Question

Demand for carpet at a carpet wholesaler stays constant at 10,000 sq. ft. per month. The wholesaler incurs a fixed transportation cost of $100 each time an order is placed and delivered. The carpet costs $3 per sq. ft. and the wholesaler has an annual holding cost rate (per sq. ft.) that is 20% of the unit purchase cost.

What should the optimal order size (or EOQ) be? Note that the carpet can be ordered in any size, so there is no need to round the EOQ to an integer number. Please keep two digits after the decimal point.

What is the time between orders? Please give your answer in days and round it to the nearest integer number of days.

What is the average cycle stock? Please keep two digits after the decimal point.

What is the annual holding cost? Please keep two digits after the decimal point.

Answer 1

a)    EOQ=√2∗D∗S/H

Where D is the annual demand

S is the setup or ordering costs

H is the holding costs

Annual demand 10,000 sq. ft. per month *12 months = 120, 000 sq. ft. per year

Setup costs = $100

Holding costs = 20% of $3 per sq. ft. = $0.6

EOQ= √2 *D *S/H

EOQ= √2 *120, 000 sq. ft. *$100 /$0.6

EOQ=√ 40,000,000 sq. ft.

= 6, 324.56 sq. ft.

b)     Time between orders =EOQ/D

EOQ= 6, 324.56 sq. ft.

D=120, 000 sq. ft. per year

Time between orders= 6,324.56sq.ft./120,000sq.ft

=0.05years∗365days/year

18 days

c)      Average inventory or cycle stock is Q/2

=120,000sq.ft./2

=60,000sq.ft.

d)     Annual holding cost =(EOQ/2∗H

=6,324.56sq.ft./2∗ $0.6

= $1,897.37