How to Join Maximization and Minimization Objectives in One Objective Function

What do you do if you have both a maximization objective for one measure, e.g. a quality measure, and a minimization objective, let’s say transportation cost, for another measure?

Apart from having opposing goals, the measures most likely also have different measuring units as well as different ranges of values.

In order to tackle the problem, we account for those obstacles and follow these steps:

  1. We scale both values to take up the same range, e.g. from 0 to 10.
  2. We set up the objective function to go in one optimization direction, say minimization, keep the sign for the values that we would like to minimize and change the sign for the values that would like to maximize.
  3. In addition, we can weigh these values with factor weights that sum up to one. The higher the weight for one measure, the more this measure will be taken into account in the optimization compared to the other measure(s).

Note that you can do this in the same manner with more than two measures in the objective function.

 

 

 

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s