I'm using Java to solve a maximization problem in Cplex. My objective function is quite complex. In a nutshell, there are two parts, A and B. Both of them contain variables.
My goal is to maximize A/B, but Cplex does now allow me to do A/B. I guess A/B will make the objective been nonlinear, which cannot be solved by Cplex.
My question is, is it possible to use a linear or almost-linear function to mimic A/B (Assume A and B are linear)? For example, A-B can roughly approximate A/B. I have tried to use A-B as the objective function, but the result is bad. So can we have a better way to approximate A/B?
Many thanks.
Assuming $A$ and $B$ are linear functions of binary variables, you can linearize the objective exactly by applying a Charnes-Cooper transformation, followed by a linearization of the resulting products. See my answer here.