Often there are many alternatives ways for formulating a MIP. For example:
- The model contains inequality constraints that must hold with equality in an optimal solution.
- The model contains continuous variables that will necessarily be integer in an optimal (or just integer feasible) solution.
- The model contains variables that have a value of at most 1 in an optimal solution.
In these cases, the modeler can decide whether to (1) include the constraints as equality constraints or not, (2) declare the variables as integer or continuous variables and (3) to declare the variables with upper bounds of 1 or not. When using commercial solvers, I have noticed that the performance may vary significantly dependent on such choices. Hence, I am wondering whether there are any rules of thumb for formulating MIPs in solvers. More generally, what information is valuable to solvers and what information may even hurt performance?