Here is an EOQ style problem that includes a very common complication in inventory management, which our textbook does not mention: Three items at a local supermarket are all ordered from the same vendor:

ITEM (FRUIT) WEEKLY DEMAND ORDERING COST PER UNIT, PER YEAR HOLDING COST

Apples 1000 $20 $1

Oranges 2000 $30 $1

Pears 500 $40 $1

In addition to the individual ordering costs listed above, the vendor charges an additional $100 fee to make any kind of fruit delivery. Thus, these three items share that $100 fee jointly, because the supermarket must pay that amount if orders for any one, two, or all three fruits are received. The vendor typically delivers within an hour of receiving an order, so you can treat the lead time on ordering as effectively zero this simplifies the problem, because ordering and receiving become the same thing.

The supermarkets current inventory policy is to receive fruit on Monday mornings, to save on the $100 fee. The current policy is to order and receive apples and oranges every Monday morning, but only order and receive pears every other Monday morning.

You may make all the classic assumptions of the original EOQ model: constant demand, average inventory is half of the order size, etc. Assume 52 weeks in the year. Please conduct and provide the following analysis:

1. What are the order sizes and the average inventories associated with each of the three fruits, using the supermarkets current inventory policy? Calculate and report the total annual relevant cost associated with this policy, including the annual holding costs, ordering costs, and joint ordering costs.

2. Draw a single sawtooth diagram that illustrates the inventory levels of all three fruits over a period of six weeks, when the supermarket is using its current policy.

3. Develop a lower cost policy. Report on the best policy you found. What should the order sizes for each of the three fruits be? What is the length of the order cycle for each of the three fruits? What are the average inventory levels? What is the total annual relevant cost, including holding, ordering and joint ordering costs? If you cannot find a policy better than the one the supermarket is using right now, report the least-worst one you found.

4. Draw a single sawtooth diagram that displays the inventory level of all three fruits over a period of six weeks, when using your proposed policy.