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