A large toy company Müttel currently allows toy retailers to place orders with delivery in 2 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Müttel has introduced. Müttel charges a wholesale price of $10 for the Gipokmon. The manager of a small boutique toy retail company, TOYS-are-MINE, plans to sell the toy for $20 and incurs a holding cost of $0.1 per toy per week. At this price, demand per week for the toy at one of their stores is estimated to be Poisson distributed with a mean of 1.5 units. Assume that the backorder cost is equal to the product's retail margin. Assume TOYS-are-MINE uses the order-up-to model to plan orders and deliveries to this store.
a. Suppose TOYS-are-MINE uses an order-up-to level of 10. After receiving their delivery for this week, they have 2 units on-hand. Last week's order was for 5 units. How many units will they order this week?
b. Again, suppose they use an order-up-to level of 10 for this store. On average, how many units will this store have on-order?
c. Suppose an order-up-to level of 5 is established. What is the resulting in- stock probability?
d. Suppose an order-up-to level of 3 is established. What would be the expected end-of-period on-hand inventory of Gipokmons?