Question

Radovilsky Manufacturing Company, in Hayward, California, makes flashing lights for toys. The company operates its production facility 300 days per year. It has orders for about 12 comma 200 flashing lights per year and has the capability of producing 100 per day. Setting up the light production costs $48. The cost of each light is $1.00. The holding cost is $0.10 per light per year.

a) What is the optimal size of the production run

b) What is the average holding cost per year? ?

c) What is the average setup cost per year?

Answer 1

Solution:

(a) Optimal size of the production run (Q):

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

where,

D = Annual demand

S = Setup cost

H = Holding cost

d = Daily demand

d = Annual demand / Number of working days = 12,200 / 300

d = 40.67

p = Daily production

Putting the given values in the above formula,

Q = SQRT [(2 x 12,200 x $48) / $0.10 x (1 - 40.67/100)]

Q = 4,443.02 or 4,443 (Rounding off to the nearest whole number)

Optimal size of the production run = 4,443 units

(b) Average holding cost per year:

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

Average holding cost = (4,443/2) x $0.10 x (1 - 40.67/100)

Average holding cost = $131.80

(c) Average setup cost per year:

Average setup cost = (D/Q) x S

Average setup cost = (12,200/4,443) x $48

Average setup cost = $131.80