A specific set of flights may be partitioned into fares and priceable units in many ways. The above diagram shows two ways to partition the four flights of a SFO to BOS round-trip journey. In both cases, four fares are used, one per flight. On the left, the four fare components are grouped into a single circle-trip priceable unit. On the right, they are grouped into two open-jaw priceable units. Each black line represents a flight and each red a fare. The boxes represent priceable units.
Because rules like the Saturday night stay restriction and advance purchase restrictions depend on how flights and fares are divided into priceable units, it is important how fare components are grouped into priceable units, and this non-determinism adds to the search space. Suppose the third fare, a BOS-DFW QE14 fare, has a 14-day advance purchase restriction and a Saturday night stay restriction, and the three other fares do not have important restrictions.
The 14-day advance purchase restriction will likely be defined as requiring 14 days to pass between the time of reservation and the departure of the first flight in the priceable unit of the fare with the restriction. In the case of the single circle-trip priceable unit that flight is the initial departure from SFO, marked in green. In the case of two open-jaw PUs, that flight is the later departure from DEN. Thus, from the perspective of the 14-day restriction, it is more likely the restriction will be met in the two-PU choice.