Weighted Sum Model (WSM)

Overview

WSM calculates one total for each option. It first puts criterion values on a comparable scale, multiplies each score by that criterion's weight, and then adds the results. The option with the highest total ranks first.

WSM allows trade-offs: strong performance in one area can offset weaker performance in another. For example, a supplier's excellent quality score can make up for a higher price if quality has enough weight.

How WSM works

1. Put each criterion value on a comparable 0-to-1 scale.
2. Multiply each normalized score by that criterion's weight.
3. Add the weighted scores to produce the option's final score.
4. Rank the options from highest final score to lowest.

Simple laptop example

Suppose Performance has a 50% weight, Battery has a 30% weight, and Price has a 20% weight. After the raw values are normalized, the calculation is:

Laptop B ranks first by 0.01. Its stronger battery and price scores slightly outweigh Laptop A's stronger performance score.

When WSM may fit

Use WSM when you want the final score to be the weighted sum of all criterion scores. WSM is intuitive, transparent, easy to verify manually, and appropriate when strong performance in one criterion is allowed to offset weaker performance in another.

• Stakeholders want to see exactly how each criterion contributes to the total.
• The selected weights represent acceptable business trade-offs.
• A calculator or spreadsheet should be enough to reproduce the result.

Verified supplier example

Quality is maximized; cost and delivery time are minimized.

{
  "algorithm": "WSM",
  "weightStrategy": "Expert",
  "criteria": [
    {"name":"Quality","weight":0.5,"direction":"Maximize"},
    {"name":"Cost","weight":0.3,"direction":"Minimize"},
    {"name":"DeliveryDays","weight":0.2,"direction":"Minimize"}
  ],
  "options": [
    {"optionId":"A","name":"Supplier A","scores":{"Quality":90,"Cost":250,"DeliveryDays":5}},
    {"optionId":"B","name":"Supplier B","scores":{"Quality":80,"Cost":180,"DeliveryDays":3}},
    {"optionId":"C","name":"Supplier C","scores":{"Quality":70,"Cost":100,"DeliveryDays":7}}
  ]
}

Supplier A: (1 * 0.5) + (0 * 0.3) + (0.5 * 0.2) = 0.6000.

{"decisionResult":{"winner":"A","ranking":[{"optionId":"A","score":0.6},{"optionId":"B","score":0.59},{"optionId":"C","score":0.3}]},"configurationUsed":{"rankingAlgorithm":{"value":"WSM","source":"ExplicitRequest"}}}

Supplier A narrowly wins because its excellent quality and mid-range delivery score offset its weak cost score. This is the practical business trade-off WSM permits: a higher price can be accepted when the weighted quality advantage is large enough.

Weights are established before WSM

Each path produces normalized effective criterion weights. WSM is a separate stage that ranks options using those weights; AHP is not an alternative ranking algorithm.

TOPSIS versus WSM

Neither method is universally better. They answer the ranking question in different ways.

API usage