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

Decision process

Model problem structureUncertaintyPreferences

Identify decision situation and understand objectives

Identify alternatives

Make the decision

Sensitivity analysis

Further analysis needed?

Implement decision

Y

N

Update model

3

Decision about purchasing new airplane

Total cost Revenue

Profit

Financecost

Price

Interest rate

Proportionfinanced

Insurance

Operating cost

Hours flown

Capacity of scheduled flights Proportion of

charter flights

Charter price

Ticket price

Purchase

4

Influence diagram for studying sensitivity to probabilities

Total cost Revenue

Profit

Financecost

Price

Interest rate

Proportionfinanced

Insurance

Operating cost

Hours flown

Capacity of scheduled flights Proportion of

charter flights

Charter price

Ticket price

Purchase

5

Decision tree

Purchase?Y

N

Operating cost

Capacitysch. 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

Decision tree after making assumptions

Purchase?Y

N

Operating cost

Capacitysch. fl.

Hours flown

$253

$237

0.5

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

Two-way sensitivity graph

M

r

q

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