# Execution time vs. Computation time in MILP

Hi,

I am using GLPK in Sage 6.9 to solve MILP problem. I am also using the Solver_parameter('timelimit') to terminate the problem after the specficied time. According to SageMath documentation, "timelimit" defines the maximum time spent on a computation. Measured in seconds. However, I am a bit confused with this definition. This is because:

I am solving the same problem with the same timelimit value for different input values (generated randomly using uniform distribution) while I was printing execution time of each. I have noticed different execution times when I am giving different inputs (ranging from 1min, 5mins, to even 10mins).

Can some one please tell me how the computation time is calculated for timelimit? Why they are different even though I used the same problem with the same timelimit? Is it something related to the size of the input, as its only difference between them? Is there any relation between computation and execution times?

Cheers, Aissan

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Aissan,

Whatever you define through solver_parameter only forwards the parameter to the lp solver. If you want a precise definition of what exactly they do, you should refer to the documentation of those solvers. I don't know more than you do on this point.

For GLPK, we copy/pasted the documentation from their manual in the doc of this function: http://doc.sagemath.org/html/en/refer...

You can go check out their official doc to see if more precisions were given.

Nathann

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