Assume a fixed-Order Quantity system. A company makes 450 bicycles per month thr
ID: 451553 • Letter: A
Question
Assume a fixed-Order Quantity system. A company makes 450 bicycles per month throughout the year. They purchase tires from a supplier with an ordering cost of $50 per order and carrying costs of $3 per tire. The lead time is 3 days. Clearly specify any reasonable assumptions that are necessary.
a. What is the EOQ?
b. What are the carrying costs, order costs and total costs at the EOQ?
c. How long is the order cycle?
d. Assuming a desired 98% service level and a standard deviation in lead time of 12 day, what is the reorder point?
e. Assuming a desired 95% service level and a standard deviation in usage of 75 tires per month, what is the reorder point?
Now assume a fixed-interval system for the company described above.
f. What is the optimal time interval for ordering?
g. What amount would be ordered if there are 400 tires in inventory and a 98% service level is desired?
Explanation / Answer
(a)Economic Order Quantity = sqrt( 2 * D * S / H)
where: D = annual demand for tire
but we have monthly demand for bicycle
let’s assume that demand is constant throughout year and one bicycle have two tires
therefore annual demand for tire is = 450 * 12 * 2= 10,800 tires
S is order cost = $ 50 per order
H is holding cost = $ 3 per tire
Now EOQ = sqrt (2 * 10,800 * 50 / 3 ) = 600 tires
(b) Economic order quantity (EOQ) is the order quantity of inventory that minimizes the total cost of inventory management.
Order cost is cost that incurred while obtaining additional inventories.
Annual order cost = ordering cost per order * annual Demand / EOQ
= 50 * 10800 / 600 = $900
Carrying costs is the cost that incurred on holding inventory in hand.
Annual carrying cost = carrying cost per tire * EOQ / 2
= 3 * 600/ 2 = $900
Total inventory costs = Order costs + Holding costs = 900 + 900 = $ 1800
(c) order cycle = number of days in a year / (D/EOQ) (assume 365 days)
= 365 / (10800 /600) = 20.28 days
(d) Reorder point = daily demand x lead time + safety stock
OR,
R = D L + z * st. dev. of lead time * sqrt (L)
Where
R is the reorder point =?
D is daily demand = monthly demand / 30 = 450*2 /30 = 30 tire (assume 30 days in a month and 2 tire in a bicycle)
L is the lead time = 3 days
z * st. dev. Of demand * sqrt (L) = safety stock
where z is the number standard deviation of 98% services level which = 2.33
Standard deviation of lead time is 1/2 day or 0.5 days
Now putting all the values in the formula
R = 30* 3 + 2.33*0.5 * sqrt(3)
= 90 + 2.02
= 92.02 tire is the reorder point
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