A town has one self-serve car wash with 4 bays. John Dow is thinking about openi

Question

A town has one self-serve car wash with 4 bays. John Dow is thinking about opening a larger size care wash with 12 bays. The table below shows the travel distance in miles from the three different areas in the community to the existing and proposed facilities and the number of customers in each area. Using the Huff retail location model and assuming A-1, answer the following Area Existing car wash Proposed car wash Number of customers 2 4 4 4 10005001000 8. What is the probability of a customer traveling from area 1 to the proposed car wash calculate the probability of a customer traveling from each area to each car wash? a. 0.43 b. 0.75 c. 0.25 d. 0.85 e. 0.06 9. What is the probability of a customer traveling from area 3 to the existing car wash calculate the probability of a customer traveling from each area to each car wash? a. 0.18 b. 0.27 c. 0.33 d. 0.40 e. 0.09 10. Assuming all consumers have the same budget, what is the market share of the proposed car wash? a. 0.82 b. 0.27 c. 0.93 d. 0.75 e. 0.36

Explanation / Answer

According to Huff location Model , ? =1

Pij = (Sj / Tj  ) /  ? (Sj / Tj  )

Pij: Probability of a consumer at point i travelling to retail location j
Sj: Size of retail location
Tij: Travel time (or distance) from consumer at point i to travel to location j

8. Existing car wash has 4 bays , so size of existing car wash (Se) = 4

Proposed Car wash has 12 Bays,so size of existing car wash (Sp) = 1

So Probablity of a customer traveling from Area 1 to proposed car wash according to the Huff location Model

P1p= (Sp/4 ) / ((Se/4) + (Sp/4)) = (12/4) / ((4/4) + 12/4)) = 3 /(3+1) = 3/4 = 0.75

So Ans is b

9.

Existing car wash has 4 bays , so size of existing car wash (Se) = 4

Proposed Car wash has 12 Bays,so size of existing car wash (Sp) = 1

So Probablity of a customer traveling from Area 3 to existing car wash according to the Huff location Model

P3e= (Se/4 ) / ((Se/4) + (Sp/4)) = (4/6) / ((4/6) + 12/4)) = 2/11 = 0.18

So Ans a

10. Similarly calculating probablity for all the cases -

Market Share.

so Ans is d 0.75

Area Total Customers Proablity of Existing Car wash Proablity of Proposed Car wash Customers going to Existing Car Wash Customers going to Proposed Car Wash 1 1000 0.25 0.75 250 750 2 500 0.4 0.6 200 300 3 1000 0.18 0.82 180 820 Total 630 1870

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