Location-allocation models

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Location-allocation models

• We have a number of existing facilities
• Each existing facility has a demand wj
• We have to place m new facilities
• And we have to decide how the existing facilities
  are allocated to the new facilities

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Location-allocation models
Existing facilities
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Location-allocation models
And how do we allocate supply?
How do we locate the new facilities?
4
One-dimensional location-allocation by dynamic
programming
Example of heuristic procedure
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1
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One-dimensional location-allocation by dynamic
programming
Example of heuristic procedure
Optimal value 2 2 9 13
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2
2
2
1
1
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One-dimensional location-allocation by dynamic
programming
Example of heuristic procedure
Optimal value 3 1 1 7 12
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One-dimensional location-allocation by dynamic
programming

• Use Dynamic programming method instead
• Assume that aj lt aj1 j 1,,n-1

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One-dimensional location-allocation by dynamic
programming

• i stages (number of new facilities which have
  not been located)
• s states (index of first facility which have not
  been allocated to a new facility)

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One-dimensional location-allocation by dynamic
programming

• i stages ( new facilities not located)
• s states (first facility not allocated to new)

Stage i
m i located
i - 1 not located
m - i
i - 1
m i 1 s n i 1 if i lt m s 1 if i
m
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One-dimensional location-allocation by dynamic
programming
Example 1 of dynamic programming
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(1)
(2)
(3)
(4)
(5)
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One-dimensional location-allocation by dynamic
programming
Example 2 of dynamic programming
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1
2½
1½
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2½
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(1)
(2)
(3)
(4)
(5)
(6)
(7)
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Two-facility with euclidean distance
A
B
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Two-facility with euclidean distance
A
A
B
B
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Two-facility with euclidean distance
A
A
B
B
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Two-facility with euclidean distance
Three collinear points
A
C
B
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Two-facility with euclidean distance
A
A
A
A
C
C
C
C
B
B
B
B
A
A
C
C
B
B
17
Two-facility with euclidean distance
Three collinear points
A
C
B
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Two-facility with euclidean distance