1. Some thoughts are so naive. You should find some ideas from the literature. Then add the novelty.

For example, the greedy commonly will not be the optimal policy, otherwise this problem will be super easy. Someone must find and publish it already.

  1. Notice the size of the problem. If it is very small, then using the solver is enough.

For example, column generation is used to solve the large-scale problem, if we focus on the small-size problem, there is no need to use it.

  1. Try to use the numerical results to prove your idea. Most of your methods can be verified or disproved with the aid of computer, do not show it by your hand.