EMGT 501

1. EMGT 501 Final Exam Due: December 17, 2002 noon

2. Remarks (How to prepare your answers) • Use only a single series of PowerPoint sheets (PPS) • Put your name and address in the first PPS. • The instructor cannot accept the copy of QSB results. All the students should summarize QSB results on PPS, according to each question. The violation of the above suggestions will cost you 20 (points) on each remark.

3. Management of the Telemore Company is considering the development and marketing of a new product. It is estimated to be twice as likely that the product would prove to be successful as unsuccessful. If it were successful, the expected profit would be $1,500,000. If unsuccessful, the expected loss would be $1,800,000. A marketing survey can be conducted at a cost of $300,000 to predict whether the product would be successful. Past experience with such surveys indicates that successful products have been predicted to be successful 80 percent of the time, whereas unsuccessful products have been predicted to be unsuccessful 70 percent of the time.

4. Develop a decision analysis formulation of this problem by identifying alternative actions, the states of nature, and the payoff table when the market survey is not conducted. • Assuming the market survey is not conducted, use the Bayes’ decision rule to determine which decision alternative should be chosen. • Find EVPI. Does this answer indicate that consideration should be given to conducting the market survey? • Assume now that the market survey is conducted. Find the posterior probabilities of the respective states of nature for each of the two possible predictions from the market survey. • Find the optimal policy regarding whether to conduct the market survey and whether to develop and market the new product.

5. Consider the following blood inventory problem facing a hospital. There is a need for a rare blood type, namely, Type AB, Rh negative blood. The demand D (in paints) over any 3-day period is given by P(D = 0) = 0.4, P(D = 1) = 0.3, P(D = 2) = 0.2 and P (D = 3) = 0.1. Note that the expected demand is 1 pint, since E(D) = 0.3 (1)+0.2(2)+0.3(3) = 1. Suppose that there are 3 days between deliveries. The hospital proposes a policy of receiving 1 pint at each delivery and using the oldest blood first. If more blood is required than on hand, an expensive emergency delivery is made. Blood is discarded if it is still on the shelf after 21 days. Denote the state of the system as the number of pints on hand just after a delivery. Thus, because of the discarding policy, the largest possible state is 7.

6. Construct the (one-step) transition matrix. • Determine the steady-state probabilities of Markov Chain. • Find the steady-state probability that a pint of blood will need to be discarded during the 3- day period. • Find the steady-state probability that an emergency delivery will be needed during the 3-day period between regular deliveries.

7. Consider the birth-and-death process with the following mean rates. The arrive rates are λ0 = 2,λ1 = 3, λ2 = 2, λ3 = 1 and λn = 0 for n > 3. The service rates are μ1 = 3, μ2 = 4, μ3 = 1, and μn = 2 for n > 4. • Construct the rate diagram for this birth-and-death process. • Develop the balance equations. • Solve these equations to find the steady-state probability distribution P0, P1, … • Use the general formulas for the birth-and-death process to calculate P0, P1, …Also calculate L, Lq, W, and Wq.

8. Speedy Wheels is a wholesale distributor of bicycles. Its Inventory Manager, Peter Anselmo, is currently reviewing the inventory policy for one popular model that is selling at the rate of 250 per month. The administrative cost for placing an order for this model from the manufacturer is $200 and the purchase price is $70 per bicycle. The annual cost of the capital tied up in inventory is 20 percent of the value (based on purchase price) of these bicycles. The additional cost of storing the bicycles – including leasing warehouse space, insurance, taxes, and so on – is $6 per bicycle per year.

9. Use the basic EOQ model to determine the optimal order quantity and the total variable inventory cost per year. • Speedy Wheel’s customers (retail outlets) generally do not object to short delays in having their orders filled. Therefore, management has agreed to a new policy of having small planned shortages occasionally to reduce the variable inventory cost. After consultations with management, Peter estimates that the annual shortage cost (including lost future business) would be $30 times the average number of bicycles short throughout the year. Use the EOQ model with planned shortages to determine the new optimal inventory policy.