1. A large law firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $30 a year per box, and it costs approximately $60 to order and receive a shipment of paper.
a) What order size would minimize the sum of annual ordering and carrying costs?
b) Compute the total annual cost using your order size from the previous part.
c) Except for rounding, are annual ordering and carrying costs always equal at the EOQ?
d) The office manager is currently using an order size of 200 boxes. 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 size instead of 200 boxes? Justify your answer.
2. Re-solve the previous problem, the first two parts, under a $10 fixed cost of ordering (S). Repeat for S = 20, 30, 40, . . . , 100. Explain in a short paragraph or two, what happens to the optimal order quantity, the time between orders, and the average inventory as S decreases.
3. A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 900 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.
a) Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month period.
b) Why is it important to be able to assume that demand will be level during each six-month period?
Note the EOQ assumption that "the demand rate is reasonably constant" does not necessarily require that the demand rate is constant across the entire year. In this problem we have a certain demand rate that will be fairly constant across the first six months of the year, and some (different) demand rate that will be fairly constant across the second six months of the year. In this case, you actually have two EOQ problems (1) solve for the order quantity that should be used during the first six months of the year, and (2) solve for the order quantity that should be used during the second six months of the year.
4. Suppose my office uses ten different kinds of inkjet printers, and as a result I need to maintain inventory of ten different types of ink cartridges. This is a large office, and the average demand for each type of cartridge is 15 cartridges per month. My ordering cost is $10.00 per order, and the carrying cost is $2.00 per cartridge per month. What is the optimal order quantity for the inkjet cartridges? (Note, I will need to be maintaining separate inventories and placing orders for each of the ten different types of cartridges. Assume we are using a Q,R system and the different cartridges will be hitting their order points at different points in time.) What is the total annual ordering plus carrying cost of the inventory system, for all ten items? HINT: Find the optimal order quantity and total cost for one of these cartridges. The total cost for all ten types of cartridge is ten times the cost for one.
5. Suppose in the problem above I could standardize the printers being used, so that all of the printers in my office all use the same inkjet cartridge. Now, instead of 10 different cartridges each having demand of 15 per month, I have one type of cartridge that experiences demand of 150 cartridges per month. What is the optimal order quantity for this standardized inkjet cartridge? How does the total annual ordering plus carrying cost compare to the total cost from problem #4? Explain.