Big-M constraints in portfolio models

In general it is important to make big-M constants as small as possible.


> But, the sample i post is really a simplification for the question.
> In some cases, i must have a value for BigM greater than 100.000,
> in order to treat the real problem. For example, if [Rn] represent
> possibles ensures for diferent investiments. In this case, possible
> values for any [Rn] can be bigger than 1.000.000 ($).
>
> If we have this situation, what is a possible strategy to treat this
> question ? Maybe use a "alternative" scale for values, dividing every
> value by a common factor (p.e: /1000) ?


In portfolio models you can often express your decision variables in
terms of fractions, or in different words, use a budget of $1 instead
of $1,000,000. In the report writing code just multiply the fractions
by the actual budget.

Otherwise look into Indicator Constraints as offered by Cplex.