Question

operation. The airline planning division based on its analysis envisages that there would fill -40 Do not introduce ne sector Probability 0.1 0.3 0.3 Chiet of Mak of the airline plans to gather additional information betore taking tinal prediction retuns Average 0.7 returns Negativ e returus Negative returns Prior probability 0.2 0.3 0.3 i Draw te ei Tris i Find EVPI and EVSI.

Answer 1

There are two actions or options available:

1. Introduce New sector
2. Do not introduce new sector

There are three states of return:

1. Good Returns
2. Average Returns
3. Negative Returns

Based on above, the payoff table is as follows:

Alternatives	Good Returns	Average Returns	Negative Returns
Introduce New sector	60	30	-40
Do not introduce new sector	0	0	0
Probability	0.4	0.3	0.3

1. Draw the decision tree.

The decision tree based on the above information:

Probability Returns Expected Value Good Returns 60 0.4 21 0.3 Average Returns30 Introduce New Sector 0.3 Negative Returns-40 Airline Planning Team Good Returns0 0.4 Do not introduce New Sector 0.3 Average Returns0 0 0.3 Negative Returns | 0

2. Calculation of Expected Value based on the payoff table:

The Expected Value for 1^st Alternative (Introduce New Sector) = 0.4(60) + 0.3(30) + 0.3(-40) = 24+9-12 = 21

The Expected Value for 2^st Alternative (Do not Introduce New Sector) = 0.4(0) + 0.3(0) + 0.3(0) = 0

Since, the best you can expect here is 21, hence, the 1^st Alternative to introduce new sector is better option.

The airline should launch the new route based on Expected Value Criterion.

3. Analyzing the survey results of research agency:

Drawing the decision tree based on the predicting ability of agency:

0.7 0.2 0.1 Good Returns 60 Average Returns 30 Negative Returns -40 EV Good Returns 42+6-4 0.4 Hire agency 0.3 0.6 0.2 0.2 Good Returns60 Average Returns30 Negative Returns -40 EVA 36+6-8 34 Average Returns 0.3 Airline Planning Team 0.1 Good Returns 60 Average Returns 30 Negative Returns 40 Negative Returns 0.2 0.7 EVN - 6+6-28 -16 Do not hire agency Expected Value 21

EV_Hire= 0.4(EV_G) + 0.3 (EV_A) +0.3 (EV_N)

= 0.4(44) +0.3(34) +0.3(-16)

= 23

EV_{No Hire} = 21

Since the Expected value is higher when the agency is hired, hence, Chief of Marketing should take the help of agency.

4. Calculating EVPI and EVSI

Expected Value of Sample Information = Expected Value with Sample Information – Expected Value without Sample Information

So, in this case, the EVSI = EV_Hire – EV_{No Hire} = 23 – 21 = 2

Expected value of Perfect Information is calculated assuming we have the perfect information before taking the decision.

So the decision tree based on perfect knowledge will be:

Introduce New Sector 60 Good Returns Do not introduce 0 New Sector 0.4 Introduce New Sector 30 Airline Planning Team Do not introduce New Sector Average Returns 0.3 0 Introduce New Sector 0.3 -40 Negative Returns Do not introduce New Sector 0

Only for Good returns and Average returns, airlines will choose to introduce new sector and for negative returns it will choose not to introduce new sector.

Hence, EV_{Perfect Information} = 0.4(60) + 0.3(30) + 0.3(0) = 33

EVPI = EV_{Perfect Information} - EV_{ImPerfect Information}

= 33 – 21 = 12

Hence, EVPI =12 and EVSI = 2