Example of enivornment decisions
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The document discusses various decision making techniques under uncertainty and risk including maximax, maximin, Hurwicz criterion, Laplace criterion, minimax regret, expected monetary value, expected value of perfect information, expected opportunity loss, and sensitivity analysis. It provides an example applying these techniques to choose the best machine for copying costs given uncertainty in monthly document volumes and costs for each machine. The Hurwicz criterion with an alpha of 0.5 suggests Machine B as the choice, while expected monetary value and minimax regret also select Machine B as the optimal decision.
Example of enivornment decisions
- 1. • Decision making environment • Under uncertainty and • Under Risk • Numerical solution • Dr.Ammara Omer Khakwani
- 2. Monthly copy costs for business analytics department 10,000 copies per month 20,000 copies per month 30,000 copies per month Machine A 950 1,050 1,150 Machine B 850 1,100 1,350 Machine C 700 1,000 1,300
- 3. Decision making under uncertainty • optimistic • Pessimistic • Criterion of realism (Hurwicz) • Equally likely (laplace) • Minimax Regret
- 4. Maximax (optimistic) 10,000 copies per month 20,000 copies per month 30,000 copies per month Best payoff maximum Machine A 950 1,050 1,150 1,150 Machine B 850 1,100 1,350 1,350 Machine C 700 1,000 1,300 1,300
- 5. Maximin (Pessimistic) 10,000 copies per month 20,000 copies per month 30,000 copies per month Worst payoff Maximin Machine A 950 1,050 1,150 950 Machine B 850 1,100 1,350 850 Machine C 700 1,000 1,300 700
- 6. Hurwicz criterion (criterion of realism) Weighted average = α(best in row) + (1-α)(worst in row)
- 7. + 10,000 copies per month 20,000 copies per month 30,000 copies per month Weighted average Machine A 950 1,050 1,150 =(0.5)(1,150)+(1-0.5)(950) =575+475= 1050 Machine B 850 1,100 1,350 =(0.5)(1,350)+(1-0.5)(850) =675+425=1100 1100 (Decision) Machine C 700 1,000 1,300 =(0.5)(1,300)+(1-0.5)(700) =650+350= 1000 Hurwicz criterion (criterion of realism) (α=0.5)
- 8. 10,000 copies per month 20,000 copies per month 30,000 copies per month average Machine A 950 1,050 1,150 950+1050+1150/3=1050 Machine B 850 1,100 1,350 850+1100+1350/3=1100 Machine C 700 1,000 1,300 700+1000+1300/3=1000 Lowest cost Equally Likely (Laplace ) approach
- 9. 10,000 copies per month 20,000 copies per month 30,000 copies per month Maximum regret Machine A 950 1150-950=200 1,050 1150-1050=100 1,150 1150-1150=0 200 Lowest value Choose machine Machine B 850 1350-850=500 1,100 1350-1100=250 1,350 1350-1350=0 500 Machine C 700 1300-700=600 1,000 1300-1000=300 1,300 1300-1300=0 600 Minimax Regret
- 10. Decision making under risk •Expected monetary value. EMV=∑XP(X) •Expected value of perfect information. (EVPI=EVwPI – Best EMV) •Expected opportunity loss. (Opportunity loss X Probability )+(Opportunity loss X probability) •Sensitivity analysis
- 11. 10,000 copies per month 20,000 copies per month 30,000 copies per month EMV Machine A 950 1,050 1,150 =0.4x(950)+0.3x(1050)+0.3x(1150) =1040 Machine B 850 1,100 1,350 =0.4x(850)+0.3x(1100)+0.3x(1350) =1075 Machine C 700 1,000 1,300 =0.4x(700)+0.3x(1000)+0.3x(1300) =970 Expected monetary value. EMV=∑XP(X)
- 12. probabilities 0.4 10,000 copies per month 0.3 20,000 copies per month 0.3 30,000 copies per month EMV= EVwPI=$925 Best EMV without perfect information=$970 EVPI=970-925=$45 Perfect information would lower the expected value by $45 Machine A 950 1,050 1,150 =0.4x(950)+0.3x(1050)+0.3x(1150)=1040 Machine B 850 1,100 1,350 =0.4x(850)+0.3x(1100)+0.3x(1350)=1075 Machine C 700 1,000 1,300 =0.4x(700)+0.3x(1000)+0.3x(1300)=970 With perfect information 700 1000 1150 Best payoff with lowest information (0.4x700)+(0.3x1000)+(1150x0.3) =280+300+345=925 Expected value of perfect information)
- 13. Probabilities 0.4 10,000 copies per month 0.3 20,000 copies per month 0.3 30,000 copies per month EOL Machine A 950 250 Max 1,050 50 1,150 0 250x0.4+0.3x50 +0.3x0=115 Machine B Best decision 850 150 1,100 100 1,350 200 Max 0.4x150+0.3x10 0+0.3x200=150 Machine C 700 0 1,000 0 1,300 150Max 0.4x0+0.3x0+0.3 x150=45 minimum Expected opportunity loss (Min EOL decision=Max EMV decision)
- 14. Sensitivity analysis • P= probability of favorable market • Express EMV in terms of P • Mi P- (1-P)mi • Find range of p values
- 15. Best alternatives Range of P values Machine A 1150P- 950(1-P) =2100P-950=0 P1 = 0.45 Machine B 1350P-850(1-P) =2200P-850=0 P2 = 0.38 Machine C 1150P- 700(1-P) 1850P-700=0 P3 = 0.378