3.7.101.1. Flow models for πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš, πš˜πš™πšŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš

FigureΒ 3.7.22 presents flow models for the πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš and the πš˜πš™πšŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraints. Blue arcs represent feasible flows respectively corresponding to the solutions πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš(〈x 1 =1, x 2 =2, x 3 =3, x 4 =4, x 5 =5βŒͺ) and πš˜πš™πšŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš({1,2,3,5},〈x 1 =1, x 2 =2, x 3 =3, x 4 =3, x 5 =4βŒͺ), while pink arcs correspond to arcs that cannot carry any flow if the constraint has a solution:

Figure 3.7.22. Flow models for the πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš and the πš˜πš™πšŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraints described in TablesΒ 3.7.22 andΒ 3.7.22.
ctrs/flow_alldifferent_open_alldifferent
Table 3.7.22. Domains of the variables for the πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraint of FigureΒ 3.7.22.
iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(x i )
1{1,2}3{1,2,3}5{3,4,5,6}
2{1,2}4{2,3,4,5}
Table 3.7.22. Domains of the variables for the πš˜πš™πšŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraint of FigureΒ 3.7.22. In addition the lower bound of the first argument of the πš˜πš™πšŽπš—_πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraint is equal to {x 1 ,x 2 ,x 3 }.
iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(x i )
1{1,2}3{1,2,3}5{3,4}
2{1,2}4{2,3}