5.326. precedence

DESCRIPTIONLINKSGRAPH
Origin

Scheduling

Constraint

πš™πš›πšŽπšŒπšŽπšπšŽπš—πšŒπšŽ(πšƒπ™°πš‚π™Ίπš‚)

Argument
πšƒπ™°πš‚π™Ίπš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πš˜πš›πš’πšπš’πš—-πšπšŸπšŠπš›,πšπšžπš›πšŠπšπš’πš˜πš—-πšπšŸπšŠπš›)
Restrictions
πš›πšŽπššπšžπš’πš›πšŽπš(πšƒπ™°πš‚π™Ίπš‚,[πš˜πš›πš’πšπš’πš—,πšπšžπš›πšŠπšπš’πš˜πš—])
πšƒπ™°πš‚π™Ίπš‚.πšπšžπš›πšŠπšπš’πš˜πš—β‰₯0
Purpose

All consecutive pairs of tasks of the collection πšƒπ™°πš‚π™Ίπš‚ should be ordered (i.e.,Β the end of the first task of a pair should be less than or equal to the start of the second task of the same pair).

Example
πš˜πš›πš’πšπš’πš—-1πšπšžπš›πšŠπšπš’πš˜πš—-3,πš˜πš›πš’πšπš’πš—-4πšπšžπš›πšŠπšπš’πš˜πš—-0,πš˜πš›πš’πšπš’πš—-5πšπšžπš›πšŠπšπš’πš˜πš—-2,πš˜πš›πš’πšπš’πš—-8πšπšžπš›πšŠπšπš’πš˜πš—-1

Since the tasks are ordered (i.e.,Β 1+3≀4, 4+0≀5, 5+2≀8) the πš™πš›πšŽπšŒπšŽπšπšŽπš—πšŒπšŽ constraint holds.

Typical
|πšƒπ™°πš‚π™Ίπš‚|>2
πšƒπ™°πš‚π™Ίπš‚.πšπšžπš›πšŠπšπš’πš˜πš—β‰₯1
Symmetries
  • πšƒπ™°πš‚π™Ίπš‚.πšπšžπš›πšŠπšπš’πš˜πš— can be decreased to any value β‰₯0.

  • One and the same constant can be added to the πš˜πš›πš’πšπš’πš— attribute of all items of πšƒπ™°πš‚π™Ίπš‚.

Arg. properties

Contractible wrt. πšƒπ™°πš‚π™Ίπš‚.

See also

common keyword: πš’πš—πšŒπš›πšŽπšŠπšœπš’πš—πšΒ (order constraint).

implies: πšπš’πšœπš“πšžπš—πšŒπšπš’πšŸπšŽ.

implies (items to collection): πš•πšŽπš‘_πšŒπš‘πšŠπš’πš—_πš•πšŽπšœπšœπšŽπšš.

Keywords

constraint type: decomposition, order constraint.

filtering: arc-consistency.

Arc input(s)

πšƒπ™°πš‚π™Ίπš‚

Arc generator
π‘ƒπ΄π‘‡π»β†¦πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšπšŠπšœπš”πšœ1,πšπšŠπšœπš”πšœ2)

Arc arity
Arc constraint(s)
πšπšŠπšœπš”πšœ1.πš˜πš›πš’πšπš’πš—+πšπšŠπšœπš”πšœ1.πšπšžπš›πšŠπšπš’πš˜πš—β‰€πšπšŠπšœπš”πšœ2.πš˜πš›πš’πšπš’πš—
Graph property(ies)
𝐍𝐀𝐑𝐂=|πšƒπ™°πš‚π™Ίπš‚|-1

Graph model

Since we are only interested by the constraints linking two consecutive items of the collection πšƒπ™°πš‚π™Ίπš‚ we use 𝑃𝐴𝑇𝐻 to generate the arcs of the initial graph.

PartsΒ (A) andΒ (B) of FigureΒ 5.326.1 respectively show the initial and final graph of the first example of the Example slot. Since we use the 𝐍𝐀𝐑𝐂 graph property, the arcs of the final graph are stressed in bold.

Figure 5.326.1. Initial and final graph of the πš™πš›πšŽπšŒπšŽπšπšŽπš—πšŒπšŽ constraint
ctrs/precedenceActrs/precedenceB
(a) (b)