# Can I do statistical analysis over a MILP problem?

I'm trying to solve a delivery problem which involves transportation of goods from a set of sources to a set of destinations within a time window. Moreover, I'm trying to check which transportation model is more efficient: 1) small number of large vehicles or 2) large number of small vehicles.

To check which way of delivering is most efficient I've created a mathematical formalization (MILP) where I'm trying to maximize the delivery efficiency (measured between 0% and 100%).

Finally, I've generated 30 datasets and solved (with CPLEX) each one 2 times: one with large vehicles and another with small vehicles. In the end, I've obtained 2 sets of solutions for the same delivery problem.

Now the questions:

• Due to LP relaxation and other global search approaches (like branch and cut) is it valid to do statistical analysis over the results? For example: can I do a t-test to check if the mean efficiency of two approaches is significantly different from each other?

• Can I consider CPLEX solver as a blackbox and just do hypothesis testing over the results?

• Is there any article that applies some statistical analysis over the results obtained from a MILP?