The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair. The annual holding cost per unit is $25, annual demand is 180,000 chairs, and the ordering cost is $150 per order. The lead time is 5 days. Because demand is variable (standard deviation of daily demand is 30 chairs), PCE has decided to establish a customer service level of 96%. The store is open 300 days per year. Required:
a. What is the optimal order quantity?
b. What is the safety stock?
c. What is the reorder point?
d. What is the optimal annual total inventory cost?

Solution :

Given data:

Annual demand, D = 180,000 chairs

Ordering cost, F = $ 150 per order

Annual holding cost per unit, C = $25

Lead time of order, L = 5 days

Standard deviation of order during lead time = 30

a). The optimal order quantity

 = 1469.69

 = 1470 (rounding off)

b). The Z value of the customer service of 90%,

i.e., the probability of 0.90 as per normal distribution table = 1.29

∴  Safety stock = Z value x standard deviation of order during lead time

                         = 1.29 x 30

                        = 38.7

                        = 39 (rounding off)

c). The reorder point

 = 3039

d). The optimal annual total inventory cost

 = 18367.34 + 18375

 = $ 36,742.34

answerthe united states of america;