A store faces demand for one of its popular products at a constant rate 2.400 un
ID: 470579 • Letter: A
Question
A store faces demand for one of its popular products at a constant rate 2.400 units per year it costs 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 unit and sells it for $160 per unit. At the moment the store uses an order quantity of 60 units. Assume EOQ model assumptions are satisfied and 300 days a year. It there are two blank boxes in any question, then you must put one of the following words in the second box units, dollars, days, year, orders per year, dollars per year, units per order Answer the following questions (you should not use any commas in your answer) You must solve questions[1] through [6] assuming the store uses the Current order quantity. Questions [8] through [10] must be solved using the optimal order quantity. To fulfill the demand, the store must place orders per year. The average inventory level The length of an inventory cycle is The annual ordering cost is The annual holding cost is The time between any two orders is days The annual purchase cost is The optimal order quantity is The optimal order quantity is The optimal annual holding cost is The optimal number of orders per year isExplanation / Answer
A = annual demand = 2,400 units per year
C = unit cost of pot = $90
S = Ordering cost per order = $70
H = Annual carrying cost ($) = $20 per unit per year
Working days = 300 per year
Lead time = 12 days
Selling price = P = $160
Situation A: Order quantity Q = 160 units
1) To fulfill the demand, the store must place 15 orders per year
Number of orders placed = Annual demand/order quantity
Number of orders placed = 2400/160 = 15 orders
2) the average inventory level = 80 units
Average inventory level = (minimum inventory + order quantity)/2
Average inventory level = (0 + 160)/2 = 80
3) the length of inventory cycle = 20 working days
length of inventory cycle = Number of working days/number of order placed
length of inventory cycle = 300/15 = 20 working days
4) The annual ordering cost is 1050 dollar per year
Annual ordering cost = Number of orders x cost per order
Annual ordering cost = 15 x $70 = $1050
5) The annual holding cost is 1600 Dollar per year
Annual holding cost = Average inventory x inventory holding cost per unit per year
Annual holding cost = 80 x $20 = $1600
6) The time between any two orders is 20 days
7) the annual purchase cost is 216000 Dollar per year
Annual purchase cost = Unit Cost x Annual Demand
Annual purchase cost = C x A = $90 x 2400 = $216,000
Situation B: W=EOQ
8) the optimal order quantity is 130 units per order
Qo=(2DS/H)=(2(2400)70/20)= 129.61 units
Qo = 130 units
9) Optimal annual holding cost is 1300 dollar per year
Annual holding cost = Average inventory x inventory holding cost per unit per year
Annual holding cost = [(0 + 130)/2] x $20
Annual holding cost = 65 x $20 = $1300
10) The optimal; number of orders per year is 19 orders per year
Number of order = A/ Qo = 2400/130 = 18.46
Number of order = 19 orders
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