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Location-allocation models

Location-allocation models. We have a number of existing facilities Each existing facility has a demand w j We have to place m new facilities And we have to decide how the existing facilities are allocated to the new facilities. Location-allocation models. Existing facilities:.

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Location-allocation models

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  1. 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

  2. Location-allocation models Existing facilities:

  3. Location-allocation models How do we locate the new facilities? And how do we allocate supply?

  4. One-dimensional location-allocation by dynamic programming Example of heuristic procedure 2 2 2 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  5. One-dimensional location-allocation by dynamic programming Example of heuristic procedure Optimal value = 2 + 2 + 9 = 13 2 2 2 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  6. One-dimensional location-allocation by dynamic programming Example of heuristic procedure Optimal value = 3 + 1 + 1 + 7 = 12 2 2 2 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  7. One-dimensional location-allocation by dynamic programming • Use Dynamic programming method instead • Assume that aj < aj+1 j = 1,…,n-1

  8. 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)

  9. 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 < m s = 1 if i = m

  10. One-dimensional location-allocation by dynamic programming Example 1 of dynamic programming 2 2 2 2 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (1) (2) (3) (4) (5)

  11. One-dimensional location-allocation by dynamic programming Example 2 of dynamic programming 2 1 2½ 1½ 2½ 4 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (1) (2) (3) (4) (5) (6) (7)

  12. Two-facility with euclidean distance A B

  13. Two-facility with euclidean distance A A B B

  14. Two-facility with euclidean distance A A B B

  15. Two-facility with euclidean distance Three collinear points A C B

  16. 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

  18. Two-facility with euclidean distance

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