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
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