Chapter 22.2, Problem 17E

To determine

Calculate the EVPI.

Explanation of Solution

The EPPI value can be calculated as follows.

$\begin{array}{c}\text{EPPI}=\left(\begin{array}{l}{\text{Payoff}}_{{\text{Maximum s}}_{\text{1}}\text{ row}}\times \text{P}\left({\text{s}}_1\right)+{\text{Payoff}}_{{\text{Maximum s}}_{\text{2}}\text{ row}}\times \text{P}\left({\text{s}}_2\right)\\ +{\text{Payoff}}_{{\text{Maximum s}}_{\text{3}}\text{ row}}\times \text{P}\left({\text{s}}_3\right)\end{array}\right)\\ =\left(\text{110}\times 0.1+\text{150}\times 0.25+\text{250}\times 0.15\right)\\ =196\end{array}$

The value of EPPI of produce is 196.

The EMV value of a₁ can be calculated as follows.

$\begin{array}{c}{\text{EMV}}_{{\text{a}}_1}=\left(\begin{array}{l}{\text{Payoff}}_{{\text{a}}_1{\text{, s}}_1}\times \text{P}\left({\text{s}}_1\right)+{\text{Payoff}}_{{\text{a}}_1{\text{, s}}_2}\times \text{P}\left({\text{s}}_2\right)\\ +{\text{Payoff}}_{{\text{a}}_1{\text{, s}}_3}\times \text{P}\left({\text{s}}_3\right)+{\text{Payoff}}_{{\text{a}}_1{\text{, s}}_4}\times \text{P}\left({\text{s}}_4\right)\end{array}\right)\\ =\left(60\times 0.1+40\times 0.25+220\times 0.5+250\times 0.15\right)\\ =163.5\end{array}$

The value of EMV of a₁ is 163.5.

The EMV value of a₂ can be calculated as follows.

$\begin{array}{c}{\text{EMV}}_{{\text{a}}_2}=\left(\begin{array}{l}{\text{Payoff}}_{{\text{a}}_2{\text{, s}}_1}\times \text{P}\left({\text{s}}_1\right)+{\text{Payoff}}_{{\text{a}}_2{\text{, s}}_2}\times \text{P}\left({\text{s}}_{21}\right)\\ +{\text{Payoff}}_{{\text{a}}_2{\text{, s}}_3}\times \text{P}\left({\text{s}}_3\right)+{\text{Payoff}}_{{\text{a}}_2{\text{, s}}_4}\times \text{P}\left({\text{s}}_4\right)\end{array}\right)\\ =\left(110\times 0.1+110\times 0.25+120\times 0.5+120\times 0.15\right)\\ =116.5\end{array}$

The value of EMV of a₂ is 116.5.

The EMV value of a₃ can be calculated as follows.

$\begin{array}{c}{\text{EMV}}_{{\text{a}}_3}=\left(\begin{array}{l}{\text{Payoff}}_{{\text{a}}_3{\text{, s}}_1}\times \text{P}\left({\text{s}}_1\right)+{\text{Payoff}}_{{\text{a}}_3{\text{, s}}_2}\times \text{P}\left({\text{s}}_{21}\right)\\ +{\text{Payoff}}_{{\text{a}}_3{\text{, s}}_3}\times \text{P}\left({\text{s}}_3\right)+{\text{Payoff}}_{{\text{a}}_3{\text{, s}}_4}\times \text{P}\left({\text{s}}_4\right)\end{array}\right)\\ =\left(75\times 0.1+150\times 0.25+85\times 0.5+130\times 0.15\right)\\ =107\end{array}$

The value of EMV of a₃ is 116.5. Since the EMV for a₁ is greater, select the option a₁.

The value of EVPI can be calculated as follows.

$\begin{array}{c}\text{EVPI}=\text{EPPI}-{\text{EMV}}_{{\text{a}}_1}\\ =196-163.5\\ =32.5\end{array}$

The value of EVPI is 32.5.