2 Factory 3 Available Units Each Month 4 6 Warehouse 7 Demand 10 Per unit shipping costs 12 13 14 15 16 Cost Function 17 18 Constraints 19 Factory A 20 Factory B 21 Factory C 22 Warehouse 1 23 Warehouse 2 24 Warehouse 3 25 Warehouse 4 26 27 Decsion Variables 28 20 B C A1 A 65 1 10 Factory A B C 20 A1 1 0 0 9 1 0 0 0 A2 D B 80 25 1 20 11 25 15 A2 A3 11 0 0 0 1 0 0 E C 30 BAGNO Dw 20 To warehouse 3 18 18 21 18 18 A3 4 50 1 0 0 0 0 9 1 0 A4 30 A4 1 0 0 0 0 0 1 B:1 G 4 30 21 27 11 B.1 0 1 0 0 1 0 0 0 B:2 H 14 B2 0 1 1 0 0 1 0 1 0 B:3 18 B3 0 1 0 10 0 0 0 19 1 0 B:4 21 B4 0 1 0 9 0 0 0 1 C:1 K 25 C:1 01 0 1 1 0 0 0 C2 18 C2 0 0 1 1 0 9 1 0 0 C:3 M 21 C3 0 0 1 S 0 U 0 0 1 0 C4 N 27 O 0 0 1 0 0 0 1 Minimize Total C4 Usage 0<= 0<= 0<= 0>= 0>= 0>= 0]>= P Q Quantity R Available/Demanded 65 80 30 10 15 20 50 S
2 Factory 3 Available Units Each Month 4 6 Warehouse 7 Demand 10 Per unit shipping costs 12 13 14 15 16 Cost Function 17 18 Constraints 19 Factory A 20 Factory B 21 Factory C 22 Warehouse 1 23 Warehouse 2 24 Warehouse 3 25 Warehouse 4 26 27 Decsion Variables 28 20 B C A1 A 65 1 10 Factory A B C 20 A1 1 0 0 9 1 0 0 0 A2 D B 80 25 1 20 11 25 15 A2 A3 11 0 0 0 1 0 0 E C 30 BAGNO Dw 20 To warehouse 3 18 18 21 18 18 A3 4 50 1 0 0 0 0 9 1 0 A4 30 A4 1 0 0 0 0 0 1 B:1 G 4 30 21 27 11 B.1 0 1 0 0 1 0 0 0 B:2 H 14 B2 0 1 1 0 0 1 0 1 0 B:3 18 B3 0 1 0 10 0 0 0 19 1 0 B:4 21 B4 0 1 0 9 0 0 0 1 C:1 K 25 C:1 01 0 1 1 0 0 0 C2 18 C2 0 0 1 1 0 9 1 0 0 C:3 M 21 C3 0 0 1 S 0 U 0 0 1 0 C4 N 27 O 0 0 1 0 0 0 1 Minimize Total C4 Usage 0<= 0<= 0<= 0>= 0>= 0>= 0]>= P Q Quantity R Available/Demanded 65 80 30 10 15 20 50 S
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
Transcribed Image Text:The Sullivan brothers run a distribution company. They are responsible for transporting the product from three factories to four possible warehouses for a private company. The
private company has already told them how much product each warehouse requires (demand) and how much each factory produces (supply). They've been told it doesn't matter
which factory supplies what warehouse, and warehouses can be supplied by multiple factories. The shipping costs are listed below. Since the brothers get paid the same amount no
matter how they choose to ship, their goal is to minimize their costs (thus increasing their profit). Your goal is to setup the LP problem and solve the optimal schedule for the
brothers. To fill in the pink table next to Cost Function, you need to use the shipping costs from each factory to each warehouse given to you above. If a good or, in this case, factory/
warehouse is involved, write down 1 in the related cell, and 0 otherwise. For example, to fill in cell E19, think whether Factory A is involved in the case of A:3 (i.e., when the product
is being transported from Factory A to warehouse 3). Since the answer is yes, we would write down 1 in cell E19. To fill in the green table (Usage), use SUMPRODUCT function.
Note that the number of products transported from each factory to each warehouse should go into the yellow table (you need to use Solver to find the optimum numbers). Use
SUMPRODUCT to fill in the Minimize Total Cost cell (i.e., green cell). Note that the costs come from the pink table (one array in SUMPRODUCT), and number of products
transported from each factory to each warehouse comes from yellow table (the other array in SUMPRODUCT). Finally, use Solver to find the optimum values and minimum total
transportation cost. Make sure you are adding proper constraints.
A
2 Factory
3 Available Units Each Month
4
5
6 Warehouse
7 Demand
8
9
10 Per unit shipping costs
11
12
13
14
15
16 Cost Function
17
18 Constraints
19 Factory A
20 Factory B
21 Factory C
22 Warehouse 1
23 Warehouse 2
24 Warehouse 3
25 Warehouse 4
26
27 Decsion Variables
28
29
30
B
C
A:1
A
65
1
10
Factory
A
B
C
20
A.1
1
0
0
11
0
0
0
A:2
D
B
80
2
15
1
20
11
25
15
A:2
1
0
0
0
1
0
0
E
C
30
3
20
12211
A:3
To warehouse
15
14
18
18
A:3
1
0
0
01
0
1
0
F
A:4
4
50
3
18
18
21
30
A:4
1
0
0
0
0
0
1
B:1
G
4
30
21
27
11
B:1
0
1
0
1
0
0
0
B:2
H
14
B2
0
1
0
0
1
0
0
B:3
I
18
B:3
0
1
0
01
0
1
0
B:4
J
21
B4
0
1
0
0
0
0
1
C:1
K
25
C:1
0
0
1
1
0
0
0
C:2
L
18
C2
0
0
1
0
1
0
0
C:3
M
21
C:3
0
0
1
0
0
1
0
C4
N
27
C:4
0
0
ol
1
0
0
0
1
O
Minimize
Total
Usage
0<=
0 <=
0 <=
0 >=
0 >=
0 >=
0 >=
P
Q
Quantity
R
Available/Demanded
65
80
30
10
15
20
50
S
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