I searched through here as best I could and though I found some relevant questions, I don't think they covered the question at hand:

Assume a single resource and a known list of requests to schedule a task. Each request includes a start_after, start_by, expected_duration, and action.

The goal is to schedule the tasks for execution as soon as possible while keeping each task scheduled between start_after and start_by.

I coded up a simple prolog example that I "thought" should work but I've been unfortunately getting errors during run time: ">=/2: Arguments are not sufficiently instantiated".

Any help or advice would be greatly appreciated

startAfter(1,0).
startAfter(2,0).
startAfter(3,0).

startBy(1,100).
startBy(2,500).
startBy(3,300).

duration(1,199).
duration(2,199).
duration(3,199).

action(1,'noop1').
action(2,'noop2').
action(3,'noop3').

can_run(R,T) :- startAfter(R,TA),startBy(R,TB),T>=TA,T=<TB.
conflicts(T,R1,T1) :- duration(R1,D1),T=<D1+T1,T>T1.
schedule(R1,T1,R2,T2,R3,T3) :- 
           can_run(R1,T1),\+conflicts(T1,R2,T2),\+conflicts(T1,R3,T3),
           can_run(R2,T2),\+conflicts(T2,R1,T1),\+conflicts(T2,R3,T3),
           can_run(R3,T3),\+conflicts(T3,R1,T1),\+conflicts(T3,R2,T2).

% when traced I *should* see T1=0, T2=400, T3=200

Edit: conflicts goal wasn't quite right: needed extra T>T1 clause.

Edit: Apparently my schedule goal works if I supply valid Request,Time pairs ... but I'm stucking trying to force prolog to find valid values for T1..3 when given R1..3?