Here is a detailed guide on **Decision Making under
✅ I. DECISION MAKING UNDER CERTAINTY
🔹 Definition:
When the outcome of each alternative is known with certainty.
🔹 Method:
Choose the alternative with the highest payoff (or lowest cost).
🔹 Example:
| Option | Profit (₹) |
|---|---|
| A | 5000 |
| B | 8000 |
| C | 7000 |
Best Choice: Option B (₹8000)
✅ II. DECISION MAKING UNDER RISK
🔹 Definition:
Outcomes are not certain, but probabilities are known.
1. Expected Monetary Value (EMV)
📘 Formula:
EMV=∑(Payoff×Probability)EMV = \sum (Payoff \times Probability)
🧮 Example:
| Option | Outcome 1 (p=0.6) | Outcome 2 (p=0.4) |
|---|---|---|
| A | ₹10000 | ₹4000 |
| B | ₹7000 | ₹5000 |
-
EMV(A) = 10000×0.6 + 4000×0.4 = 6000 + 1600 = ₹7600
-
EMV(B) = 7000×0.6 + 5000×0.4 = 4200 + 2000 = ₹6200
✅ Choose A (Higher EMV)
2. Expected Opportunity Loss (EOL)
📘 Formula:
EOL=∑(Opportunity Loss×Probability)EOL = \sum (Opportunity\ Loss \times Probability) Opportunity Loss=Max Payoff in state−Payoff of alternative\text{Opportunity Loss} = \text{Max Payoff in state} - \text{Payoff of alternative}
🧮 Example (Same as above):
| Outcome | Best Payoff | A’s Loss | B’s Loss |
|---|---|---|---|
| 1 | 10000 | 0 | 3000 |
| 2 | 5000 | 1000 | 0 |
EOL(A) = 0×0.6 + 1000×0.4 = ₹400
EOL(B) = 3000×0.6 + 0×0.4 = ₹1800
✅ Choose A (Lower EOL)
3. Expected Value with Perfect Information (EVwPI)
📘 Formula:
EVwPI=∑(Max payoff per state×Probability)EVwPI = \sum (Max\ payoff\ per\ state \times Probability)
🧮 Example:
From earlier table:
-
Max Outcome 1 = ₹10000 (A)
-
Max Outcome 2 = ₹5000 (B)
EVwPI=10000×0.6+5000×0.4=6000+2000=₹8000EVwPI = 10000×0.6 + 5000×0.4 = 6000 + 2000 = ₹8000
4. Expected Value of Perfect Information (EVPI)
📘 Formula:
EVPI=EVwPI−Best EMVEVPI = EVwPI - Best\ EMV
🧮 Example:
EVPI=8000−7600=₹400EVPI = 8000 - 7600 = ₹400
✅ Value of having perfect information = ₹400
✅ III. DECISION MAKING UNDER UNCERTAINTY
🔹 Definition:
Outcomes are unknown, and probabilities are not available.
1. Maximax Criterion (Optimistic)
📘 Formula:
Choose action with max(Maximum payoff)Choose\ action\ with\ \max(\text{Maximum payoff})
🧮 Example:
| Option | Worst | Best |
|---|---|---|
| A | 2000 | 9000 |
| B | 3000 | 7000 |
| C | 1000 | 8000 |
✅ Choose A (best max = ₹9000)
2. Maximin Criterion (Pessimistic)
📘 Formula:
Choose action with max(Minimum payoff)Choose\ action\ with\ \max(\text{Minimum payoff})
| Option | Min Payoff |
|---|---|
| A | ₹2000 |
| B | ₹3000 |
| C | ₹1000 |
✅ Choose B (max of mins = ₹3000)
3. Minimax Regret Criterion
📘 Steps:
-
Create regret table by subtracting each value from column maximum.
-
Choose option with minimum of maximum regrets.
| Outcome | A | B | C |
|---|---|---|---|
| 1 | 2000 | 3000 | 1000 |
| 2 | 9000 | 7000 | 8000 |
Max in O1 = 3000, Max in O2 = 9000
→ Regret Table:
| Option | R1 | R2 | Max |
|---|---|---|---|
| A | 1000 | 0 | 1000 |
| B | 0 | 2000 | 2000 |
| C | 2000 | 1000 | 2000 |
✅ Choose A (min of max regrets)
4. Laplace Criterion (Equal Probabilities)
📘 Formula:
Average Payoff=Sum of PayoffsNumber of StatesAverage\ Payoff = \frac{Sum\ of\ Payoffs}{Number\ of\ States}
| A = (2000 + 9000)/2 = 5500
| B = (3000 + 7000)/2 = 5000
| C = (1000 + 8000)/2 = 4500
✅ Choose A
5. Hurwicz Criterion
📘 Formula:
H=α×(Best)+(1−α)×(Worst)H = \alpha × (\text{Best}) + (1-\alpha) × (\text{Worst})
Let α = 0.6
| Option | H-Score |
|---|---|
| A | 0.6×9000 + 0.4×2000 = 5400 + 800 = 6200 |
| B | 0.6×7000 + 0.4×3000 = 4200 + 1200 = 5400 |
| C | 0.6×8000 + 0.4×1000 = 4800 + 400 = 5200 |
✅ Choose A
📝 Sample Exam Question:
A manager must choose between three investment options A, B, and C. The payoffs (in ₹) for three different market conditions are given:
Option Strong (S1) Medium (S2) Weak (S3) A 12000 8000 4000 B 10000 9000 6000 C 15000 7000 3000 Probabilities: S1 = 0.3, S2 = 0.4, S3 = 0.3
a) Calculate EMV for each option
b) Calculate EOL and choose best option
c) Compute EVPI
Would you like this sample solved as well?