80
Chapter 8
The Transportation Model
8.6
Add the stone cell in the
Atlanta to LA cell, which is
one of those with no stone
path.
Let K
1
= 0
C
ij
= R
i
+ K
j
(stone cells
only)
∆
Z
ij
= C
ij
– (R
i
+ K
j
)
The only cell with a
negative
∆
Z
ij
is the Boston
to LA cell.
The stone path
for this cell goes through
the E cell (Atlanta to LA), and an amount E is all we can move around
this path.
Therefore, the “improved” solution will not
be any better,
but simply has the E in a different cell.
Our VAM solution is
therefore optimal.
3 cars to Atlanta from Miami
3 cars to Boston from Miami
5 cars to Boston from New York
3 cars to Chicago from Los Angeles
8 cars to Detroit from Los Angeles
Since the Dummy destination is supplied from Los Angeles, one extra car
will stay in LA.
Total miles = 33,700
.
LA
Miami
New York
Atlanta
Boston
Chicago
Detroit
Dummy
12
6
5
23
23
9
31
16
7
2
22
14
8
24
14
6
0
0
0
3
8
3
3
5
1
3
8
3
8
1
23
32
22
24
0
0
16
30
+8
+6
+16
+16
+16
+12
+30
E
1
+
+

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MULTIPLE SOLUTION TRANSPORTATION PROBLEMS
8.7
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 Spring '10
 Koslov
 U.S. state, Stone, The Dummy

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