow
Origin
Plant_capacity
Plant_net_outflow
Total_cost
29
4
0.8
0.
<3=
200
30
200
く=
200
31
7
12
0.
く=
200
32
7
1
180
く=
200
Unit_Cost
Warehouse_net_outflow
33
7
7
0.
く=
200
34
35 Objective to minimize
36 Total cost
$3,260

Table 5.5 Shipping Costs for RedBrand Example (in $1000s)
To node
From node
1
2
3
4
5
6.
7
5.0
3.0
5.0
5.0
20.0
20.0
9.0
9.0
1.0
1.0
8.0
15.0
0.4
8.0
1.0
0.5
10.0
12.0
4
1.2
2.0
12.0
0.8
2.0
12.0
1.0
7.0
123t567

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