Fixed-Size vs. Variable-Size Intervals

Distinguishes between fixed-size interval variables (whose size is locked to a single value) and variable-size interval variables (whose size ranges over an interval). Computes domains of the end given domains of the start and size, and tightens domains in the presence of release dates and deadlines.

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Tutorial

Fixed-Size Intervals

An interval variable consists of three quantities: a start $s$ , a size $d$ , and an end $e$ , related by

e = s + d.

A fixed-size interval is an interval variable whose size $d$ is locked to a single value $c$ . Once the size is fixed, the end is fully determined by the start:

e = s + c.

If the start ranges over $[s_{\min}, s_{\max}]$ , then the end ranges over $[s_{\min} + c, \; s_{\max} + c]$ -- a shift of the start domain by $c$ .

For example, suppose an interval has fixed size $d = 4$ and start domain $s \in [1, 8]$ . Then

e \in [1+4, \; 8+4] = [5, 12].

And if we choose $s = 3$ , the end is locked to $e = 3 + 4 = 7$ .