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Two Stage Modeling-Regret and Bounding

# Two Stage Modeling-Regret and Bounding - REGRET ANALYIS AND...

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Unformatted text preview: REGRET ANALYIS AND BOUNDING Prof. Miguel Bagajewicz CHE 4273 1 MINIMAX REGRET ANALYSIS Motivating Example s1 H igh Maximize Average…select A Optimistic decision maker s3 L ow Average A Traditional way s2 M edium 19 14 -3 10 B 16 7 4 9 C 20 8 -4 8 D 10 6 5 7 M ax 20(C) 14(A) 5(D) 10(A) MaxiMax … select C 20 Pessimistic decision maker C \$ Million MaxiMmin … select D A 15 10 5 B D 0 1 -5 s 1 2 s2 3 s3 2 MINIMAX REGRET ANALYSIS MINIMAX Motivating Example A … regret = 8 @ low market C … regret = 9 @ low market D … regret = 10 @ high market s1 High s2 Medium s3 Low Maximum Regret A 1 0 8 8 B Calculate regret: find maximum regret 4 7 1 7 C 0 6 9 9 D 10 8 0 10 10 8 B In general, gives conservative decision but not pessimistic. \$ Million B … regret = 7 @ medium market MINIMAX D B 6 C 4 2 A 0 s1 1 s2 2 s3 3 3 MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory s1 d1 19.01 d2 11.15 d3 12.75 d4 5.41 d5 15.09 Max 19.01 s1 d1 d2 d3 d4 d5 0.00 7.86 6.26 13.60 3.92 NPV s4 15.48 20.54 22.25 32.02 12.48 32.02 s2 10.38 14.47 7.81 9.91 7.40 14.47 s3 10.57 8.87 16.02 12.63 8.81 16.02 s5 10.66 10.58 9.16 8.08 15.05 15.05 ENPV 13.22 13.12 13.60 13.61 11.77 13.61 s2 4.09 0.00 6.66 4.56 7.07 Regret s3 s4 s5 5.45 16.54 4.39 7.15 11.48 4.47 0.00 9.77 5.89 3.39 0.00 6.97 7.21 19.54 0.00 Min Max Min 19.01 10.38 20.54 8.87 22.25 7.81 32.02 5.41 15.09 7.40 32.02 10.38 Max 16.54 11.48 9.77 13.60 19.54 9.77 4 SAMPLING ALGORITHM Generate h(s) d=d+1 d=1 Outer Loop yes h=h(d) EXIT Fix First-Stage Variables s=1 h=h(s) Solve Deterministic Model no d<=d_max Solve Deterministic Model no Inner Loop yes s= s+1 s<=s_max Store NPV(d,s) This generates several solutions 5 UPPER AND LOWER BOUNDS Risk 1 D 0.8 C B 0.6 Lower Bound 0.4 Upper Bound A 0.2 0 0.0 2.0 4.0 6.0 8.0 10.0 This is very useful because it allows nice decomposition, That is, there is no need to solve the full stochastic problem 6 UPPER AND LOWER BOUNDS Example: Gas Commercialization in Asia 1.0 0.8 Mala-GTL Ships: 4 & 3 ENPV:4.540 0.6 Lower Envelope-2 ENPV:4.328 0.4 Upper Envelope ENPV:4.921 0.2 Indo-GTL Ships: 6 & 3 ENPV:4.63 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 7 UPSIDE POTENTIAL Point measure for the upside Risk 1.0 0.9 0.8 0.7 OV =3.075 0.6 OV =0.75 0.5 E(Pro f it ) = 3.4 E(Pro f it ) = 3.0 0.4 0.3 0.2 0.1 VaR =0.75 VaR =1.75 0.0 0 1 2 3 4 5 Profit 6 7 8 9 10 8 AREA RATIO Comparison measure Risk 1.0 0.9 Risk(x2,NPV) 0.8 O_Area 0.7 Risk(x1,NPV) 0.6 0.5 0.4 R_Area 0.3 0.2 0.1 0.0 0 1 ENPV2 ENPV1 2 3 4 5 6 7 8 9 NPV 10 9 UTILITY THEORY UTILITY Utility Functions Money does not always have the same value for a company A Risk Averse Decision Maker values more low profits than large ones Utility Value Real Value A Risk Taker values more high profits Utility Value Real Value 10 UTILITY THEORY Use Utility Value instead of real profit for evaluation Effect on Risk Curves 955 Risk Taker's Utility 855 755 Risk Averse Utility 1 0.9 655 0.8 555 455 455 Risk Taker's View 0.7 0.6 555 655 755 855 0.5 0.4 Original Risk Curve 0.3 0.2 Risk Averse View 0.1 0 400 500 600 700 800 900 1000 11 CONCLUSIONS CONCLUSIONS • Regret Analysis can help in identifying good solutions (It can also fail) • The sampling Algorithm is an important tool to identify upper bounds and good solutions. • The upper potential is important to be considered. References • • Riggs J. L. Economic Decision Models for Engineers and Managers. McGraw Hill, NY, 1968 Economic Aseeri A. and M. Bagajewicz. New Measures and Procedures to Manage Financial Risk with New Applications to the Planning of Gas Commercialization in Asia. Computers and Chemical Engineering 12 ...
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