Monte waited patiently for the board of directors of AgroPest International to absorb his presentation. The company, which produced agricultural fertilizers and pesticides, has a new CEO that valued evidence$-$based decision making. The board of directors were used to presentations that relied on instinct and theory. They were not used to what they just saw, which was a decision tree with probabilities, expected values, and return to risk ratios. They just wanted to hear how staying with the old pesticide was the best idea because that$$s what they were comfortable with. But Monte had just shown that the best decision based on evidence would be to go with the new pesticide. He knew there were concerns with the new product being delayed for release because it was still in development. But the old product might get banned due to health concerns! Shouldn$$t that be reason enough? He shook his head as he leaned back and waited for the comments to begin.

To Monte$$s surprise, the chair of the board Carlo quickly cut off conversation, $$I know you have a lot of questions and suggestions but that was a lot to absorb$.$ Carlo turned to Monte, $$Your presentation was very well organized and clear. Could you please make an executive summary that lets us know the key points of your argument? I$$d like us to come back next week having reviewed that so that we can ask Monte some hard questions.$$ Carlo laughed. $$Not that hard, Monte. I just want to give these folks some time to reflect.$$

$($This case is taken and modified from pp$.228-9$ of Clemen, R$.$ T$.,$ & Reilly, T$.(2014).$ Making hard decisions $(3$rd edition$).$ Cengage Learning.$)$

Goals:

Using the decision tree in Excel, replicate how Monte arrived at his recommendation.

Put together a succinct argument for why the new product is the better decision.

NOTE: For all of the Excel work that you are asked to do$.$ Do NOT remove formulas. For example, leave your EMV cell as something like $=$A$2*$B$2+$A$3*$B$3$ instead of typing in the final answer. You will be marked on your answers and your work. The work is what is written in the cells.

Step $0$: Look in the associated Excel file for your group$$s decision tree in the tab $$Decision tree for Part $2.$

Step $1$: Create a payoff table. Put the answer in the tab $$Steps $1$ & $2-$ Part $2$ in Excel.

In class, the conditions were always the same regardless of the decision $($e$.$g$.,$ demand of clams$).$ But in this case, the conditions are different depending on the decision.

Stop and think: What are the TWO decisions?

Stop and think: For each decision, what are the associated conditions? Hint: One decision has two conditions. The other has four conditions.

Due to this, you cannot create a table where each row represents the same thing. Instead, you$$ll need to create a table that looks like this:

Table $1-$ Payoff table

Conditions for Decision $1$

Decision $1$

Conditions for Decision $2$

Decision $2$

$($payoff$)$

$($payoff$)$

$($payoff$)$

$($payoff$)$

$($payoff$)$

$($payoff$)$

Step $2$: Create a table with the probabilities. Put the answer in the tab $$Steps $1$ & $2-$ Part $2$ in Excel. In Excel, leave the calculations in place for the probabilities for Decision $2.$ For example, leave them as $=0\mathrm{.}5*0\mathrm{.}5$ instead of $0\mathrm{.}25$ so that your instructor can click on the cell and see how you arrived at your answer.

Table $2-$ Probability table

Conditions for Decision $1$

Probabilities for Decision $1$

Conditions for Decision $2$

Probabilities for Decision $2$

$($probability$)$

$($probability$)$

$($probability$)$

$($probability$)$

$($probability$)$

$($probability$)$

Hint: The probabilities for Decision $1$ can be read straight off the tree. But the probabilities for Decision $2$ need to be calculated. Look at p$.165$ of the textbook $($Multiplication rules$)$ for help on how to do this. You may also find this article useful.

Step $3$: Engage in decision making by finding the optimal decision using each of the following decision methods. Put work in the tab $$Step $3-$ Part $2$ in Excel.

Maximax

Maximin

Expected monetary value

Coefficient of variation

Return to risk ratio

Then in the tab $$Step $3$ write a one or two sentence interpretation of each decision method to a$)$ indicate what each method indicated about the best decision, and b$)$ to demonstrate understanding of what each decision method means.

Step $4$: Based on your analysis, write a final report to the board that highlights the key points as to why the new product is the optimal decision.

Note: You$$ve already demonstrated your understanding of the five decision methods in Step $3.$ Therefore, do not repeat that work. Rather, pick and choose the most relevant decision methods that support Monte$$s argument.