3. A company is about to begin production of a new production. The manager pf th
ID: 371742 • Letter: 3
Question
3. A company is about to begin production of a new production. The manager pf the department that will produce one of the components for the product wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of 200 units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, 50 weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $400. Inventory holding costs will be $10 a year. a. What run quantity should be used to minimize total annual cost? b. How many days does it take to produce the optimal run quantity? c. How often does the department have to run the production for this component (i.e., cycle time)? d. What is the average amount of inventory? e. What is the annual total cost?
Explanation / Answer
This case will be solved using Economic Production Quantity ( EPQ ) model.
Given are following data :
‘d = Daily requirement = 80 units
‘p = Daily production rate = 200 units
D = Annual requirement = 80 units/day x 5 days/ week x 50 weeks = 20,000 units
Cs = Machine set up cost = $400
Ch = Annual unit inventory holding cost = $10
Therefore ,
EPQ = Square root ( 2 x Cs x D / Ch x ( 1 – d/p))
= Square root ( 2 x 400 x 20000 / 10 x ( 1 – 80/200)))
= Square root ( 2 x 400 x 20000 / 6)
= 1633
Production run quantity to minimize total annual cost = 1633
PRODUCTION RUN QUANTITY TO MINIMIZE TOTAL ANNUAL COST = 1633
Number of days it takes to produce optimal production quantity
= Optimal production run quantity / Daily production rate
= 1633 / 200
= 8.165
NUMBER OF DAYS IT TAKES TO PRODUCE OPTIMAL RUN QUANITY = 8.165 DAYS
Annual requirement of 20,000 units are catered in 250 days
Therefore, Number of days corresponding to requirement of 1633 units = 250/ 20000 x 1633 = 20.41 days
CYCLE TIME = 20.41 DAYS
Average amount of inventory
= ½ x Optimal production quantity ( 1 – d/p)
= 1/ 2 x 1633 x ( 1 - 80/200 )
= 0.5 x 1633 x 0.6
= 489.9 (490 rounded to nearest whole number)
AVERAGE AMOUNT OF INVENTORY = 490
Annual inventory holding cost = Unit inventory holding cost x Average inventory = 10 x 490 = $4900
Annual set up cost = Machine set up cost ( Cs ) x Number of set ups
= CS x Annual demand /Optimal production quantity
= 400 x 20000/1633
= 4898.95 ( $4899 rounded to nearest whole number )
Annual total cost
= Annual inventory holding cost + Annual set up cost
= $4900 + $4899
= $9799
ANNUAL TOTAL COST = $9799
PRODUCTION RUN QUANTITY TO MINIMIZE TOTAL ANNUAL COST = 1633
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