Becky manages the inventory of printing paper for the Operations Management (OM) group at Harvard. Printing paper comes in boxes containing 5 reams of paper with 500 sheets per ream and is ordered from Office Depot at a price of $25 per box, plus shipping. The shipping cost is equal to a fixed fee of $60 per order, plus $5 per box ordered. Shipping always takes exactly 5 business days. When she places an order for printing paper, Becky needs to fill out a purchase order form and submit it for approval to the Deans office. This process always takes her exactly 2 hours. Becky works a fixed schedule of 9 am to 6pm every weekday and is paid a yearly salary of $35,000. When the order arrives, it is delivered to the central receiving office at Harvard and needs to be brought to Beckys office where it will be stored. The delivery is done by students working at the central receiving office who are paid by Becky a fixed fee of $20 for each such delivery job they take. Storing paper in Beckys office does not directly cost anything; however, she has noticed over the years some unexplained shrinkage in the stock of printing paper boxes, that is, some of the boxes mysteriously disappear from her office. She finds that the rate at which boxes disappear is proportional to the amount of stock she holds in her office and estimates the associated shrinkage cost at $5 per box in inventory per week. Consumption of paper by staff and faculty members of the OM group is stable and equal to 20 boxes per week (this number includes the boxes which disappear). The interest rate on the OM departments bank account is currently 0.25% per year. Recently the faculty members in the OM department have decided to invest any working capital the department has into Professor Beans new business venture about a smartphone app for encouraging kids to eat fruits and vegetables. This project is guaranteed to generate a return on investment of 20% per year.

Assume 50 weeks per year and 5 business days per week.

1. Write down the value of all the relevant parameters, specifically, what are D, C, K and h equal to?
2. Becky currently places orders for printing paper every 2 weeks and the quantity she orders is exactly the quantity needed to satisfy the consumption of printing paper between two orders. Also she times the ordering so that the delivery arrives just as she runs out of printer paper. What is her total cost per week (setup + inventory holding + purchasing)?

1. How much does she order every time she places an order?
2. What is the inventory level at the time the order is placed, i.e., what is her reorder point?
3. What is the total cost (setup + inventory holding + purchasing) per order cycle?
4. What is the total cost (setup + inventory holding + purchasing) per week?

3. How much should Becky order every time she places an order if she wants to minimize her total cost per week? the total cost (setup + inventory holding + purchasing) per week?
4. Suppose that Becky catches the thief who has been stealing boxes of printing paper so that, from now on, no more paper disappears. Should her order frequency increase or decrease? Explain carefully why.

5. Suppose that Becky can only store up to 10 boxes of printing paper in her office. How often and how much printing paper should she order then? Explain carefully why.