I cannot tell from your explanation whether your superscript indices mean raise to a power or not. If not, then I believe that you can use the Optimization Toolbox™ intlinprog solver. In any case, you might want to take a look at some of the Mixed-Integer Linear Programming Examples to see whether your problem fits into this framework.
Be aware that there are now two ways of solving mixed-integer linear problems, the new problem-based way, and the older solver-based way. The problem-based approach is new for R2017b.
Alan Weiss
MATLAB mathematical toolbox documentation