Arthur Meiners is the production manager of Wheel-Rite, a small producer of meta
ID: 363443 • Letter: A
Question
Arthur Meiners is the production manager of Wheel-Rite, a small producer of metal parts. Wheel-Rite supplies Cal-Tex, a larger assembly company, with
11,300
wheel bearings each year. This order has been stable for some time. Setup cost forWheel-Rite is
$39,
and holding cost is
$0.80
per wheel bearing per year. Wheel-Rite can produce
510
wheel bearings per day.Cal-Tex is a just-in-time manufacturer and requires that
46
bearings be shipped to it each business day.
a) What is the optimum production quantity?
nothing
units (round your response to the nearest whole number).
b) What is the maximum number of wheel bearings that will be in inventory at Wheel-Rite?
c) How many production runs of wheel bearings will Wheel-Rite have in a year?
d) What is the total setup plus holding cost for Wheel-Rite?
Explanation / Answer
The optimal production quantity ( EPOQ ) will be defined as :
EPQ = Square root ( 2 x Cs x D / Ch )
Where,
Cs = Cost of set up for wheel rite = $39
D = Annual demand = 11300 wheel bearing
Ch = Annual inventory holding cost = $0.80 per unit
‘d = Daily demand = 46
P = Daily production capacity = 510
Therefore ,
EPQ = Square root ( 2 x 39 x 11300 / 0.80 x ( 1 – 46/510))
= Square root ( 2 x 39 x 11300 / 0.80 x 0.9098)
= 1100.44 ( 1100 rounded to nearest whole number )
OPTIMAL PRODUCTION QUANTITY = 1100
Maximum number of wheel bearings that will be in inventory at wheel rite
= EPQ X ( 1 – d/p)
= 1100 x ( 1 – 46/510)
= 1100 x 0.9098
= 1000.78 ( 1001 rounded to nearest whole number )
MAXIMUM NUMBER OF WHEEL BEARINGS THAT WILL BE IN INVENTORY = 1001
Number of production runs wheel bearing will have in a year
= Annual demand / EPQ
= 11300 / 1100
= 10.27 ON AVERAGE
NUMBER OF PRODUCTION RUNS = 10.27 ON AVERAGE
Total annual set up cost
= Set up cost ( Cs) x Number of set ups in a year
= Cs x Annual Demand / EPQ
= 39 X 11300 / 1100
= $400.63
Total annual holding cost
= Annual unit holding cost ( Ch ) x Average inventory
= Ch x Maximum inventory/ 2
= Ch x EPQ x ( 1 – d/p) / 2
= 0.8 x 1100 x ( 1 - 46/510)/ 2
= $400.31
Thus total set up plus holding cost = $400.63 + $400.31 = $800.94
TOTAL SET UP COST PLUS HOLDING COST = $800.94
OPTIMAL PRODUCTION QUANTITY = 1100
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