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Weekly demand for Canon printers at a BestBuy store is normally distributed with a mean of...

  1. Weekly demand for Canon printers at a BestBuy store is normally distributed with a mean of 250 and a standard deviation of 80. Inventory is continuously monitored and an order of 1,000 printers is placed each time the inventory drops to 950 printers. The replenishment lead-time is three weeks.
  1. How much safety inventory does the store carry? What is the CSL?
  2. Assume that the supply lead-time from Canon is normally distributed with a mean of 3 weeks and a standard deviation of 2 weeks. How much safety inventory should BestBuy carry if it wants to provide a CSL of 97 percent?
Math   Statistics-And-Probability   
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Answer #1

ANSWER::

a)

Reorder point = Average demand during lead time+safety stock

or, 950 = 3*250 +safety stock

or, safety stock = 200 (Ans)


safety stock = z*standard deviation of daily demand *sqrt(lead time) = z*80*sqrt(3)

or, z = 200/(80*sqrt(3))

= 1.443375673

CSL = NORM.S.DIST(1.443375673,TRUE)

= 0.925542663

= 92.5542663%

b)

If lead time is also variable then standard deviation of daily demand during lead time = sqrt(lead time*standard deviation of daily demand^2+daily demand^2* standard deviation of lead time^2) = sqrt(3*80^2+250^2*2^2)

= 518.8448708

Safety stock = z*standard deviation of daily demand during lead time = normsinv(0.97)*518.8448708

= 975.8401166

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