Interesting idea, and very nice and simple web page! I have no idea if people are willing to pay for it, but good on you for making an attempt.
A question though, isn't Monte Carlo a bit overkill? Would you lose much by modelling each deadline as a normal distribution? Then you could just calculate things analytically.
And once you're committed to using monte carlo, you're free to include one-off events -- sick days, vacations, social loafing, etc, that are really hard to model analytically, since they are roughly uniform in time -- the longer the project runs, the more days off make the project run longer.
As another alternative, could you convolve the probability distributions numerically? I’m not sure of the trade-offs between that approach and Monte Carlo, but if it’s something you’ve considered I’d be interested to hear your thoughts.
Once I took a few steps down the simulation path, it seemed so easy and powerful that I didn't look back. There is some computational cost, but for me it's more than made up for by how easy it is to, for instance, say "I'd like to model sick days";
* let the government tell me how often people are sick (https://www.bls.gov/cps/cpsaat47.htm, see "Computer and
# mathematical occupations", absence rate, due to illness or injury),
* make my simulated workers take days off at that rate.
And everything else, all the statistics etc, can stay exactly the same. And I can have a lot of trust that it's producing sane results because I can look at a run, and say yes, that's a plausible number of sick days.
Monte carlo requires you to be clever once, setting up the simulation, and then you almost never have to be clever later when you want to introduce new twists. Any other statistical model you have to keep being cleverer for every additional complication.
A question though, isn't Monte Carlo a bit overkill? Would you lose much by modelling each deadline as a normal distribution? Then you could just calculate things analytically.