# Weighted sum in the objective function

I am working on my actual model.

The objective function aims to maximize the preferences related to each criterion pc to select the best contract that fits with the project characteristics( c1= size, c2= design complexity, c3= construction complexity, c4= flexibility, c5 = site conditions, etc.). Totally I have 10 criteria. The objective function is as follows : maximize sum (alpha(k)*pc(i)*X(i,j))

• alpha(k) is the weight affected to the criteria c(i),
• c(i) is the criterion that depends on other parameters, I set of projects
• X(i,j) binary decision variable = 1 if the contract i is assigned to the project j and 0 otherwise, J set of contracts

Actually, I would like to evaluate the impact of each criterion on the results and the decision variables, that is why I am adding the weights alpha (i) to the objective function.

I started by putting the following values : alpha1 = 0.91 and the other ones = 0.01 to test the results of c1, such as sum of alpha(i) = 1, i=1..10

I would like to know if there is any method to help me choose the right weights, or it is correct to make my own choice as I did.

## 1 Answer

We typically normalize on seconds, minutes xor dollars, for as far as that is possible. And then leave it to a business stakeholder alignment meeting to tweak the weights. But normalization is not always possible.

For example, a "shift overtime work" can be measured in number of seconds of overtime. A "travel time minimization" can be measured in seconds of travel time. But it's fundamentally hard to measure and normalize a "rejected day off request" - a form of employee happiness - in seconds or dollars.

Just know, there is no "optimal weight" for the constraints. It depends to who you talk too. The financial stakeholder will see a very different weight tuning than the operations stakeholder.