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.