I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically:
1. Is it possible to formulate the problem below using indicators constraints, without using big-M? If so, how? I know that some solvers do it automatically but I am interested in doing it manually
2. How to formulate it using big-M?
For a more detailed example, assume that you have certain obligation at times 1, 2 and 3. You have 10 assets. First you want to see if you can meet the obligations by the first 5 assets before considering the remaining 5. The objective is to find the minimum amount of asset that you can invest in to meet the obligations.