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 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?

Answer 1

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