Final answer:
A Category II or III (CAT II/III) Instrument Landing System (ILS) approach typically allows for the lowest forecast weather minimums to file without requiring an alternate airport because it supports landings with lower decision heights and runway visual range.
Step-by-step explanation:
The approach procedure that would allow the lowest forecast weather minimums to file without requiring an alternate is typically a Category II or Category III (CAT II/III) Instrument Landing System (ILS) approach. These approaches allow for lower decision heights (DH) and runway visual range (RVR) requirements, meaning an aircraft can land in poorer weather conditions without the need for an alternate airport. CAT II/III approaches are designed with precise navigational guidance and advanced ground and aircraft systems that provide accurate positional information to the pilot during the landing phase, even in reduced visibility scenarios such as those encountered after a significant temperature drop due to a cold front.