Total supply = 100+100+150 = 350
Total demand = 50+70+60+80 = 260
Supply > demand --> add a dummy demand column
|
From/To
|
NY
|
FW
|
SD
|
MI
|
Dummy
|
Supply
|
|
Boulder
|
7
|
11
|
8
|
13
|
0
|
100
|
|
Macon
|
20
|
17
|
12
|
10
|
0
|
100
|
|
Gary
|
8
|
18
|
13
|
16
|
0
|
150
|
|
Demand
|
50
|
70
|
60
|
80
|
90
|
350
|
LP formulation:
Let Xij: lots of 1000 shipped from Plant i to destination j, where i: B, M, G, and j: N, F, S, M, D
Max Profit = 7XBN + 11XBF + 8XBS + 13XBM + 20XMN + 17XMF + 12XMS + 10XMM + 8XGN + 18XGF + 13XGS + 16XGM
s.t.
XBN + XBF + XBS + XBM + XBD <= 100
XMN + XMF + XMS + XMM + XMD <= 100
XGN + XGF + XGS + XGM + XGD <= 150
XBN + XMN + XGN = 50
XBF + XMF + XGF = 70
XBS + XMS + XGS = 60
XBM + XMM + XGM = 80
XBD + XMD + XGD = 90
Xij >= 0
Excel Solution:
|
|
NY
|
FW
|
SD
|
MI
|
Dummy
|
Supply
|
|
Boulder
|
0
|
0
|
0
|
10
|
90
|
100
|
|
Macon
|
50
|
50
|
0
|
0
|
0
|
100
|
|
Gary
|
0
|
20
|
60
|
70
|
0
|
150
|
|
Demand
|
50
|
70
|
60
|
80
|
90
|
350
|
Total profit = $4,240,000
(a)Excel Solution:
|
|
D
|
E
|
F
|
G
|
Supply
|
|
A
|
25
|
0
|
25
|
0
|
50
|
|
B
|
10
|
0
|
0
|
30
|
40
|
|
C
|
15
|
60
|
0
|
0
|
75
|
|
Demand
|
50
|
60
|
25
|
30
|
165
|
Total cost = $720
(b) By setting the moving cost from A to D as $0:
|
|
D
|
E
|
F
|
G
|
Supply
|
|
A
|
$0
|
$8
|
$6
|
$5
|
50
|
|
B
|
$9
|
$8
|
$8
|
$0
|
40
|
|
C
|
$5
|
$3
|
$3
|
$10
|
75
|
|
Demand
|
50
|
60
|
25
|
30
|
165
|
Excel Solution:
|
|
D
|
E
|
F
|
G
|
Supply
|
|
A
|
50
|
0
|
0
|
0
|
50
|
|
B
|
0
|
10
|
0
|
30
|
40
|
|
C
|
0
|
50
|
25
|
0
|
75
|
|
Demand
|
50
|
60
|
25
|
30
|
165
|
Total cost = $755