n

Problem 4. Let Dn denote the demand for Canon Rebel cameras at Lenox Photo on day n. Suppose that D1, D2,... are independent and identically dis- tributed with P(D = 0) = 0.3, P(D = 1) = 0.3, P(D = 2) = 0.4, and P(D = m) = 0 when m > 2. Suppose that Lenox Photo uses an (s,S) inventory policy with s = 1 and S = 3 (i.e., when inventory is lower than 1, order up to 3). Orders must be placed at the end of each business day; they are filled before the store opens the next morning. If Lenox Photo does not have a Canon Rebel camera in stock when a customer arrives to purchase such a camera, then the customer will go to a different store and purchase the camera, and so the sale is lost. The cost of lost profit and loss of customer satisfaction associated with losing a customer is $40. Placing an order for m cameras costs $50+10 x m ($50 is a fixed cost regardless of the size of the order, and $10 is the cost per ordered camera). Finally, the cost of storing Canon Rebel cameras is $5 per day per camera. (a) Model this situation as a Markov chain. (b) Determine the steady-state probabilities. (c) Determine the long-run average cost per unit time.