DL computers tell the gate agent which passenger to involuntarily bump on each flight so there is already such logic programed for that purpose. If I were to implement such a program I would first ask people to fill out a hardship card to detail problems that might not be obvious and require documentation and turn it into the counter. I would then review the hardship request, followed by connection considerations such as can the airline get you to your destination today or not, then a mix of status and highest fare paid followed by the cheap guys like me who would be the very last.

1st humanitarian
2nd logic
3rd revenue