Question

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?

Answer 1

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

   $=\sqrt{\frac{2FD}{C}}$

  $=\sqrt{\frac{2\times 150 \times 180,000 }{25}}$

 = 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

 $= \text{Average demand per day} x \text{Demand lead time (day) + Safety stock}$

 $=\frac{\text{annual demand}}{\text{300 days}} \times \text{ Demand Lead time (days) + Safety stock}$

 $=\frac{180,000}{300} \times 5 + 39$

 = 3039

d). The optimal annual total inventory cost

  $\text{= Annual ordering cost + Annual Inventory carrying cost}$

  $\text{= Number of orders} \times \text{Ordering cost + Average inventory} \times }$ $\text{Inventory holding cost per unit per year}$

  $=\frac{\text{annual demand}}{\text{optimum order quantity}} \times \text{ordering cost+}\frac{\text{optimum ordering cost}}{2}\times C$

  $=\frac{180,000}{1470} \times 150 + \frac{1470}{2} \times 25$

 = 18367.34 + 18375

 = $ 36,742.34