Question

A large law firm uses an average of 10 packages of copier paper a day. Each package contains 500 sheets. The firm operates 260 days a year. Storage and handling costs for the paper are $1 per year per package, and it costs approximately $10 to order and receive a shipment of papers. a) What order quantity would minimize total annual ordering and holding cost? b) Calculate the total annual inventory control cost using your order quantity from part a. c) Except for rounding, are annual ordering and holding costs equal at the EOQ? d) The office manager is currently using an order quantity of 100 packages. The partners of the firm expect the office to be managed in a cost-efficient manner. Would you recommend that the office manager use the optimal order quantity instead of 100 packages? Justify your answer.

Answer 1

(a):Annual demand = 10 packages per day*260 days per year = 2600 packages per year.

H = $1 and S = $10.

Thus Order quantity = (2*2600*10/1)^0.5 = 228 packages

(b): Total annual inventory control cost = Q/2*H + D/Q*S

= 228/2*1 + 2600/228*10

= 114 + 114.03

= 228.03

(c): Yes both annual ordering costs and holding costs are equal at $114.

(d): In case of order quantity of 100 packages the cost will be = 100/2*1 + 2600/100*10

= 50 + 260

= 310.

Thus the cost figure of $310 in case of 100 packages is more than the cost of $228.03 when 228 packages are ordered. Hence I will recommend that the office manager use the optimal order quantity instead of 100 packages.