# [AMPL 24594] need to write a temporal constraint

Hi all,
I have some troubling with the following problem:
I have a set of aircraft and i need to construct intervals which contains the overlapped aircraft, such intervals are defined starting from an array like ad:=[9,9:30,10,11,14,15] where each adjacent pairs form an interval, and this interval is formed by two vectors, one of departure time and one of arrival time, so, we have:

set F:= flight1 flight2 flight3;
param a{i in F}; # arrival time of the flights
a{i in F}:=
flight1 9
flight2 10
flight3 11;

param d{i in F}; # departure time of the flights
a{i in F}:=
flight1 9:30
flight2 15
flight3 14;

the first thing i need is to union the two array, meanig a and d, in a new vector, ad, such that the vector is ordered in ascending order.
the second step is once i have the new array ad, i need to define intervals, like:
I1 that has extreme time 9 and 9:30, I2 that has extreme time 9:30 and 10 and so on.
Next step i need to make a condition such that if that condition is true that the i-th flight,Fi, need to be in the j-th interval, Ij.
Once a have all interval i need only to keep intervals with more than one element.

thank you for the attention

For some of the concepts you descripbe, it would be very helpful to have more explanation:
need to make a condition