Question

A product with an annual demand of 1000 units has C_o = $25.5 and C_h = $8. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 25 and σ = 5.

1. What is the recommended order quantity? If required, round your answer to two decimal places.
   
   Q^* = __________
   
2. What are the reorder point and safety stock if the firm desires at most a 2% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number.
   
   Record point = __________
   
   Safety stock = __________
   
3. If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? If required, round your answer to four decimal places.
   
   P(Stockout/cycle) = _________
   
   How many times would you expect a stock-out during the year if this reorder point were used?
   
   Number of Orders = _______

Answer 1

Given

µ = 25 and σ = 5

Demand D = 1000

C_o = $25.5

C_h = $8

a)

Recommended order quantity, Q = sqrt( 2*D*C0/Ch) = sqrt(2*1000*25.5/8) = 79.84

b)

2% probability of stock-out

alpha = 0.98

Z-value at 0.98 = 2.054

Reorder point = µ + z*σ = 25 + 2.054*5 = 35.27 ~ 35

Safety stock = z*σ = 2.054*5 = 10.27 ~ 10

c)

Reorder point at 30

Reorder point = µ + z*σ

35 = 30 + z * 5

z = 1

Corresponding service level at z=1, = 0.8413

P(Stock out/cycle) = 1-0.8413 = 0.1587 = 15.87%

Number of Order = D/Q = 1000/79.84 = 12.5250