3.7.101.2. Flow models for πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™, πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™_πš—πš˜_πš•πš˜πš˜πš™

Figure 3.7.23. Flow models for the πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™ and the πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™_πš—πš˜_πš•πš˜πš˜πš™ constraints described in TablesΒ 3.7.23 andΒ 3.7.23.
ctrs/flow_global_cardinality_low_up
Table 3.7.23. Domains of the variables and minimum and maximum number of occurrences of each value for the πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™ constraint of FigureΒ 3.7.23.
iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(x i )i[π‘œπ‘šπ‘–π‘› i ,π‘œπ‘šπ‘Žπ‘₯ i ]i[π‘œπ‘šπ‘–π‘› i ,π‘œπ‘šπ‘Žπ‘₯ i ]
1{1,2}5{1,2,3}1[1,2]5[0,2]
2{1,2}6{2,3,4,5}2[1,2]
3{1,2}7{3,5}3[1,1]
4{1,2}4[0,2]
Table 3.7.23. Domains of the variables and minimum and maximum number of occurrences of each value for the πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™_πš—πš˜_πš•πš˜πš˜πš™ constraint of FigureΒ 3.7.23.
iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(x i )i[π‘œπ‘šπ‘–π‘› i ,π‘œπ‘šπ‘Žπ‘₯ i ]i[π‘œπ‘šπ‘–π‘› i ,π‘œπ‘šπ‘Žπ‘₯ i ]
1{1,2}5{1,2}loop[2,2]4[1,2]
2{1,2}6{2,4,5}1[1,2]5[0,2]
3{1,2}7{3,4,5}2[2,3]
4{1,2,3}3[1,1]

FigureΒ 3.7.23 presents flow models for the πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™ and the πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™_πš—πš˜_πš•πš˜πš˜πš™ constraints. Blue arcs represent feasible flows respectively corresponding to the solutions πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™ (〈x 1 =1,x 2 =1,x 3 =2,x 4 =2,x 5 =3,x 6 =5,x 7 =5βŒͺ,βŒ©πšŸπšŠπš•-1 πš˜πš–πš’πš—-1 πš˜πš–πšŠπš‘-2,πšŸπšŠπš•-2 πš˜πš–πš’πš—-1 πš˜πš–πšŠπš‘-2,πšŸπšŠπš•-3 πš˜πš–πš’πš—-1 πš˜πš–πšŠπš‘-1,πšŸπšŠπš•-4 πš˜πš–πš’πš—-0 πš˜πš–πšŠπš‘-2,πšŸπšŠπš•-5 πš˜πš–πš’πš—-0 πš˜πš–πšŠπš‘-2βŒͺ) and πšπš•πš˜πš‹πšŠπš•_πšŒπšŠπš›πšπš’πš—πšŠπš•πš’πšπš’_πš•πš˜πš _πšžπš™_πš—πš˜_πš•πš˜πš˜πš™ (2,2,〈x 1 =1,x 2 =2,x 3 =2,x 4 =2,x 5 =1,x 6 =4,x 7 =3βŒͺ,βŒ©πšŸπšŠπš•-1 πš˜πš–πš’πš—-1 πš˜πš–πšŠπš‘-2,πšŸπšŠπš•-2 πš˜πš–πš’πš—-2 πš˜πš–πšŠπš‘-3,πšŸπšŠπš•-3 πš˜πš–πš’πš—-1 πš˜πš–πšŠπš‘-1,πšŸπšŠπš•-4 πš˜πš–πš’πš—-1 πš˜πš–πšŠπš‘-2,πšŸπšŠπš•-5 πš˜πš–πš’πš—-0 πš˜πš–πšŠπš‘-2βŒͺ), while pink arcs correspond to arcs that cannot carry any flow if the constraint has a solution: