Such a discussion is going on on LinkedIn. There are three concepts that should not be confused.
1. The business problem you aim to solve.
2. The solver you use to tackle your problem.
3. The model you use to tell the solver what the problem is that you need solved.

Doesn’t the model come before the solver? Carlos Armando Zetina highly recommends investing time in selecting the right model/formulation before selecting the right solver. Meinolf Sellmann says: “No! This is not the order that achieves the best results for the business.” What do you think? Link

“The model is the simplification of the world that you make to support your solver. Therefore, the solver dictates the simplifications you should make. This is not the order that achieves the best results for the business.

1. First, you understand the business problem. We all agree on that.

2. Next, you decide what capabilities will your solver require to create business value. Such as:
– Handling non-linear relationships.
– Multi-objective optimization.
– Handling uncertain data estimates.
– Managing risk.
– Providing the best solutions within a given timeframe.
– And most importantly: Ability to handle changes in the model later!

3. And then, when you have chosen your solver, you start modeling your problem.

Why? Because simplifications we make in the model are always made to support our solver technology.”