Wicomico 3DeLight makes 3D printers for entrepreneurs. The business is open 275
ID: 364414 • Letter: W
Question
Wicomico 3DeLight makes 3D printers for entrepreneurs. The business is open 275 days per year. It has been selling 9000 3D printers per year and can produce 100 per working day. Getting a production run started costs $175, and the holding cost for a 3D printer is $1500/printer/year. The manufacturing cost of each 3D printer is $500. Part a - What is the size of the optimal production run for the company? Part b – what is Wicomico 3DeLight’s total costs for the year, including the cost of the 3D printers? Please walk me through this question step by step!
Explanation / Answer
By consolidating multiple SKUs, the overall variability of such consolidate groups are reduced Since overall variability (i.e. standard deviation) of such group is less than sum of standard deviation of individual items, safety stock requirement of such consolidated groups also thus gets reduced. As a result, the overall safety stock requirement thus gets reduced from 6600 to 1040
The problem will be solved using Economic Production Quantity ( EPQ ) model
EPQ = Square root ( 2 x Cs x D / Ch x ( 1 – d/p))
Where,
D = Annual demand = 9000
Cs = Production run set up cost = $175
Ch = Annual unit holding cost = $1500 per printer per year
‘d = Daily demand = 9000/275
P = Daily production capacity = 100
Therefore ,
EPQ = Square root ( 2 x 175 x 9000/ 1500 x ( 1 – 9000/( 275 x 100))
= Square root ( 2 x 175 x 9000/ ( 1500 x 0.672))
= Square root ( 3125)
= 55.90 ( 56 rounded to nearest whole number )
SIZE OF OPTIMAL PRODUCTION RUN FOR THE COMPANY = 56 UNITS
Annual purchase cost = Manufacturing Cost / unit x Annual demand = $ 500 x 9000 = $4500000
Annual ordering cost = Ordering cost / order x Number of orders
= Cs x Annual demand / POQ
= 175 x 9000/56
= $28125
Annual holding cost = Annual unit holding cost x Average inventory
= $1500 x EPQ X ( 1 – d/p) /2
= $1500 X 56x 0.672 /2
= $28224
Thus total cost for the year
= Annual purchase cost + Annual ordering cost + Annual holding cost
= $4500000 + $28125 + $28224
= $4556349
WICOMICO 3DELIGHT’S TOTAL COST FOR THE YEAR = $4556349
SIZE OF OPTIMAL PRODUCTION RUN FOR THE COMPANY = 56 UNITS
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