Here's a fun test case for parallelization. In essence we're populating a matrix by simulation, with each row corresponding to one simulation of a given firm's inventory process.

The firm's inventory process is of (s, S) type with stochastic IID demand.

The notebook "inventory_dynamics.ipynb" is just for background. I (jstac) wrote it for a workshop.

The notebook "efficient_inventory_dynamics.ipynb" runs the simulation described above.

I parallelize the task with numba.prange. Numba does a great job of parallelizing this task efficiently --- which is non-trivial, because the execution time of each round of the loop is very small (firm's inventory is simulated for only 400 periods).

Question: How do Matlab and Julia's simple parallelization implementations do on this task?

I'm mainly interested in naive implementations that leave most of the logic unchanged. That is, I want to know how good each of the parallelization interfaces is at collecting low hanging fruit.