Ross White’s machine shop uses 2500 brackets during the course of a year, and th
ID: 450930 • Letter: R
Question
Ross White’s machine shop uses 2500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a sup plier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per bracket per year is $1.50 (or 10% of the unit cost) and the ordering cost per order is $18.75. There are 300 working days per year.
a. Develop a total cost model for this system.
b. What is the EOQ for this problem?
c. What is the cycle time?
d. What is the reorder policy?
e. What are the total annual holding and ordering costs associated with your recommended EOQ?
f. What is the total annual cost associated with your recommended EOQ?
Explanation / Answer
1. Total cost = purchase cost + ordering cost + holding cost
In the given problem, purchase cost = number of units x cost per piece
Ordering cost = cost per order x number of orders
Holding cost = holding cost x order quantity / 2
2. Economic order quantity is the quantity at which the total cost w.r.t quantity is equal to 0. It is calculated as sqrt (2 x Annual Demand x Cost per order / Carrying cost per unit)
In the given problem Annual Demand = 2500, Cost per order = 18.75, Carrying cost oer unit = Carrying cost % x cost per unit = 1.5
Thus EOQ = sqrt(2 x 2500 x 18.75 / 1.5) = 250
3. Order cycle time is the time between placing 2 orders. In the given problem at EOQ of 250, the number order orders to be placed = 2500 /250 = 10. Thus order cycle time is 300 / 10 = 30 days
4. The reorder policy is that an order for 250 brackets is placed at the 28th day since there is a 2 day lead time for delivering the brackets
5. Annual holding cost at EOQ = holding cost x order quantity / 2 = 1.5 x 250 / 2 = 187.5
Ordering cost = Cost per order x number of orders = 18.75 x 10 = 187.5 (number of orders from answer 3)
6. Total annual cost associated with EOQ = purchase cost + order cost + holding cost = 2500 x 15 + 187.5 +187.5 = 37875
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