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Probability- minimum inventory to satisfy demand

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data
    There are 20 customer locations, the demand in each location is normal with mean 60 and SD 20. All 20 locations have independent probabilities.
    The goal is to cover all of the demand in a month at least 95% of the times. What's the minimum total inventory the company should hold?


    2. Relevant equations



    3. The attempt at a solution

    It doesn't sound like I need to find the confidence interval. So, I know that the total mean is 1200 and the total standard deviation is 400. So, since the sum is also normal, I just go two SDs to the right to find the 95%.
    If I got 2 SDs to the right, I get 2000.

    Is this the correct method to use here?
     
    Last edited: Sep 13, 2011
  2. jcsd
  3. Sep 13, 2011 #2

    Ray Vickson

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    G

    How do you figure that the total standard deviation is 400? I get something very different.

    RGV
     
  4. Sep 13, 2011 #3
    oh shoot, that's the variance I guess.
    so, SD is just 20.

    But, now I'm thinking maybe I should use the gaussian pdf...?
    EDIT:
    I used excel's =NORMINV(0.975,1200,20)
    And I get 1240 both ways... so I think its good.
    But if wanted to use the gaussian pdf, how would you calculate it?
     
    Last edited: Sep 13, 2011
  5. Sep 14, 2011 #4

    Ray Vickson

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    (i) You still don't have the correct standard deviation.

    (ii) Where does the 0.975 come from?

    RGV
     
  6. Sep 14, 2011 #5
    Ya I'm a lil rusty
    it's sqrt(20)*20
    and the prob is just .95
     
  7. Sep 14, 2011 #6

    Ray Vickson

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    Right!

    RGV
     
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