A product with an annual demand of 900 units has Co = $23 and Ch = $5. The deman

Question

A product with an annual demand of 900 units has Co = $23 and Ch = $5. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with =26 and =6. a.What is the recommended order quantity? b. What are the recorder point and safety stock if the firm desires at most a 7% probability of stockout on any given order cycle? c. If a manager sets the reorder point at 31, what is the probability of a stockout on any given order cycle? d. How many times would you expect a stockout during the year if the reorder point were used?

Explanation / Answer

a)

Annual demand of the product = D = 900 units

Cost of ordering = Co = $23

Cost of holding   = Ch = $5

Recommended order quantity

= ( 2 x Co X D /Ch )

= ( 2 x 23 x 900 /5)

=91

b)

Probability of stockout = 7%

Therefore, Service level = 100% - probability of stockout = 100% - 7% = 93%

Z value for service level of 93% = NORMSINV (0.93) in excel = 1.476

Safety stock = Zvalue x Standard deviation of demand during led time =1.476 x 6 = 8.856

( 9 when rounded to next higher integer)

Thus,

Reorder point = Lead time demand + Safety stock = 26+9=35

c)

At reorder point = 31:

Reorder point = Demand during lead time + Zvalue x Standard deviation of demand during lead time

Or, 31 = 26 + 6.Z

Or, Z = 5/6 = 0.8333

From Normal distribution table , corresponding probability = 0.7967

Therefore probability of stockout = 1 – 0.7967 = 0.2033

d)

Average number of orders in a year

= Annual demand / Optimum order quantity

= 900/91

Therefore expected number of stockouts

= Average number of stockouts x Probability of stockout

= 900/91 x 0.2033

= 2 ( rounded to nearest integer)

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