Multiple_Criteria_Decisions HO

# Multiple_Criteria_Decisions HO - 1 Slide Multiple Criteria...

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Unformatted text preview: 1 Slide Multiple Criteria Decisions Chapter 10 2 Slide Multi-Criteria Decision Problems • In this chapter we focus on situations in which the decision maker needs to consider multiple criteria when making a decision . • Efficient Solutions • Goal Programming 3 Slide Decision Making with Multiple Criteria • In the previous chapters we focused on making decisions by optimizing a single objective . • In many situations, there are several relevant but usually conflicting objectives. It is usually difficult to combine all the objectives into one single objective. • Unlike in the single-objective problems for which you have an optimal solution, in multi-objective problems, there are usually many “efficient” solutions for the decision-maker to consider. 4 Slide Efficient Solutions • We say a feasible solution B dominates a feasible solution A if • B is no worse than A with respect to every objective and • B is strictly better than A with respect to at least one objective. • Solution A is called efficient if no other feasible solution dominates A . 5 Slide Efficient Frontier • The decision maker can limit his/her choices to only efficient solutions. • When only two objectives exist, if we graph the objective values for the efficient solutions (in two dimensions), we obtain a trade-off curve , also called the efficient frontier . 6 Slide Trade-off Curve for Two Objectives When maximizing both objectives: Objective 2 Objective 1 Dominated Solutions Efficient Frontier B A 7 Slide Example 1 A client has \$80,000 to invest. He wants his investment portfolio to be restricted to two stocks. Estimated Annual Risk Stock Price/Share Return/Share Index/Share US Oil \$25 \$3 0.50 Bisco \$50 \$5 0.25 • The client wants to maximize the annual return from his investments. • The c lient also wants to avoid high risk. 8 Slide Example-cont’d Some Alternatives (feasible solutions): 1. Purchase only US Oil shares (\$80,000/\$25= 3200 shares). 2. Purchase only Bisco shares (\$80,000/\$50= 1600 shares). 9 Slide Example-cont’d More Alternatives (feasible solutions): 3. Invest \$20,000 in US Oil (purchase 800 shares) and \$60,000 in Bisco (purchase 1200 shares). 5. Invest \$25,000 in US Oil (purchase 1000 shares) and \$50,000 in Bisco (purchase 1000) shares Which of these solutions, if any, are dominated? 10 Slide 200 400 600 800 1000 1200 1400 1600 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Risk Index Annual Return The Trade-off Curve (Efficient Frontier) Invest \$80,000 Invest \$70,000 Invest all \$80,000 Into US Oil Invest all \$80,000 Into Bisco Invest all money Into US Oil Invest all money Into Bisco Invest \$20,000 What is the efficient frontier? 11...
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Multiple_Criteria_Decisions HO - 1 Slide Multiple Criteria...

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