Talisman Games, a local gaming store, stocks the 4th edition of the rulebook of a popular pen-and-paper role-playing game Daggers and Dungeons. Talisman orders the rulebooks directly from its publisher- Wizards of the Shore (WotS). Talisman orders a rulebook at a wholesale price of S1S and sells it for $20. The lead-time from the supplier is 2 weeks and there is a fixed order cost of S10. Demand for the rulebook each week is independent of demand in previous week standard deviation of 3 per week. The owners of the store estimate that their opportunity cost of capital is around 15% per year.
If a customer comes looking to buy a rule book but finds Talisman is stocked out, their copy is backordered and picked up when the next shipment arrives at Talisman from WotS. The customers are always eager to pick up their book, so no sales are lost. To reward loyalty, Talisman throws in a free set of dice (worth $2) with every backordered book purchase.
a. What is Talisman's optimal inventory control policy; that is, its optimal order quantity Q* and re-order point R*?
b. How long does the average rulebook spend in Talisman before it is sold to a customer?
