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 10,300 wheel bearings each year. This order has been stable for some time. Setup cost for wheel rite is $42 and holding cost is $0.70 per wheel bearing per year. Wheel rite can produce 530 wheel bearings per day. Cal tex is just in time manufacturer and requires that 48 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

Solution:

Annual demand (D) = 10,300 wheel bearings

Setup cost (S) = $42

Holding cost (H) = $0.70 per wheel bearing per year

Daily production (p) = 530 wheel bearings per day

Daily Demand (d) = 48 bearings

(a) Optimum production quantity (Q):

Q = SQRT [(2 x D x S) / H x (1 - d/p)]

Q = SQRT [(2 x 10,300 x $42) / $0.70 x (1 - 48/530)]

Q = 1,165.80 or 1,166 (Rounding off to the nearest whole number)

Optimum production quantity (Q) = 1,166 units

(b) Maximum inventory (Imax):

Imax = Q x (1 - d/p)

Imax = 1,166 x (1 - 48/530)

Imax = 1,060.4 or 1,060 (Rounding off to the nearest whole number)

Maximum inventory = 1,060 units

(c) Number of production runs:

Production runs = Annual demand / Production quantity

Production runs = 10,300 / 1,166

Production runs = 8.83 runs

(d) Setup plus holding cost:

Total Setup cost = (Annual demand / Production quantity) x Setup cost

Total Setup cost = (10,300 / 1,166) x $42

Total Setup cost = $371.01

Total holding cost = (Q/2) x H x (1 - d/p)

Total holding cost = (1,166/2) x $0.70 x (1 - 48/530)

Total holding cost = $371.14

Total cost = Total Setup cost + Total holding cost

Total cost = $371.01 + $371.14

Total cost = $742.15