Can I find a simple algorithm or heuristic for my problem?

(a) Will brute force solve my problem correctly by searching through all subsets or arrangements and picking the best one?

i. If so, why am I sure that this algorithm always gives the correct answer?

ii. How do I measure the quality of a solution once I construct it?

iii. Does this simple, slow solution run in polynomial or exponential time? Is my problem small enough that this brute-force solution will suffice?

iv. Am I certain that my problem is sufficiently well defined to actually have a correct solution?

(b) Can I solve my problem by repeatedly trying some simple rule, like picking the biggest item first? The smallest item first? A random item first?

i. If so, on what types of inputs does this heuristic work well? Do these correspond to the data that might arise in my application?

ii. On what types of inputs does this heuristic work badly? If no such examples can be found, can I show that it always works well?

iii. How fast does my heuristic come up with an answer? Does it have a simple implementation?