I have used deterministic optimisation approaches before but never ventured into stochastic optimisation.
In my problem there are a number of decision variables that the optimiser must choose from in order to maximise the objective function. Each decision variable represents a gamble that it will either pay off or return 0.
i.e. choosing between a selection of scratch cards each with a different prize and a different likelihood of winning.
my gut feeling is that I can just put my objective function as
Maximise sum( choose[i] * prize[i] * likelihood[i] for i in scratchcards) within some constraints
where choose is the binary decision variable that is solved for
In my simple (lazy) understanding the above is valid because it represents maximising the expected winnings.
So my question is; do I need to bother with some sort of stochastic optimisation approach? or can I get away with the above?