Question

A produce distributor uses 787 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 36 percent of the purchase price per crate. Ordering costs are $28. Currently, the manager orders once a month. How much could the firm save annually in ordering and carrying costs by using the EOQ? (Round intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.)

Savings $______ per year

Answer 1

Given values:

Monthly demand = 787 crates

Annual demand, D = 787 x 12 = 9444 crates

Cost, C = $10 each

Annual carrying cost, Cc = 36% of purchase price per crate = 36% of $10

Annual carrying cost, Cc = $3.6

Ordering costs, Co = $28

Current order size, Q = 787 crates (orders once a month)

Solution:

Economic order quantity (EOQ) is calculated as;

EOQ = SQRT (2*D*Co) / Cc

where,

D = Annual demand

Co = Ordering costs

Cc = Annual carrying cost

Putting the given values in the above formula, we get;

EOQ = SQRT [(2 x 9444 x 28) / 3.6]

EOQ = SQRT (146906.67)

EOQ = 383.28 crates

Total costs is calculated as;

Total cost = Annual ordering cost + Annual carrying cost

Total cost = (D/Q x Co) + (Q/2 x Cc)

where,

Q = Order quantity

D = Annual demand

Co = Ordering costs

Cc = Annual carrying cost

Total cost, when Q = 787 crates:

Total cost = (D/Q x Co) + (Q/2 x Cc)

Total cost = (9444/787 x 28) + (787/2 x 3.6)

Total cost = $336 + $1416.6

Total cost = $1,752.6

Total cost, when EOQ = 383.28 crates:

Total cost = (D/EOQ x Co) + (EOQ/2 x Cc)

Total cost = (9444/383.28 x 28) + (383.28/2 x 3.6)

Total cost = $689.92 + $689.90

Total cost = $1,379.82

Annual Savings = Difference between the above two costs

Annual Savings = $1,752.6 - $1,379.82

Annual Savings = $372.78 per year