Multiple_Criteria_Decisions_H

Multiple_Criteria_Decisions_H - Multi-Criteria Decision...

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1 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
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2 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.
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3 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 .
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4 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 .
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5 Slide Trade-off Curve for Two Objectives When maximizing both objectives: Objective 2 Objective 1 Dominated Solutions Efficient Frontier B A
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6 Slide Click to edit Master subtitle style 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.
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7 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).
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8 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). 4. 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?
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9 Slide Trade-off Curve for the Example Maximize Annual Return Minimize Risk Annual Return Risk Index 400 800 1200 1600 2000 9500 1000 0 9000 8500 8000 7500 0 0
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Slide 0 200 400 600 800 1000 1200 1400 1600 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Risk Index Annual Return The Trade-off Curve (Efficient Frontier) Invest $800,000 Invest $700,000 Invest all $800,000 Into US Oil Invest all $800,000 Into Bisco Invest all money
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Multiple_Criteria_Decisions_H - Multi-Criteria Decision...

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