Question

The Big Buy Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year (365 days). It costs the store $60 per order of Munchies, and it costs $0.80 per box per year to keep the cereal in stock. Once an order for Munchies is placed, it takes 4 days to receive the order from a food distributor. Determine the following:
a. The optimal order size
b. The minimum total annual inventory cost
c. The reorder point

Answer 1

Answer:

a. 775 units

b. $670

c. 44 units

Explanation:

a. The computation of the economic order quantity is shown below:

= $\sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}$

= $\sqrt{\frac{2\times \text{4,000}\times \text{\ 60}}{\text{\ 0.80}}}$

= 775 units

b. The minimum total annual inventory cost is

= Ordering cost + carrying cost

where,

Ordering cost =

The number of orders would be equal to

= Annual demand ÷ economic order quantity

= 4,000 ÷ 775 units

= 5.61 orders

Ordering cost = Number of orders × ordering cost per order

= 6 orders × $60

= $360

The carrying cost is

The average inventory would equal to

= Economic order quantity ÷ 2

= 775 units ÷ 2

= 387.5 units

The total cost of ordering cost and carrying cost equals to

Carrying cost = average inventory × carrying cost per unit

= 387.5 units × $0.80

= $310

So, the minimum total annual inventory cost is

= $360 + $310

= $670

The computation of the reorder point is shown below:

= Demand × lead time + safety stock

where, Demand equal to

= Expected demand ÷ total number of days in a year

= 4,000 ÷ 365 days

= 10.95890

So, the reorder point would be  

= 10.95890 × 4 + $0

= 44 units