What are the crewing requirements for a B787 flying LAX to SIN?
I can't provide a specific answer but rest times are contract matter and airline specific. Also, most curiously, you won't find rest crews on private jets. 

Depending on the airline you will have anything between 3 and 5 pilots on longer flights (anything above 8h). Three being the most common. Start and landing are handled by captain and co pilot, in between the aircraft is flown by a "cruise pilot" of a lower rank.

Rest crew regulations can cause problems, if there is a delay. Even a small delay may cause to require a standby crew, which will incur a further delay. 

As a rule of thumb, airlines have around 10 flight crews per aircraft to allow for relief crews, training, holidays, ...