Suppose you talk to someone, who is not familiar with mathematics and has never heard about optimization problems. You want to get to know if this person has a problem, which can be solved as a optimization problem. What would you say to them to help them spot optimization problems? How would you explain to them what optimization is about and how they can spot problems? asked 04 Oct '17, 13:37 opt3 
Before such a discussion, make sure you know what you mean by "optimization problem". Some things (linear/quadratic/integer programs come to mind) will likely be obvious, but what about questions you might answer with a discrete choice model (Bayesian decision analysis, analytic hierarchy process, ...)? The reason I start with this is that as OR people, we frequently look at this sort of question from the methodological perspective: I have a hammer and I'm looking for a nail to whack. Your target audience will be looking at it from an application/end result perspective (I need to get these two pieces of wood to stick together, but I'm not sure how to do it). If you're willing to take a broad perspective, you might frame the characteristics of a problem along the following lines:
The second bullet translates to being able to define the variables in a model, the third to being able to crank out an objective function (or functions, if multiple criteria are involved) and the last to being able to articulate any pertinent constraints. This is (necessarily, in my mind) rather broad, so your target user may wind up describing something too large/complex/intractable/scary to pull off, and quite possibly something not consistent with your personal tool kit. When I taught modeling to a nontechnical but captive audience (MBAs), I used to suggest that they start with the decision variables ("what do I need to decide?"), move to the objective function ("what makes a feasible decision better or worse?"), and then to the constraints ("what stops me from doing whatever I damn well please?"), adding ancillary variables along the way as needed. (For example, production quantities might be decision variables, inventory levels what I would call ancillary variables  there to make the model work, but not something you would explicitly decide). You don't want to start talking variables/objectives/constraints to your target customer, but I think the notions of decisions/evaluations/limitations are fairly straightforward to convey. Lastly, remember that people like examples (but not subscripts and superscripts). answered 04 Oct '17, 15:16 Paul Rubin ♦♦ Yes, examples are king.
(05 Oct '17, 06:26)
Geoffrey De ... ♦

I am struggling with this question myself, for years. Generally, I haven't found a silver bullet yet. I use this slide from my slide deck, with mixed results: And then show use cases. Needless to say that this format doesn't translate well into an elevator pitch :) One thing I learned the hard way is to avoid words like "NPcomplete", "linear vs quadratic", "simulated annealing" during the introduction, at least for a business or technical audience. You can see their eyes glazing over. In front of an academic audience, it's ok to use those terms early on. answered 05 Oct '17, 06:24 Geoffrey De ... ♦ 