Management Science – Decision Tree Analysis
Management Science in Practice - Case 1 – Decision Tree Analysis MEDICAL SCREENING TEST North Carolina A new medical screening test developed at the Duke University Medical Center involved using blood samples from newborns to screen for metabolic disorders. A positive test result indicated that a deficiency was present while a negative test result indicated that a deficiency was not present. However, it was understood that the screening test was not a perfect predictor; that is, false positive test results as well as false negative test results were possible. A false positive test result meant that the test detected a deficiency when in fact no deficiency was present. This case resulted in unnecessary further testing as well as unnecessary worry for the parents of the newborn. A false negative test result meant that the test did not detect the presence of an existing deficiency. Using probability and decision analysis, a research team analyzed the role and value of the screening test. A decision tree with six nodes, 13 branches, and eight outcomes was used to model the screening test procedure. A decision node with the decision branches “Test” and “No Test” was placed at the start of the decision tree. Chance nodes and branches were used to describe the possible sequences of a positive test result, a negative test result, a deficiency present, and a deficiency not present. The particular deficiency in question was rare, occurring at a rate of one case for every 250,000 newborns. Thus, the prior probability of a deficiency was 1/250,000 = 0.000004. Based on judgments about the probabilities of false-positive and false-negative test results, Bayes’ theorem was used to calculate the posterior probability that a newborn with a positive test result actually had a deficiency. This posterior probability was 0.074. Thus, while a positive test result increased the probability the newborn had a deficiency from 0.000004 to 0.074, the probability that the newborn had a deficiency was still relatively low (0.074). The probability information was helpful to doctors in reassuring worried parents that even though further testing was recommended, the chances were greater than 90% that a deficiency was not present. After the assignment of costs to the eight possible outcomes, decision analysis showed that the decision alternative to conduct the test provided the optimal decision strategy. The expected cost criterion established the expected cost to be approximately $6 per test. Decision analysis helped provide a realistic understanding of the risks and costs associated with the screening test. In 1998, the test was being given to every child born in the state of North Carolina. Based on James E. Smith and Robert L. Winkler, “Casey’s Problem: Interpreting and Evaluating a New Test,” Interfaces 29, no. 3 (May-June 1999): 63-76. Management Science in Practice - Case 2 – Decision Analysis DECISION ANALYSIS AND DRUG TESTING FOR STUDENT ATHLETES The athletic governing board of Santa Clara University considered whether to implement a drug testing program for the university’s intercollegiate athletes. The decision analysis framework contains two decision alternatives; implement a drug-testing program and do not implement a drug–testing program. Each student athlete is either a drug user or not a drug user, so these two possibilities are considered to be the states of nature for the problem. If the drug-testing program is implemented, student athletes will be required to take a drug-screening test. Results of the test will be either positive (test indicates a possible drug user) or negative (test does not indicate a possible drug user). The test outcomes are considered to be the sample information in the decision problem. If the test result is negative, no follow-up action will be taken. However, if the test result is positive, follow-up action will be taken to determine whether the student athlete actually is a drug user. The payoffs include the cost of not identifying a drug user and the cost of falsely identifying a nonuser. Decision analysis showed that if the test result is positive, a reasonably high probability still exist that the student athlete is not a drug user. The cost and other problems associated with this type of misleading test result were considered significant. Consequently, the athletic governing board decided not to implement the drug-testing program. Charles D. Feinstein, “Deciding Whether to Test Student Athletes for Drug Use,” Interfaces 20, no. 3 (May-June 1990): 80-87. Management Science in Practice - Case 3 – Decision Analysis INVESTING IN A TRANSMISSION SYSTEM* Oglethorpe Power Corporation (OPC) provides wholesale electrical power to consumer-owned cooperatives in the state of Georgia. Florida Power Corporation proposed that OPC join in the building of a major transmission line from Georgia to Florida. Deciding whether to become involved in the building of the transmission line was a major decision for OPC because it would involve the commitment of substantial OPC resources. OPC worked with Applied Decision Analysis, Inc., to conduct a comprehensive decision analysis of the problem. In the problem formulation step, three decisions were identified: (1) deciding whether to build a transmission line from Georgia to Florida; (2) deciding whether to upgrade existing transmission facilities; and (3) deciding who would control the new facilities. Oglethorpe was faced with five chance events: (1) construction costs, (2) competition, (3) demand in Florida, (4) OPC’s share of the operation, and (5) Pricing. The consequence or payoff was measured in terms of dollars saved. The influence diagram for the problem had three decision nodes, five chance nodes, a consequence node, and several intermediate nodes that described intermediate calculations. The decision tree for the problem has more than 8000 paths from the starting node to the terminal branches. An expected value analysis of the decision tree provided an optimal decision strategy for OPC. However, the risk profile for the optimal decision strategy showed that the recommended strategy was very risky and had a significant probability of increasing OPC’s cost rather than providing a savings. The risk analysis led to the conclusion that more information about the competition was needed in order to reduce OPC’s risk. Sensitivity analysis involving various probabilities and payoffs showed that the value of the optimal decision strategy was stable over a reasonable range of input values. The final recommendation from the decision analysis was that OPC should begin negotiations with Florida Power Corporation concerning the building of the new transmission line. * Based on Adam Borison, “Oglethorpe Power Corporation decides about investing in a major transmission system,” Interfaces (March – April 1995): 25-36 Note: The three cases on Decision Analysis are adopted from the Text Book “Management Science” by Anderson Sweeney Williams, Thomson South-Western publication for academic purpose with the objective of providing the participants live real business situations in Decision Analysis MANAGEMENT SCIENCE IN ACTION (Decision Tree Analysis) OHIO EDISON COMPANY* AKRON, OHIO Ohio Edison Company is an operating company of FirstEnergy Corporation. Ohio Edison and its subsidiary, Pennsylvania Power Company, provide electrical service to more than 1 million customers in central and northeastern Ohio, and western Pennsylvania. Most of the electricity is generated by coal-fired power plants. Because of evolving pollution-control requirements, Ohio Edison embarked on a program to replace the existing pollution-control equipment at most of its generating plants. To meet new emission limits for sulfur dioxide at one of its largest power plants. Ohio Edison decided to burn low-sulfur coal in four of the small units at the plant and to install fabric filters on those units to control particulate emissions. Fabric filters use thousands of fabric bags to filter out particles and function in much the same way as a household vacuum cleaner. It was considered likely, although not certain, that the three larger units at the plant would burn medium-to-high-sulfur coal. Preliminary studies narrowed the particulate equipment choice for these larger units to fabric filters and electrostatic precipitators (which remove particles suspended in the flue gas by passing it through a strong electrical field). Among the uncertainties that would affect the final choice were the way some air quality laws and regulations might be interpreted, potential future changes in air quality laws and regulations, and fluctuations in construction costs. Because of the complexity of the problem, the high degree of uncertainty associated with factors affecting the decision, and the cost impact on Ohio Edison, decision analysis was used in the selection process. A graphical description of the problem, referred to as a decision tree, was developed. The measure used to evaluate the outcomes depicted on the decision tree was the annual revenue requirements for the three large units over their remaining lifetime. Revenue requirements were the monies that would have to be collected from the utility, customers to recover costs resulting from the installation of the new pollution-control equipment. An analysis of the decision tree led to the following conclusions. The expected value of annual revenue requirements for the electrostatic precipitators was approximately $1 million less than that for the fabric filters. The fabric filters had a higher probability of high revenue requirements than the electrostatic precipitators. The electrostatic precipitators had nearly a 0.8 probability of having lower annual revenue requirements. · These results led Ohio Edison to select the electrostatic precipitators for the generating units in question. Had the decision analysis not been performed, the particulate-control decision might have been based chiefly on capital cost, a decision measure that favored the fabric filter equipment. It was felt that the use of decision analysis identified the option with both lower expected revenue requirements and lower risk, In this chapter we will introduce the methodology of decision analysis that Ohio Edison used. The focus will be on showing how decision analysis can identify the best decision alternative given on uncertain or risk-filed pattern of future event DECISION ANALYSIS AT EASTMAN KODAK Clemen and Kwit conducted a study to determine the value of decision analysis at the Eastman Kodak company. The study involved an analysis of 178 decision analysis projects over the 10-year period from 1990 to 1999. The projects involved a variety of applications including strategy development, vendor selection, process analysis, new product brainstorming, product-portfolio selection, and emission-reduction analysis. These projects required 14,372 hours of analyst time and the involvement of many other individuals at Kodak over the 10-year period. The shortest projects took less than 20 hours, and the longest projects took almost a year to complete. Most decision analysis projects are one-time activities, which makes it difficult to measure the value added to the corporation. Clemen and Kwit used detailed records that were available and some innovative approaches to develop estimates of the incremental dollar value generated by the decision analysis projects. Their conservative estimate of the average value per project was $6.65 million and their optimistic estimate of the average value per project was $16.35 million. Their analysis led to the conclusion that all projects taken together added more than $1 billion in value to Eastman Kodak. Using these estimates, Clemen and Kwit concluded that decision analysis returned substantial value to the company. Indeed, they concluded that the value added by the projects was at least 185 times the cost of the analysis’ time. In addition to the monetary benefits, the authors point out that decision analysis adds value by facilitating discussion among stakeholders, promoting careful thinking about strategies, providing a common language for discussing the elements of a decision problem, and speeding implementation by helping to build consensus among decision makers. In commenting on the value of decision analysis at Eastman Kodak, Nancy L.S. Sousa said, “As General Manager, New Businesses, VP Health Imaging, Eastman Kodak, I encourage all of the business planners to use the decision and risk principles and processes as part of evaluating new business opportunities. The processes have clearly led to better decision about entry and exit of businesses”. Although measuring the value of a particular decision analysis project can be difficult, it would be difficult to dispute the success that decision analysis had at Kodak. Based on Robert T.Clemen and Robert C.Kwit, “The Value of Decision Analysis at Eastman Kodak Company, 1990-1999,” Interfaces (September/October 2001): 74-92.