Interval Variables: Start, Size, End

Introduction to interval variables in constraint programming. An interval variable models a task by its start $s$ , size $d$ , and end $e$ , linked by the fundamental relation $s + d = e$ . We learn to compute any one quantity from the other two, and to propagate bounds among their domains.

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Introduction

In constraint programming, an interval variable models a task that occupies a contiguous span of time. Every interval variable has three attributes:

the start $s$ — the time the task begins,
the size $d$ — the duration of the task,
the end $e$ — the time the task finishes.

These attributes are linked by the fundamental relation

s + d = e.

For example, a task that starts at $s = 4$ and has size $d = 3$ ends at

e = s + d = 4 + 3 = 7,

and we picture the task as occupying the time slots from $4$ up to (but not including) $7$ .