Ross White’s machine shop uses 2500 brackets during the course of a year, and th
ID: 2767945 • 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
Solution:
a. The total cost model for this system is as follows:-
TC = ½ (1 – D/P)QCh + (D/Q)Co
Where TC is total cost
D is Daily Demand rate for the product
P is Daily Production rate for the product
Q is units at a daily production rate
Ch is the annual holding cost and
Co is the annual ordering cost
b. The Economic Order Quantity (EOQ or Q) is
Q = (2DCo/Ch)
Q = (2*2500*18.75/1.5)
Q =250
c. Since we need to order 2500/250 = 10 times a year, and the lead time is 2 days, the time between orders is
365/10 – 2 = 34.5 (days)
d. The Reorder Point (ROP) is
ROP=LT*D
ROP = (2/365)*2500
ROP =13.6986 ~14
e. Average inventory =Q/2
Average inventory =250/2
Average inventory =125
Annual inventory holding cost=Q*Ch/2
Annual inventory holding cost =125*1.5
Annual inventory holding cost =$187.5
D/Q=2500/250=10, so 10 orders would be made each year.
Annual ordering cost = Co*D/Q = 18.75*10=$187.5
f. Total annual cost= Annual inventory holding cost+ annual ordering cost + purchase cost
Total annual cost =187.5+187.5+2500*15
Total annual cost =$37875
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