Unformatted text preview: is
INVERSELY
proportional to
SQUARE ROOT of
number of facilities Analytic Model Inputs & Costs
1
Total cost = f · N + c · ⇢A ·
3
fixed cost demand
$/item/demand N =A
⇤ p 2c⇢
6f !2/3 r 2A
N (In)sensitivity to Number of Sites • Cost components Costs Fixed cost
Mileage cost
Total Cost Optimum See any similarity with
the inventory model?
Number of sites Single Facility Models
• Assumptions:
•
• • Knowing the population density
Can locate anywhere in the space GOAL: Determine where to locate the facility
to minimize the sum of the
• travel distance of all population A onedimensional Model
• n points on a line • At each point i, there is a population of size wi • The position of each point i is xi • Choose which point to locate your facility?
Minimize Z = X wi (xs xi ) + xi <xs X
dZ
wi
=
dxs
x <x
i s X xi >xs X xi >xs wi wi (xi xs ) A onedimensional Model
Population 7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8 9 10 11 12 12 14 15 16 17 18 19 20 21 22 23 24 25 A twodimensional Model
• n points on a space • At each point i, there is a population of size wi • The position of each point i is (xi, yi) • Choose which point to locate your facility?
Metropolitan vs. Euclidean Minimize Z =
Minimize Z = n
X i=0
n
X
i=0 wi {xs xi  + ys wi [(xs xi ) + (ys
2 yi }
yi ) } 2 1 /2 A twodimensional Model
crossmedan approach
5
4 7
3 3 1
5 2
1
0 0 1 2 3 4 Does distance
matter? Huff Location Model
• A gravity analogy is used to estimate
attractiveness of store j for customers in area i. • Aij = Attraction to store j for customers in area i • Sj = Size of the store (e.g. square feet) • Tij = Travel time from area i to store j Huff Location Model
• To account for competito...
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 Fall '14
 huff location model, Square Root Law

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