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Introduction to CP and Modeling a Constraint Problem

Introduction to CP and Modeling a Constraint Problem

Modelling with Variables

Modelling with Variables for the Products (1)assignment(T1,T2,T3,T4) :-T1 in 1..4,T2 in 1..4,T3 in 1..4,T4 in 1..4,all_distinct([T1,T2,T3,T4]),element(T1,[7,8,4,3],TP1),element(T2,[1,2,3,1],TP2),element(T3,[3,5,7,6],TP3),element(T4,[4,1,2,3],TP4),P #= TP1 + TP2 + TP3 + TP4,P #>= 19,labeling([],[T1,T2,T3,T4]).cS.Abdennadher 31Modelling with variables for the products (2):- assignment(T1,T2,T3,T4).T1 = 1, T1 = 2, T1 = 2, T1 = 2T2 = 2, T2 = 1, T2 = 3, T2 = 4T3 = 3, T3 = 3, T3 = 4, T3 = 3T4 = 4, T4 = 4, T4 = 1, T4 = 17 derivation steps in totalReason: Better propagation because profit depends more on theproduct than on the workerTP1 in 3..8, TP2 in 1..3, TP3 in 3..7, TP4 in 1..4TP 1 ≥ min(P) − max(TP 2 ) − max(TP 3 ) − max(TP 4 )yields TP 1 ≥ 5. The constraintelement(T1,[7,8,4,3],TP1) then reduces the domain ofT1 to 1..2.cS.Abdennadher 32

Modelling ComparisonA difficult task• Efficiency• Propagation of the constraints• Number of variables (in general: the less the better)• Flexibility: Additional constraints• Depends on the type of the constraintscS.Abdennadher 33Modelling Comparison: Our Example• Ensure, that never worker 1 is allocated product 1 and worker4 is allocated product 4.• Boolean constraints: B 11 + B 44 ≤ 1• More difficult in the other models• Worker 3 is allocated a product with a number greater thanthe number of the product done by worker 2• Variables for the workers: W 3 > W 2• More difficult with Boolean constraintsB 31 = 0 ∧ B 32 ≤ B 21 ∧ B 33 ≤ B 21 + B 22 ∧ B 34 ≤B 21 + B 22 + B 23 ∧ . . .• Even more difficult with variables for the productsSolution:Combination of different modellings: redundant constraints.cS.Abdennadher 34

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