1. 1 Sensitivity analysis Finds most important issues that matter in a decision Helps develop requisite model (a model that addresses all issues that matter most) Tools for sensitivity analysis –One-way sensitivity analysis: examines effect of variables on consequences by considering one variable at a time. Tornado diagrams. –Two-way sensitivity analysis: examines effect of changes of two variables on consequences. Two-way sensitivity graph showing regions in which each strategy is optimum in the space of the two variables. –Sensitivity to probabilities of uncertain events. Two-way sensitivity graph showing regions in which each strategy is optimum in the space of two probabilities.

2. 2 Decision process Identify decision situation and understand objectives Identify alternatives Model problem structure Uncertainty Preferences Make the decisionSensitivity analysis Further analysis needed? Implement decision Y N Update model

3. 3 Decision about purchasing new airplane Total costRevenue Profit Finance cost Price Interest rate Proportion financed Insurance Operating cost Hours flown Capacity of scheduled flights Proportion of charter flights Charter price Ticket price Purchase

4. 4 Influence diagram for studying sensitivity to probabilities Total costRevenue Profit Finance cost Price Interest rate Proportion financed Insurance Operating cost Hours flown Capacity of scheduled flights Proportion of charter flights Charter price Ticket price Purchase

5. 5 Decision tree Purchase? Y N Operating cost Capacity sch. fl. Hours flown $253 $237 p 1-p 45% q 55% 1-q 650, r 900, 1-r 650, s 900, 1-s 45% q 55% 1-q 650, r 900, 1-r 650, s 900, 1-s -$9,725 -$4,225 $6,525 $18,275 $675 $10,175 $16,925 $32,675 $4,200 Consequence

6. 6 Decision tree after making assumptions Purchase? Y N Operating cost Capacity sch. fl. Hours flown $253 $237 0.5 45% q 55% 1-q 650, r 900, 1-r 650, 0.8r 900, 1-0.8r 45% q 55% 1-q 650, r 900, 1-r 650, 0.8r 900, 1-0.8r -$9,725 -$4,225 $6,525 $18,275 $675 $10,175 $16,925 $32,675 $4,200 Consequence

7. 7 Two-way sensitivity graph Inv. Money Market Buy airplane A B A: uncertainty in probabilities p and q does not affect decision: buy airplane is the best decision B: decision is sensitive to probabilities p and q