Demand for gold-filled lockets at Sam\'s Bargain Jewelry is normally distributed

Question

Demand for gold-filled lockets at Sam's Bargain Jewelry is normally distributed with a mean of 10 lockets per day and a standard deviation of 2 lockets. Lead time is 16 days. Sam orders the lockets every 9 days and desires a 95% customer service level. 19. What is the desired safety stock level? a. 160 b. 8 d. 10 e. none of the above 20. What is the target inventory level? a. 250 b. 176 c. 263 d. 267 e. none of the above 21. Suppose two days before receiving order from the supplier, the supplier informed Sam that the order would arrive in 4 days instead of 2 days. Sam has 45 units on hand, what the probability of a stockout before the order arrives? a. 24% b. 31% C. 4% d. 11% e. none of the above 0 F2 F3 F4 FS F7 F9

Explanation / Answer

Q 19. c. 17

Q 20. d. 267

Q 21. d. 11%

demand during 4 days = 4*10 = 40

Std dev of demand duing 4 days = 2*4 = 4

z-stat = (45 - 40)/4 = 1.25

F(z) = NORMSINV(1.25) = 0.89

Probability of stockout = 1 - 0.89 = 0.11 = 11%

Daily Demand µ = 10 Standard Deviation of Daily Demand = 2 Lead Time (Days) L = 16 Service level = 95% Z-value corresponding to Service Level z = NORMSINV() 1.65 Review Period (days) P = 9 Standard Deviation of Demand over P+L = * (P+L) 10 Safety stock ss = z**(P+L) 17 Target Inventory Level T = µ*(L+P) + ss 267 On-Hand Inventory OH = 200 Order Quantity Q = T - OH 67

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