121 MS&E Introduction to Stochastic Modeling Prof. Peter W. Glynn
Assignment 8 March 9, 2009 Page 1 of 1
Assignment 8 - Due Sunday March 15th
1. (H&L 19.611.) The campus bookstore must decide how many textbooks to order for a course that will be oered only once. The number of students who will take the course is a random variable D, whose distribution can be approximated by a (continuous) uniform distribution on the interval [40, 60]. After the quarter starts, the value of D become known. If D exceeds the number of books available, the known shortfall is made up by placing a rush order at a cost of $14 plus $2 per book over the normal ordering cost. If D is less than the stock on hand, the extra books are returned for their original ordering cost less $1 each. What is the order quantity that minimizes the expected cost? 2. (H&L 19.612.) Consider the following inventory model, which is a singleperiod model with known density of demand D () e = for 0 and D () = 0 elsewhere. There are two costs connected with the model. The rst is the purchase cost, given by c(y x). The second is a cost p that is incurred once if there is any unsatised demand (independent of the amount of unsatised demand). (a) If x units are available and goods are ordered to bring the inventory level up to y (if x < y), write the expression for the expected loss and describe completely the optimal policy. (b) If a xed cost K is also incurred whenever an order is placed, describe the optimal policy. 3. Suppose that you hold an American op...