Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights
ID: 359203 • Letter: R
Question
Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300 days per year. It has orders for about 12,200 flashing lights per year and has the capability of producing 100 per day. Setting up the light production costs $51. The cost of each light is $1.05. The holding cost is $0.15 per light per year.
(round your response to the nearest whole number).
a) What is the optimal size of the production run:
b) Average Holding cost per year:
c) Average setup cost per year:
d)Total cost per year= Average holding cost per year + Average setup cost per year+ Cost to purchase 12200 light.
Explanation / Answer
This problem will be solved by standard Economic Production Quantity ( EPQ) model. The EPQ can be formulated as :
EPQ = Square root ( 2 x Cs X D/ Ch x ( 1 – d/p))
Where,
Cs = Set up cost = $ 51 / set up
D = Annual Demand = 12200 flashing light
Ch = Annual unit holding cost = $0.15 light per year
‘d = Daily demand = 12200 / 300 days
‘p = Daily production capacity = 100
Therefore ,
EPQ = square root ( 2 x 51 x 12200 / 0.15 x ( 1 – 12200/(300 x 100))
= Square root ( 2 x 51 x 12200 / 0.15 x 0.594)
= 3737.15 ( 3737 rounded to nearest whole number )
OPTIMAL SIZE OF PRODUCTION RUN = 3737
Maximum Inventory = EPQ x ( 1 – d/p) = 3737 x ( 1 – 12200/30000) = 3737 x0.594 =2219.77 ( 2220 rounded to nearest whole number )
Minimum Inventory = 0
Average Inventory
= ( Maximum Inventory + Minimum Inventory )/ 2
= ( 2220 + 0 )/ 2
= 1110
Thus , Average Holding cost per year
= Average inventory x Holding cost per light per year
= 1110 x 0.15
= $ 166.50
Average set up cost per year
= Cost per set up ( Cs) x Number of set ups
= Cs x Annual demand /EPQ
= 51 x 12200 /3737
=$166.50
Cost to purchase = Unit cost x Annual demand = $1.05 x 12200 = $12810
Therefore,
Total cost per year
= Annual holding cost + annual set up cost + Cost to purchase
= $ 166.50 + $166.50 + $12810
= $333 + $12810
= $ 13143
AVERAGE HOLDING COST PER YEAR = $166.50
AVERAGE SET UP COST PER YEAR = $166.50
TOTAL COST PER YEAR = $13143
OPTIMAL SIZE OF PRODUCTION RUN = 3737
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