Question

optimal reorder point in terms of number of cups)? 1. A product with an annual demand of 1000 units has C = $25.50 and Ch = $8. The demand exhibits some variability such that the lead-time demand follows a normal prob- ability distribution with u = 25 and 6 = 5. a. What is the recommended order quantity? b. 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? c. If a manager sets the reorder point at 30, what is the probability of a stock-out on any given order cycle? How many times would you expect a stock-out during the year if this reorder point were used?

Answer 1

Annual demand, D = 1000 units

a)

Recommended order quantity = sqrt(2DCo/Ch)

= sqrt(2*1000*25.5/8)

= 80 units

-----------------------------------------

b)

for 2% probability of stockout, z value = NORMSINV(1-2%) = 2.05

Safety stock = z$\sigma$ = 2.05*5 = 10 units (rounded off)

Reorder point = $\mu$ +safety stock

= 25+10

= 35 units

-----------------------------------------

c)

For given reorder point (R) of 30, z value = (R-$\mu$)/$\sigma$

= (30-25)/5

= 1

P(z) = NORMSDIST(1) = 0.84

Probability of stockout = 1-0.84

= 16 %

Number of order cycles per year = D/Q

= 1000/80

= 12.5

Number of times stockout = 12.5*16%

= 2 times