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 10,700
wheel bearings each year. This order has been stable for some time. Setup cost for Wheel-Rite is $41 and holding cost is $0.50 per wheel bearing per year. Wheel-Rite can produce 480 wheel bearings per day. Cal-Tex is a just-in-time manufacturer and requires that 50 bearings be shipped to it each business day.
a) What is the optimum production quantity?.
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?
Production rate(p) = 480 per day
Demand rate(d) = 50 per day
Annual demand(D) = 10700 units
Set up cost(S) = $41
Holding cost (H) = $0.50
A) Optimum production size(Q) = sqrt of {2DS / H [1-(d/p)]}
= sqrt of {(2x10700x41) /0.50[1-(50/480)]}
= Sqrt of [877400/0.50(1-0.10417) ]
= sqrt of [877400/(0.50 x 0.89583)]
= sqrt of (877400/0.447915)
= √1958853.8003
= 1400 units
b) Maximum inventory ( I - max) = (Q/p) (p-d) = (1400/480)(480-50) = 2.917 x 430 = 1254.31 or rounded off to 1254 units
C) Number of production run per year = D/Q = 10700/1400 = 7.64
d) Annual holding cost = [(I-max / 2) H] = (1254/2)0.50 = $313.50
Annual setup cost = (D/Q) S = (10700/1400)41 = $313.36
Total cost = Annual holding cost + Annual setup cost
= $313.50 + $313.36
= $626.86
Arthur Meiners is the production manager of Wheel-Rite, a small producer of metal parts. Wheel-Rite supplies...
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 10,700wheel bearings each year. This order has been stable for some time. Setup cost for Wheel-Rite is $39 and holding cost is $0.60 per wheel bearing per year. Wheel-Rite can produce 520 wheel bearings per day. Cal-Tex is a just-in-time manufacturer and requires that 48 bearings be shipped to it each business day. a) What is the optimum...
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