Decision Analysis How to make decisions when faced with uncertain or imperfect information. Definitions: States of Nature - future events not under the decision makers control Alternatives - different courses of action intended to solve a problem Criteria - factors that are important to the decision maker and influenced by the alternatives Decision making under uncertainty – non probabilistic Can’t quantify probabilities associated with states of nature Helps us understand our own attitudes and preferences toward risk. Decision making under risk - probabilistic Involve probabilistic information about the likelihood of states of nature.

Non probabilistic methods – Decision making under uncertainty Decision options given alternate states of nature without any probabilities (nonprobabilistic approach - avoiding the process of quantifying probabilities). Four simple approaches: Laplace - treat each state equally likely, hence select the decision with the best average (the best average is either the lowest average, e.g. cost, waiting time, etc., or the highest average, e.q., for profit, revenue, etc.) Maximax (or Minimin) - optimist (aggressive decision maker) Maximin (or Minimax) - pessimist (conservative decision maker) Minimax Regret - minimize the maximum opportunity loss Note that this approach works for both maximization and minimization problems the same way. (hint: no negative regret figures).

Example Excel time…

Probabilistic methods - Decision making under risk States of nature are now assigned probabilities. P(Sj) or pj = likelihood of state j Expected (monetary) value decision rule (EMV) Select the decision with the highest expected monetary value Expected regret or expected opportunity loss (EOL) Results the same decision as EMV (functionally equivalent) Expected value of perfect information (EVPI) For each state, determine the best decision, and using the best decisions for each state, calculate “EMV" minus previously selected best decision via EMV. Decision trees

Multistage Decision Making Many problems involve a series of decisions Multistage decisions can be analyzed using decision trees COMTECT Example Submit a proposal or not If awarded the grant which technology to use Sketch the decision tree first Then use Risk Solver’s Decision Tree menu (or use “TreePlan.xla” add-in if you do not have Risk Solver installed) Excel time…

COM- TECH The Occupational Safety and Health Administration (OSHA) has recently announced that it will award an $ 85,000 research grant to the person or company submitting the best proposal for using wireless communications technology to enhance safety in the coal-mining industry. Steve Hinton, the owner of COM-TECH, a small communications research firm located just outside of Raleigh, North Carolina, is considering whether or not to apply for this grant. Steve estimates that he would spend approximately $ 5,000 preparing his grant proposal and that he has about a 50-50 chance of actually receiving the grant. If he is awarded the grant, he then would need to decide whether to use microwave, cellular, or infrared communications technology. He has some experience in all three areas, but would need to acquire some new equipment depending on which technology is used. The cost of the equipment needed for each technology is summarized as: Microwave $ 4,000; Cellular $ 5,000; and Infrared $ 4,000. In addition to the equipment costs, Steve knows that he will spend money in research and development ( R& D) to carry out the research proposal, but he does not know exactly what the R&D costs will be. For simplicity, Steve estimates the following best-case and worst-case R&D costs associated with using each technology, and he assigns probabilities to each outcome based on his degree of expertise in each area. Steve needs to synthesize all the factors in this problem to decide whether or not to submit a grant proposal to OSHA.

Another Decision Tree Example Dean Kuroff started a business of rehabbing old homes. He recently purchased a circa-1800 Victorian mansion and converted it into a three-family residence. Recently, one of his tenants complained that the refrigerator was not working properly. As Dean's cash flow was not extensive, he was not excited about purchasing a new refrigerator. He is considering two other options: purchase a used refrigerator or repair the current unit. He can purchase a new one for $400, and it will easily last three years. If he repairs the current one, he estimates a repair cost of $150, but he also believes that there is only a 30 percent chance that it will last a full three years and he will end up purchasing a new one anyway. If he buys a used refrigerator for $200, he estimates that there is a .6 probability that it will last at least three years. If it breaks down, he will still have the option of repairing it for $150 or buying a new one. Develop a decision tree for this situation and determine Dean's optimal strategy.  

Multiple criteria decision making Decision problems often involve two or more sometimes conflicting criterion or objectives There is no “single best/optimal” solution Only exception is that if a decision alternative is rated the best for all criteria, which will make it a trivial “toy” problem!) Analytical Hierarchy Process (AHP) developed by Dr. Thomas Saaty A structured approach for determining the scores and weights in a multi-criteria “scoring model” Based on pairwise comparisons between the decision alternatives on each of the criteria, as well as pairwise comparisons between the criteria to determine their relative importance Develop rankings from pairwise comparison matrices Which product to launch Selecting software/IT solutions City of CLT, Life Cycle Assessment (LCA) software for the purpose of green purchasing – utilized AHP (Winner: Sima Pro 4.0) Facility site selection/relocation decisions

Scale for pairwise comparisons in AHP

An AHP example In class, we will: About seven years ago C.S. and his lovely wife D.R.C. were shopping for a sports car. They had four principal decision criteria: price, reliability, performance, and style. They were able to narrow their search to three cars: (1) 2001 BMW Z3 ($27K), (2) 2003 Mazda Miata ($24K), and (3) 2001 Honda S 2000 ($26K). In class, we will: Step 1: Breakdown the problem: Top level: Buy a sports car. Major criteria: price, reliability, performance and style Decision alternatives: Z3, Miata, S2000 Step 2: Decision maker(s) develop comparison matrices (this is us!) Step 3: Develop a comparison matrix for criteria Step 4: Compute relative priorities via a “normalization process”. sum column-wise, divide elements in that column with the sums. calculate avg. (score) for each row --> relative priorities per row Compute consistency ratios for each matrix (are we consistent?) Step 5: Using the “relative priorities for each criterion” calculate the weighted average for each decision alternative. The car they will buy is…

Practice Problems and Cases Suggested practice problems: #7, 8, 30, 31 Group exercises: Case 14.2 Case 14.3 The End!

ANALYTICS READING LIST FOR MS STUDENTS Supercrunchers, Ian Ayers Moneyball: The Art of Winning an Unfair Game, Michael M. Lewis Revenue Management, Robert H. Cross The Future of Pricing, E. Andrew Boyd Competing on Analytics, Thomas H. Davenport and Jeanne G. Harris Analytics at Work, Thomas H. Davenport and Jeanne G. Harris