Question

Problem 14-31 (Algorithmic)

A product with an annual demand of 1100 units has C_o = $24.5 and C_h = $7. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 30 and σ = 6.

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 3% 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 35, 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

Annual demand, D = 1,100
Ordering cost, Co = $24.5
Unit holding cost, Ch = $7 per annum
µ_LTD = 30 and σ_LTD = 6.

(a)

Q* = (2.D.Co / Ch)^1/2 = sqrt(2*1100*24.5 / 7) = 87.75

(b)

In-stock probability = 97%, So, z = Normsinv(0.97) = 1.88

Safety stock = z.σ_LTD = 1.88*6 = 11 units

Reorder point = µ_LTD + Safety stock = 30+11 = 41 units

(c)

Reorder point = 35

So, safety stock = ROP - µ_LTD = 35 - 30 = 5 units

So,

z.σ_LTD = 5
or, z = 5 / 6

So, In-stock probability = Normsdist(5/6) = 0.7977

So, P(Stockout/cycle) = 1 - 0.7977 = 0.2023

Total number of orders per year = D / Q* = 1100 / 87.75 = 12.536

So, number of order cycles for which the stock-out happens = 12.536 * 0.2023 = 2.54