there are a number of hetterim but also a number of caveats on this matter.
Firstly, if you have CONTRACTED for a job and the non-Jew has the option of when to do the work, then clearly, he can do it whenever he wants to, including shabbos.it is for HIS benefit, not yours that he chooses whatever day he wishes.
For employess,the original heter is based on the concept of “behavla-ah”, being “swallowed up”. This means that you pay an employee a “weekly” wage and he works the hours that he needs,including Shabbos. Because you do NOT pay him directly for the work on shabbos, it is not deemed that you have paid him for “meleches shabbos”,but only for his work in the rest fo the week. This is why so many non-Jews are able to work for jews on shabbos,as long as it is not expressly said that he has to work on shabbos. Otherwise, no gentile would be able to work for a Jew.
The idea of “amirah lenochri”, telling a non-Jew to do work on shabbos, is mitigated only if it benefits him also too.
Additionally, if you own a business and you have a gentile PARTNER, then all the profits of shabbos are deemed to accrue to the non-Jewish partner.Hence, you do not profit from “meleches shabbos”.
These are ,generally, the hetterim of having work done on shabbos or owning a business that is open on shabbos. HOWEVER, in case of a business, if it is CLEAR that the busniess is jewish-owned (say the name or the reputation) then you cannot have it open on shabbos because it is so public that a “jewish” business is open on shabbos.I don’t know the basis of the heter for the business named above-unless it was not really clear that it was Jewish-owned and it was only part-owned by jews.
The above are only guidelines and it may differ from case to case. Ask your local Rabbi!