Understanding Decision Analysis
Understanding Decision Analysis · Structuring a choice with goals, alternatives and criteria
What makes a choice a good one? It starts with being clear about the outcome you want and comparing the alternatives on the same criteria. Every day we decide which product to buy, where to open a store, or which project to fund with a limited budget. With only one alternative the judgment is simple, but once several alternatives each have their own strengths and weaknesses, things change. A cheap product may be low in quality, and a highly profitable project may also carry high risk.
Decision analysis is a way to organize and compare such choices systematically. The aim is not just to find the best alternative, but to make clear what you care about and to build a rationale for the choice from the information and assumptions at hand.
What is a decision made of?
What are you trying to achieve?
e.g., raise customer satisfaction while cutting costs.
What can you actually choose?
e.g., choose one of products A, B and C.
What will you use to judge whether an alternative is good or bad?
e.g., price, quality, durability, after-sales service.
The three elements are different things. The goal is the outcome you want, the alternatives are the options you can choose, and the criteria are the yardsticks for judging each alternative. Without a clear goal it is hard to set proper criteria, and with unclear criteria it is hard to compare the alternatives objectively.
An example: choosing a laptop
Cheap and easy to carry
Excellent performance but expensive
Long battery life and light weight
If price matters most, A may be the better fit; if you do a lot of heavy work, B; if you travel often, C. In other words, which alternative is better is not decided by the alternatives' features alone; it also depends on what you care about.
| Element | Laptop purchase |
|---|---|
| Goal | Pick a laptop that suits how you will use it |
| Alternatives | Laptops A, B, C |
| Criteria | Price, performance, battery, weight |
| Constraints | Budget, required software, minimum performance |
| Final decision | Pick one alternative, given the criteria and constraints |
Conditions that must be met, such as the budget, should be kept separate from the criteria. If the budget is $3,000 or less, any laptop above that is dropped from consideration before the comparison, however many other strengths it has. A constraint is a "pass/fail" condition that cannot be offset by scores.
How do you choose the criteria?
Rather than listing every item that comes to mind, choose criteria by checking whether each one actually relates to the goal.
| Criteria | Question it asks |
|---|---|
| Price | How much does it cost to buy? |
| Performance | How smoothly does it handle the work you need? |
| Battery | How long can you use it without charging? |
| Weight | How easy is it to carry? |
| Durability | Will it work reliably for a long time? |
It must relate to the decision's goal.
Every alternative must be comparable on the same yardstick.
Don't evaluate the same thing twice.
If you include both "portability" and "weight" as criteria, the two reflect similar information, which in effect gives weight double the weight. They can sometimes be used together, but you should check that overlapping criteria don't have an outsized influence. Also, price can be compared in dollars, but design satisfaction or service quality needs a separate scale, such as ratings or expert evaluations.
Comparing alternatives on the same criteria
Once the goal and criteria are set, summarize how each alternative performs on each criterion. Below is a hypothetical score table for illustrating the idea (1–5 points; higher is better on every criterion).
| Criteria | Laptop A | Laptop B | Laptop C |
|---|---|---|---|
| Price score | 5 | 2 | 4 |
| Performance score | 3 | 5 | 3 |
| Battery score | 3 | 4 | 5 |
| Portability score | 5 | 3 | 5 |
A is strong on price and portability, B on performance, and C on battery and portability. Can we just add up the scores? If every criterion is equally important, the totals can be compared, but if you care about performance far more than price, a simple total does not reflect your real preferences. What you need then is the importance of each criterion, that is, a weight.
Reflecting importance with weights
| Criteria | Weights |
|---|---|
| Price | 40% |
| Performance | 30% |
| Battery | 20% |
| Portability | 10% |
| Total | 100% |
These weights reflect a preference that puts price first, and they are set to sum to 100%. Combining the weights with the scores gives the weighted sum.
Si: overall score of alternative i · wj: weight of criterion j · rij: score of alternative i on criterion j · m: number of criteria
| Alternatives | Calculation | Overall score |
|---|---|---|
| Laptop A | 0.4×5 + 0.3×3 + 0.2×3 + 0.1×5 | 4.00 |
| Laptop B | 0.4×2 + 0.3×5 + 0.2×4 + 0.1×3 | 3.40 |
| Laptop C | 0.4×4 + 0.3×3 + 0.2×5 + 0.1×5 | 4.00 |
Under these assumptions A and C tie at 4.00 and B is lowest at 3.40. A gets there through price (a 2.0-point contribution), while C reaches the same score by collecting points evenly from price (1.6) and battery (1.0). A tie means these weights sit right on the boundary between the two alternatives, so even a small change in the weights can change the ranking.
So the weighted-sum result does not mean "A or C is the best laptop for everyone." It is a result that holds on the premise that the weights and score scales are appropriate and that the chosen criteria reflect the goal well. Also, raw data where lower is better, such as price, must not go straight into the weighted sum; as in the example above, you need to align the direction so that a more favorable value gets a higher score.
If the weights change, does the conclusion change?
Weights are not given objectively; they are the decision maker's preferences expressed as numbers. That is why sensitivity analysis, which checks how easily the conclusion flips when the weights change, is important.
Figure 4 shows the result of varying the price weight from 0% to 80% while the other three criteria keep a 30 : 20 : 10 ratio. With a price weight below about 14%, B ranks first; between 14% and 40%, C; and above 40%, A. The lesson's assumption (40%) sits exactly on the boundary between A and C, so this decision is very sensitive to how much you value price.
As Figure 5 shows, A (4.30) scores highest for someone who values price (50%), B (4.10) for someone who values performance, and C (4.55) for someone who travels a lot. Even with the same score table, the winner depends on the weights, so it is important to record the rationale for how the weights were set. Systematic ways to set weights are covered in a later lesson (multi-criteria decision making).
What if there is uncertainty?
So far we have assumed that each alternative's scores are known. In real decisions, though, the outcome often cannot be known in advance. A new store's sales depend on changes in the trade area, new competitors and consumer demand, so you cannot assume that the location with the highest expected return is necessarily the best choice.
In the hypothetical example in Figure 6, trade area Y's expected profit ($208K) is slightly larger than trade area X's ($200K), but there is a 60% chance of no profit at all. Looking only at expected value, you pick Y; if you want to avoid losses, X. In situations like this you need to ask the following questions.
Estimate how likely each outcome is.
Set the size of each outcome.
Reflect your attitude toward risk.
See whether more information would change the choice.
Problems like these are analyzed with methods such as expected value, expected utility and decision trees.
Three laptops meeting the budget of $3,000 or less were compared by a weighted sum of 5-point scores on price, performance, battery and portability (weights 40 : 30 : 20 : 10). Laptops A and C tied at 4.00 points and B scored 3.40. In a sensitivity analysis varying the price weight, A ranked first when the price weight exceeded 40% and C when it was 14–40%, so the final choice depends on the relative importance of price.
A good decision starts not from a right answer but from a consistent rationale that states the goal and criteria.
- Goal · alternatives · criteria: Distinguish the outcome you want, the options you can choose, and the yardsticks for judging them.
- Constraints: Conditions that must be met, such as the budget or required performance, are screened out first, separately from the scores.
- Weights and weighted sum: Express the importance of each criterion as a weight, then multiply by the direction-aligned scores and add up.
- Sensitivity analysis: Check how easily the ranking changes when the weights change.
- Uncertainty: When outcomes are probabilistic, separate methods such as expected value or decision trees are needed.
Next is 02 Decision trees. We will lay out choices and chance events as a tree and compare alternatives by expected value using each outcome's probability and value.