At which point does CPLEX go out of memory on the 16 core machine? Does it require a larger search tree and eventually runs out of memory or does it run out of memory rather early in the search?
One problem could be that with 16 cores CPLEX by default uses 16 threads and thus requires 16 copies of your model. Depending on how big your model is that may already eat quite a lot of your 32 GB memory. Does it help to reduce either CPX_PARAM_THREADS or CPX_PARAM_AUXROOTTHREADS?
Another problem could be performance variability. If you change anything in the environment of the solver (machine, thread count, RAM, parameters, ...) then small and subtle differences may make the algorithm take a different path through the search tree and this may change solution time from seconds to hours (or vice versa). If this is the case then you should just get a very large search tree on that 16 core machine and eventually run out of memory.
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