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# 23 r 2a n insensitivity to number of sites cost

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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 one-dimensional 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 one-dimensional 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 two-dimensional 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 two-dimensional Model cross-medan 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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