A Project Management Problem (V)

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Constraints describing the net:

pn3(A,B,C,D,E,F,G,X,Y):-
A #>= 0, G #<= 10,
X #>= 2, Y #>= 2, X + Y #= 6,
B #>= A, C #>= A, D #>= A,
E #>= B + X, E #>= C + 2,
F #>= C + 2, F #>= D + Y,
G #>= E + 4, G #>= F + 1.

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Query:

?- pn3(A,B,C,D,E,F,G,X,Y), mindomain(G,G).
A = 0, B = 0, C = 0, D::0..1, E = 2,
F::4..5, X = 2, Y = 4, G = 6, F #>= 4 + D

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I.e., we must devote more resources to task X

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All tasks but F and D are critical now

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In some cases, mindomain/2 is not enough to provide the best solution (pending constraints)

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A labeling + branch-and-bound procedure is provided:

?- pn3(A,B,C,D,E,F,G,X,Y),
minimize(labeling([G]),G).