Demand during lead-time for HP printers at a Sam\'s club store is normally distr

Question

Demand during lead-time for HP printers at a Sam's club store is normally distributed, with a mean of 500 and a standard deviation of 150. The store manager continuously monitors inventory and order 1,000 printers when the inventory drops to 800 printers. How much safety inventory does the store carry? What service level does Sam's club achieve as a result of this policy?

Please show all steps clearly. I will give the points to who can provide an answer with all steps included showing how they got the answer.

Explanation / Answer

How much safety inventory does the store carry?

ROP = 800

DL = DL = 250*2 = 500

ss = ROP %u2013 DL = 800 %u2013 500 = 300

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Average demand per unit time R = 500

Lead time, L = 2

SD of demand per unit time sR = 150

Order quantity Q= 1000

Reorder Point 800 =============================== Distribution of demand during replenishment lead time Mean demand during lead time RL = 1000

SD of demand during lead time sL = 212

Outputs Safety Inventory ss = -200

Cycle Service Level CSL = 0.17

Expected shortage per replenishment cycle ESC = 219.68

Fill Rate fr = 0.78

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