Question

A firm orders 400 wheels each month. The ordering cost is $8 per order. The cost to buy one wheel is $4 per wheel. Annual carrying costs are 50% of unit cost. The supplier lead time is 2 operating days. The firm operates 240 days per year. Each order is received from the supplier in a single delivery. There are no quantity discounts. Please clearly write down the formulation and calculation for your answers.

What quantity should the firm order with each order?

How many times per year will the firm order?

How many days will elapse between two consecutive orders?

What is the reorder point if the firm carries a safety stock of 10 wheels

Answer 1

1) What quantity should the firm order with each order?

the economic order quantity (EOQ) = √(2SD/H)

• S = cost per order = $8
• D = annual demand = 400 x 12 = 4,800
• H = holding cost per year = $4 x 50% = $2

EOQ = √[(2 x $8 x 4,800) / $2] = √38,400 = 195.96 ≈ 196 units

2) How many times per year will the firm order?

4,800 units / 196 units = 24.49 times

3) How many days will elapse between two consecutive orders?

240 working days / 24.49 times = 9.8 days

4) What is the reorder point if the firm carries a safety stock of 10 wheels

reorder point = (average daily unit sales x delivery lead time) + safety stock

• average daily unit sales = monthly demand / number of days worked per month = 400 / 20 = 20 units
• delivery lead time = 2 days
• safety stock = 10 units

reorder point = (20 units x 2) + 10 = 50 units