Bryson Carpet Mills produces a variety of different carpets. Changing from produ
ID: 359873 • Letter: B
Question
Bryson Carpet Mills produces a variety of different carpets. Changing from production of one carpet to another involves a setup cot of $1,000. One particular carpet costs $5 per yard to produce. Annual demand for this style is 120,000 yards. BCM produces carpet 300 days per year. The production process is most efficient when 4,000 yards per day are produced. Inventory carrying cost is estimated at 20% annually.
Given the information above, on a cost basis, what is the optimum run size for the carpets? ____
How many batches of the carpets will be run each year? __________
At EPQ, what will be the maximum inventory for each run cycle (batch)?______________
On average, how many yards of carpets will the factory have in its inventory? ____________
For each production run, over how many days will the factory be producing carpets (round up to a full day)? ___________
How many days (round up to a full day) will the maximum inventory last? _____________
Bryson Carpet Mills produces a variety of different carpets. Changing from production of one carpet to another involves a setup cot of $1,000. One particular carpet costs $5 per yard to produce. Annual demand for this style is 120,000 yards. BCM produces carpet 300 days per year. The production process is most efficient when 4,000 yards per day are produced. Inventory carrying cost is estimated at 20% annually.
Explanation / Answer
This problem will be solved using Standard Economic Production Quantity ( EPQ) model
Accordingly ,
EPQ = Square root ( 2 x Co x D /Ch x ( 1 – d/p) )
Where,
Co = Set up cost = $1000
Annual demand = D = 120,000 yard
Ch = Inventory carrying cost per yard = 20% of $5 = $1 per yard
‘d = Daily demand
= Annual demand / Number of days in a year
= 120,000/ 300
= 400
.p = Daily production capacity = 4000
Therefore ,
EPQ = Square root ( 2 x 1000 x 120000/ 1 x ( 1 – 400/4000))
= Square root ( 2 x 1000 x 120000 / 0.9)
= 16329.93 ( 16330 rounded to nearest whole number )
Therefore , optimum run size for the carpets = 16330 yards
Number of batches which will run in a year
= Annual demand / EOPQ
= 120000/ 16330
=7.35 ( rounded to 2 decimal places )
Maximum Inventory for each batch cycle
= EPQ x ( 1 – d/p )
= 16330 x ( 1 – 400/4000)
= 16330 x 0.9
= 14697
Average number of yards of carpet factory will have in inventory
= Maximum Inventory / 2
= 14697/ 2
= 7348.5 yards
For each production run, number of days the factory will be producing item
= EPQ/ Daily Production quantity
= 16330/4000
=4.08 days ( rounded to two decimal places )
Number of days the maximum inventory will last
= Maximum inventory / Daily demand
= 14697 / 400
= 36.74 days ( rounded to two decimal places )
OPTIMUM RUN SIZE FOR THE CARPETS = 16330 YARDS
NUMBER OF BATCHESOF THE CARPETS WILL RUN EACH YEAR = 7.35
MAXIMUM INVENTORY FOR EACH RUN CYCLE = 14697 YARDS
YARDS OF CARPETS THE FACTORY WILL HAVE IN INVENTORY ON AVERAGE = 7348.5 YARDS
NUMBER OF DAYS THE FACTORY WILL PRODUCE FOR EACH PRODUCTION RUN = 4.08 DAYS
NUMBER OF DAYS MAXIMUM THE INVENTORY WILL LAST = 36.74 DAYS
OPTIMUM RUN SIZE FOR THE CARPETS = 16330 YARDS
NUMBER OF BATCHESOF THE CARPETS WILL RUN EACH YEAR = 7.35
MAXIMUM INVENTORY FOR EACH RUN CYCLE = 14697 YARDS
YARDS OF CARPETS THE FACTORY WILL HAVE IN INVENTORY ON AVERAGE = 7348.5 YARDS
NUMBER OF DAYS THE FACTORY WILL PRODUCE FOR EACH PRODUCTION RUN = 4.08 DAYS
NUMBER OF DAYS MAXIMUM THE INVENTORY WILL LAST = 36.74 DAYS
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