Problem
I. YB Sporting Apparel prints up novelty T-shirts commemorating major sports events (e.g., the Super Bowl, the World Series, Northwestern University winning the NCAA Basketball Tournament). The T-shirts cost $5 to make and distribute and sell for $20. Company policy is to dispose of any excess inventory after the event by discounting the T-shirts by 80 percent, that is, sell them for $4. In 1994, YB printed shirts for the World Cup soccer playoffs in Chicago. It estimated demand at 12,000 shirts, with a significant amount of uncertainty. Because of this uncertainty, YB printed only 10,000 shirts. What do you think of this decision? What quantity would you have recommended printing?
II. Slaq Computer Company manufactures notebook computers. The economic lifetime of a particular model is only 4 to 6 months, which means that Slaq has very little time to make adjustments in production capacity and supplier contracts over the production run. For a soon-to-be-introduced notebook, Slaq must negotiate a contract with a supplier of motherboards. Because supplier capacity is tight, this contract will specify the number of motherboards in advance of the start of the production run. At the time of contract negotiation, Slaq has forecasted that demand for the new notebook is normally distributed with a mean of 10,000 units and a standard deviation of 2,500 units. The net profit from a notebook sale is $500 (note that this includes the cost of the motherboard, as well as all other material, production, and shipping costs). Motherboards cost $200 and have no salvage value (i.e., if they are not used for this particular model of notebook, they will have to be written off ).
i. Use the news vendor model to compute a purchase quantity of motherboards that balances the cost of lost sales and the cost of excess material.
ii. Comment on the appropriateness of the news vendor model for this capacity planning situation. What factors are not considered that might be important?
III. Jill, the office manager of a desktop publishing outfit, stocks replacement toner cartridges for laser printers. Demand for cartridges is approximately 30 per year and is quite variable (i.e., can be represented using the Poisson distribution). Cartridges cost $100 each and require three weeks to obtain from the vendor. Jill uses a (Q,r) approach to control stock levels.
Questions i and ii are as in the textbook Hint: In question a. Jill wants on average twice per year, but she still wants to follow fixed-quantity policy (rather than fixed order-time).
Task
i. Jill wants 98% of volume of customers not to wait for cartridges. (Please explain which one is it: service level or fill rate.)
ii. When ordering cartridges from vendor, Jill wants probability of 98% that she will not run out of inventory from that order.
I suggest using spreadsheet to answer these questions. An alternative is to look at various formulas in the textbook (this, however, would be more work).