One way to automatize that could be to simply allow your minions to have sex with each other when they want to. There could be a "sexual autonomy" setting where the player can decide for each slave separately whether or not they are permitted to engage in consensual sex with other slaves, demand sex from other slaves and/or are obligated to fulfill demands for sex from other slaves.
So the player could decide what kinds of sexual morals to enforce in their household. Either a celibate household where nobody has sex without the masters permission, a free love community where everyone is allowed to enjoy each other if there is mutual consent, a free-use household where anyone can demand sex from anyone or a strict hierarchy of sex slaves and those who are entitled to use them.
This could also be tied into the rank system - a character of higher rank might be entitled to demand sex from any character of lower rank (if they have the permission of their master, of course) while sex with a character of equal or higher rank requires mutual consent.