Q:

How to decide number of ants in Ant Colony Optimization

In the ant colony optimization algorithm we have to provide number of ants. Is there any mathematical formula to select number of ants?

A:

Not to this day.
Theoretically you may go for "the more the merrier". But this will lead eventually to performance issues, which depend on your setup.
Finding the exact number of ants required to solve a problem in evolutionary algorithms is to this day an empirical problem based on fine tuning. 
Statistically speaking, you will have to graph the time of reaching a solution (if any) vs your number of ants. There will be an stabilization point where adding an extra ant to the problem will not affect the time to reach the solution as drastically as before. This specific number depends on your problem. 
Reaching the optimal number of ants is also an important part of a dissertation, this stabilization point is like pure gold in your paper if you publish one. It helps others researches check the problem and start from that number of agents. 
You don't charge you clients because you can implement aco, you charge them because you can adapt their problem and solve it using aco. This includes defining the number of ants your customer's setup can handle. 

