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a store faces demand for one its popular products at a constant rate of 4800 uni

ID: 470641 • Letter: A

Question

a store faces demand for one its popular products at a constant rate of 4800 units per year. it cost the store $70 to process an order to replenish stock and $20 per unit per year to carry the item in inventory. A shipment from the supplier is typically received 12 working days after an order is placed. The store buys the product for $90 per units and sells it $160 per unit. At the moment the store uses an order quantity of 480 units. Assume EOQ model assumptions are satisfied and 300 days a year. What is the demand order per yr? Average inventory level? length of an inventory cycle?Annual holding cost?Time between any two orders? Annual purchasing cost? Optimal order quantity? Optiaml annual holding cost? Optimal number of orders per yr?

Explanation / Answer

We have following information

Annual demand D = 4800 unit per year

Ordering cost S = $ 70 per order

Holding or carrying cost H = $20 per unit per annum

Lead time = 12 days

Present Order quantity = 480 units

The cost of the item = $90 per unit

Sale price =$ 160 per unit

Number of days in a year = 300 days

For minimum cost, first we have to calculate Optimum Order quantity per order which is EOQ

EOQ = sqrt (2* D*S/H) = sqrt(2*4800*70/20) = 183.3 units

Total Annual Inventory cost = total ordering cost + total carrying cost

= (D/Q)* S + (H*Q)/2 = (4800/183.3)*70 + (20*183.3)/2

=$ 1833+ $1833 = $ 3666

Here EOQ = Q

Now Optimal number of order per year = annual demand / EOQ = 4800/183.3 = 26.2 orders

And Optimal number of days between two orders = No. of days per year / number of orders per year

= 300 / 26.2 = 11.5 days

Average inventory level = Q / 2 = 183.3 /2 = 91.65 units

Where Q = EOQ = 183.3 units

There we have,

What is the demand order per yr? 4800 units

Average inventory level? 91.65 units

length of an inventory cycle? = EOQ/ D = 183.3/4800 = 0.038

Annual holding cost? $1833

Time between any two orders? 11.5 days

Annual purchasing cost? 4800* $90 = $432,000

Optimal order quantity? 183.3 units

Optimal annual holding cost? $1833

Optimal number of orders per yr? 26.2 orders