Demand for devil’s food whipped-cream layer cake at a local pastry shop can be approximatedusing a Poisson distribution with a mean of six per day. The manager estimates it costs $9 to prepare each cake. Fresh cakes sell for $12. Day-old cakes sell for $9 each. What stocking level isappropriate if one-half of the day-old cakes are sold and the rest thrown out?

Suppose that the newsvendor faces integer-valued demand and must choose an integer value of y. We make no assumptions about the demand distribution (other than that it is an integer) or about the relationship between h and p. Prove that y* is the smallest integer y such that F(y) ≥ (r − c)/(r − v) where F is the cdf of the demand distribution. (Hint: Consider calculating the cost difference between two consecutive integer values.)

A. To provide a 98 percent service probability, what must the reorder point be? B. Suppose the production manager is told to reduce safety stock of this item by 125 units. If this is done, what will the new service probability be?

Dalia, 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 (Le., can be represented using the Poisson distribution). Cartridges cost $100 each and require three weeks to obtain from the vendor. Dalia uses a (Q, r) approach to control stock levels (a). If Dalia wants to restrict replenishment orders to twice per year on average, what batch size Q should she use? If she wants to ensure a service level (i.e., probability of having the cartridge in stock when 2 out of 2 needed) of at least 98 percent, what reorder point r should she use? (Hint: Use Table 2.6.(b). If Dalia is willing to increase the number of replenishment orders per year to six, how do Q and r change? Explain the difference in r.