3.7.101.3. Flow models for 𝚞𝚜𝚎𝚍_πš‹πš’, πšœπšŠπš–πšŽ

FigureΒ 3.7.24 presents flow models for the 𝚞𝚜𝚎𝚍_πš‹πš’ and the πšœπšŠπš–πšŽ constraints. Blue arcs represent feasible flows respectively corresponding to the solutions 𝚞𝚜𝚎𝚍_πš‹πš’(〈x 1 =2,x 2 =4,x 3 =6βŒͺ,〈y 1 =2,y 2 =4βŒͺ) and πšœπšŠπš–πšŽ(〈x 1 =2,x 2 =4,x 3 =5βŒͺ,〈y 1 =2,y 2 =4,y 3 =5βŒͺ), while pink arcs correspond to arcs that cannot carry any flow if the constraint has a solution. Within the context of the πšœπšŠπš–πšŽ constraint, the assignment x 1 =1 is forbidden since 1βˆ‰π‘‘π‘œπ‘š(y 1 )βˆͺπ‘‘π‘œπ‘š(y 2 )βˆͺπ‘‘π‘œπ‘š(y 3 ). Consequently x 1 =2 and, since y 1 is the only variable of {y 1 ,y 2 ,y 3 } that can be assigned value 2, the assignment y 1 =3 is forbidden. Now since 3βˆ‰π‘‘π‘œπ‘š(y 1 )βˆͺπ‘‘π‘œπ‘š(y 2 )βˆͺπ‘‘π‘œπ‘š(y 3 ) the assignment x 2 =3 is also forbidden. Finally x 3 =6 is forbidden since 6βˆ‰π‘‘π‘œπ‘š(y 1 )βˆͺπ‘‘π‘œπ‘š(y 2 )βˆͺπ‘‘π‘œπ‘š(y 3 ).

Figure 3.7.24. Flow models for the 𝚞𝚜𝚎𝚍_πš‹πš’ and the πšœπšŠπš–πšŽ constraints described in tablesΒ 3.7.24 andΒ 3.7.24.
ctrs/flow_used_by_same
Table 3.7.24. Domains of the variables for the 𝚞𝚜𝚎𝚍_πš‹πš’ constraint of FigureΒ 3.7.24.
iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(y i )
1{1,2}1{2,3}
2{3,4}2{4,5}
3{4,5,6}
Table 3.7.24. Domains of the variables for the πšœπšŠπš–πšŽ constraint of FigureΒ 3.7.24.
iπ‘‘π‘œπ‘š(x i )iπ‘‘π‘œπ‘š(y i )
1{1,2}1{2,3}
2{3,4}2{4,5}
3{4,5,6}3{4,5}