# Discrete optimization in transport economics

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?

• Welcome to OR.SE! Your question is very broad. If you would like help with a specific problem, then it would help if you provide the formulation and ask about specific elements of it -- that will give us the best chance to provide good answers. In general, optimization problems have some quantities that are fixed and given (called parameters) and others that are to be decided by the model (called decision variables). Choosing which is which is sometimes as much art as science, and it takes practice. – LarrySnyder610 Feb 19 '20 at 22:01
• If, instead, your question is not about a specific model but is about how to learn about mathematical optimization, then I would ask that by itself. You'll get some responses, but if you search our Q&A archive, you'll find other similar questions, and those might help you as well. – LarrySnyder610 Feb 19 '20 at 22:01