Weekly demand for Barilla pasta at a Hy-Vee store is normally distributed, with

Question

Weekly demand for Barilla pasta at a Hy-Vee store is normally distributed, with a mean of 250 boxes and a standard deviation of 150 boxes. The store manager continuously monitors inventory and currently orders 1,000 boxes of pasta each time the inventory drops to 600 boxes. Barilla currently takes two weeks to fill an order.
(a) (8 pts) How much safety inventory does the store carry given the current policy?
(b) (8 pts) What service level does store achieve for Barilla pasta with the current policy?
(c) (8 pts) What fill rate does the store achieve with the current policy?
(d) (8 pts) If the Hy-Vee store would like to have a 99% service level, what should the reorder point be?
(e) (13 pts) If the Hy-Vee store would like to have a 99% fill rate, what should the reorder point be?

Explanation / Answer

Answered --
a) How much safety inventory does the store carry?

ROP = 600

DL = DL = 250*2 = 500

ss = ROP – DL = 600 – 500 = 100

b) You may use Excel or the table below. What CSL does Sam’s Club achieve as a result of this policy?

F(600,500,300)

0.631

F(600,250,212.13)

0.951

F(600,500,212.13)

0.681

F(1000,500,300)

0.952

F(1000,250,212.13)

0.999

F(1000,500,212.13)

0.991

sL = ÖLsD = Ö2*150 = 212.13

CSL = F(ROP,DL,sL) = F(600,500,212.13) = 0.681

c) You may use Excel or the table below. What product fill rate does Sam’s Club achieve as a result of this policy?

ESC

–100*(1 – Fs(0.471)) + 212.13*fs(0.471)

43.861

–100*(1 – Fs(0.471)) + 426.26*fs(0.471)

120.317

–50*(1 – Fs(0.235)) + 212.13*fs(0.235)

62.356

–50*(1 – Fs(0.117)) + 426.26*fs(0.117)

146.221

–200*(1 – Fs(0.471)) + 426.26*fs(0.471)

87.723

–200*(1 – Fs(0.235)) + 426.26*fs(0.235)

88.001

Q = 1000

ss = ROP – DL = 600 – 500 = 100

sL = ÖLsD = Ö2*150 = 212.13

ESC = -ss(1 – F(ss/sL,0,1)) + sLf(ss/sL,0,1) = -100*(1 – F(0.471,0,1)) + 212.13*f(0.471.13,0,1)

= 43.861

fr = 1 – ESC/Q = 1 – (43.861/1000) = 0.956

d)You may use Excel or the table below. What is the resulting safety inventory that is achieved as a result of the new CSL value?

F-1(0.95,500,212.13)

848.926

F-1(0.95,500,300)

993.456

F-1(0.95,600,212.13)

948.926

F-1(0.95,600,300)

1093.456

F-1(0.95,1000,300)

1493.456

Fs-1(0.95)

1.645

There are two ways to calculate the resulting safety inventory

Option 1

ss = Fs-1(CSL)*sL = Fs-1(0.95)*212.13 = 348.926

Option 2

ROP = F-1(CSL, DL, sL) = F-1(0.95, 500, 212.13) = 848.926

ss = ROP – DL = 848.926 – 500 = 348.926

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