Structured Approach to Decision Making: Decision Analysis Tools and Examples

1. DECISION ANALYSIS A STRUCTURED APPROACH TO DECISION MAKING

2. DECISION ANALYSIS TOOLS Expected monetary values (EMV) Expected opportunity losses (EOL) Coefficients of variation (CV) Return to Risk Ratio (RTRR) Payoff & Regret Tables Maximax/Maximin

3. THE PAYOFF TABLE “Quantifies” risk/reward A table with: All possible decisions that can be made All possible outcomes Also known as “events” Profits/losses attached to each possible outcome

4. THE PAYOFF TABLE The decisions: All options the company is considering Placed across the rows of the table The outcomes/events: All possible outcomes Placed down columns No control over events

5. EXAMPLE 1 – THE WOOD PELLET PLANT A large manufacturer of wood products is trying to decide whether to build a new pellet plant. Pellets are made of sawdust, wood chips, bark and other organic byproducts). Common uses: Heating homes (pellet stoves) Cat litter Demand seems to be growing The manufacturer is considering building a new pellet plant or keeping the existing plant

6. EXAMPLE 1 – THE PROFITS Profits if build new plant: No change in demand – $28 million (loss) Demand increases$93.5 million Profits if don’t build: No change $50 million Significant Increase  $65 million ?

7. EXAMPLE 1 – THE PAYOFF TABLE ($ millions) Build new plant? Demand Yes No No Change -$28.00 $50.00 Increases $93.50 $65.00

8. EXAMPLE 1 – THE DECISIONS ($ millions) Build new plant? Demand Yes No No Change -$28.00 $50.00 Increases $93.50 $65.00 DECISIONS ARE LISTED ACROSS THE ROWS

9. EXAMPLE 1 – EVENTS/OUTCOMES ($ millions) Build new plant? Demand Yes No No Change -$28.00 $50.00 Increases $93.50 $65.00 EVENTS LISTED DOWN THE COLUMNS

10. EXAMPLE 2 –COSTS & CAPACITIES Building a new plant  $53 million Keeping the existing plant  $0 extra Current Production capacity: 280,000 metric tonnes/yr With the new plant: 200,000 more tonnes/yr Total: 480,000 tonnes/yr ?

11. EXAMPLE 2 – ADDING DEMANDS Anticipated demands: 100,000 metric tonnes  5% probability 200,000 metric tonnes  10% probability 300,000 tonnes 25% 400,000 tonnes  50% 500,000 tonnes  10%

12. EXAMPLE 2 – ADDING REVENUES Revenues per metric tonne of pellets sold: $250/metric tonne sold We need to be mindful of production capacity in this example We can’t sell more than we can produce!

13. EXAMPLE 2: PAYOFF TABLE: See the excel file “Payoffs_Pellets.xlsx” for this table & watch the video on making this table

14. EXAMPLE 3 – MORE COSTS The overhead per plant $2.27 million/year Production costs/metric tonne  $178 Distribution costs/metric tonne  $ 33 Profit/tonne = $250 – $178 – $33 = $39

15. EXAMPLE 3: NEW PAYOFF TABLE: See the excel file “Payoffs_Pellets.xlsx” for this table & watch the video on making this table

16. EXAMPLE 4 – 10 YEAR PAYOFFS The new factory is not lucrative after 1 year Let’s look at 10 years of production Profit/tonne  still $39/metric tonne Overhead  10 x $2.27M Build plant  still $53M ? X

17. EXAMPLE 4 –CAPACITY & DEMAND Let’s assume capacities remain constant 10 year cap – w/ extra plant = 480,000 x 10 10 year cap – w/o extra plant = 280,000 x 10 Let’s assume demands remain constant Lowest = 100,000 x 10 Next lowest = 200,000 x 10 … Highest = 500,000 x 10

18. EXAMPLE 4: NEWER PAYOFF TABLE: See the excel file “Payoffs_Pellets.xlsx” for this table & watch the video on making this table

19. THE MAXIMAX The “best of the best” case scenarios Take the maximum down each column: Choose the largest of these max values Maximax value = max value = $88,800,000 Maximax decision = decision associated w/ value = build the new plant Yes

20. THE MAXIMIN The “best of the worst” case scenarios Take the minimum down each column: Choose the largest of these min values Maximin value = max value = $16,300,000 Maximax decision = decision associated w/ value = build the new plant No

21. THE EMV The “weighted average” of the payoffs with probabilities Use the “sumproduct” call in excel: Choose the largest of these EMV values EMV value = max EMV value = $79,870,000 EMV decision = decision associated w/ value = build the new plant No

22. EXAMPLE 5 – CALCULATING EMVS Let’s revisit the pellet plant example: Let’s calculate the following values for the 10 year payoffs: The maximax The maximin The EMV

23. EXAMPLE 5 – CALCULATING EMVS Assume the following probabilities: 1,000,000 MT demand  5% probability 2,000,000 MT demand  10% probability 3,000,000 MT  25% 4,000,000 MT  50% 5,000,000 MT  10% MT stands for “metric tonnes” of wood pellets

24. EXAMPLE 5 – CALCULATING EMVS See the Excel file for the solutions to this problem: “Payoffs_PelletPlant_SOLUTIONS.xlsx According to the Maximax decision rule: Build the new plant According to the Maximin & EMV decision rules: Don’t build the new plant.

25. REGRET & OPPORTUNITY LOSS

26. THE REGRET TABLE Or “Opportunity Loss” table Possible missed profits/payoffs Calculate the max value for each outcome (across each row) Regret = max - actual (do for each payoff)

27. THE MINIMAX REGRET The “best of the worst” case scenarios Take the maximum down each column: Choose the smallest (min) of these max values Minimax value = min value = $2,300,000 Minimax decision = decision associated w/ value = build the new plant No A little trick I use to remember what to do first “Min of Maxes” add the word ‘of’ in the middle, so “Minimax” becomes – take the minimum of the Maxes (take the maxes first, take the min of those)

28. THE EOL The “weighted average” of the regrets with probabilities Use the “sumproduct” call in excel: Choose the smallest of these EOL values EOL value = min EOL value = $230,000 EOL decision = decision associated w/ value = build the new plant No EOL stands for “expected opportunity loss”

29. THE COEFFICIENT OF VARIATION The ratio of the standard deviation to expected value for each decision. The standard deviation formula (do this for each decision): 2× ?? payoff?− ??? ? = The coefficient of variation formula (do this for each decision): ???????? ????????? ??? The higher the coefficient of variation, the higher the risk associated with a decision ?? = × 100%

30. THE RETURN-TO-RISK RATIO The ratio of the expected value to standard deviation for each decision. ??? ???? = ???????? ????????? The higher the return-to-risk ratio, the large the gain for a decision in relation to its risk – therefore the better the decision

31. EXAMPLE 7 – CALCULATING CV & RTRR See the Excel file for the calculated standard deviation, CV and RTRR for the pellet plant example (see the Example 7 tab) Based on the Coefficient of variation: Don’t build the new plant According to the RTRR Don’t build the new plant.