Excel Solver, way to maximize two values?

Question

I am a user of microsoft excels solver, and am pretty sure it is not possible to solve to maximize for two values. I was wondering if anyone might have another clever way to do this.

Basically I have a column of numbers between 1 and 30 that I need to look over about and pull out 9 to 10 values (out of 200) based on a couple other constraints. I would also like to not just maximize this value, but also a probability value (range from 0 to 1) that I would also like to maximize.

Adding them up won't work as that would grossly undervalue the probability value and multiplying may do the opposite by overvaluing the probability. Any Strategies to handle this problem would be greatly appreciated.

Answer 1

This is an example of multi-objective optimization , which has an extensive literature. As the Wikipedia article shows, this can lead to some pretty deep waters.

By far the easiest approach is that of linear scalarization. This refers to replacing a vector of 2 (or more) objective functions by a single (hence scalar) objective function which is a linear combination of the objective function. What you can do with the solver is to create 2 cells to hold the relative weights to assign to the two objectives. These will be 2 numbers in the range 0 and 1 which sum to 1. Then create a new objective function which is the SUMPRODUCT (linear combination) of these weights and the objectives. Then -- jut use the solver to optimize this objective function. If you aren't happy with the results -- adjust the weights. There is no one right answer. One of the advantages of this approach is that it allows a decision maker to clarify the relevant importance of the objectives.