  Temporal planning often involves numeric effects that are directly
proportional to their action's duration. These include continuous effects,
where a numeric variable is subjected to a rate of change while the action is
being executed, and discrete duration-dependent effects, where the variable is
updated instantaneously but the magnitude of such change is computed from the
action's duration. When these effects are linear, state--of--the--art temporal
planners often make use of Linear Programming to ensure that these numeric
updates are consistent with the chosen start times and durations of the plan's
actions. This is typically done for each evaluated state as part of the search
process. This exhaustive approach is not scalable to solve real-world problems
that require long plans, because the linear program's size becomes larger and
slower to solve. In this work we propose techniques that minimise this overhead
by computing these checks more selectively and formulating linear programs that
have a smaller footprint. The effectiveness of these techniques is demonstrated
on domains that use a mix of discrete and continuous effects, which is typical
of real-world planning problems. The resultant planner also outperforms most
state-of-the-art temporal-numeric and hybrid planners, in terms of both
coverage and scalability.
