I was working on a problem in transport economics where the optimal number of trips in a given duration of time is to be found out. The profit is a function of the price vector $p$ and time cost $c$ which is negatively related to the prices due to demand-side factors.
I used linear programming initially and interpreted the results stochastically.
But I seek to go for discrete optimization or integer programming as they seem more natural for this problem.
I have very little knowledge of these, however. While I have read some algorithms (unfortunately without proof or justification), in all such problems specific values are used (say $p=(1,3)$ and $c=1$ per trip). How do I solve discrete optimization or integer programming problems without specifying the exact value of the parameters, keeping them as general as possible?
And what are some good resources, books, papers, articles, videos, etc. that I can use to understand and approach such problems?