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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?

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You can and should do statistical analysis on this sort of experiment. (But unfortunately, many operations researchers [including me] fail to do so regularly.)

Anyway, this paper might be of interest: https://pubsonline.informs.org/doi/abs/10.1287/ijoc.12.1.24.11899

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  • $\begingroup$ Thank you very for your response and the link that you've provided. Is there any specific reason for not doing statistical analysis? $\endgroup$ – CrzCki May 20 at 17:01
  • $\begingroup$ No good reason, IMO. This is something that our field should get better about. $\endgroup$ – LarrySnyder610 May 20 at 17:11

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