PL Pareto Examples 121101 ------------------------- Peter Lohmander 121101 Example 0: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 0; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 0.000000 Infeasibilities: 0.000000 Total solver iterations: 0 Variable Value Reduced Cost TOT_H_KOSTNAD 0.000000 0.000000 TOT_S_INTAKT 0.000000 0.000000 S_TOT 0.000000 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 0.000000 1000.000 Q( 2) 0.000000 500.0000 Q( 3) 0.000000 1000.000 Row Slack or Surplus Dual Price 1 0.000000 -1.000000 2 0.000000 -1.000000 3 0.000000 0.000000 S_KRAV 0.000000 0.000000 5 0.000000 0.000000 6 1000.000 0.000000 7 800.0000 0.000000 8 1000.000 0.000000 ----------------------------------------------------------------------- Example 1: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 1000000; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 500000.0 Infeasibilities: 0.000000 Total solver iterations: 0 Variable Value Reduced Cost TOT_H_KOSTNAD 500000.0 0.000000 TOT_S_INTAKT 1000000. 0.000000 S_TOT 1000000. 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 0.000000 750.0000 Q( 2) 0.000000 250.0000 Q( 3) 500.0000 0.000000 Row Slack or Surplus Dual Price 1 500000.0 -1.000000 2 0.000000 -1.000000 3 0.000000 0.5000000 S_KRAV 0.000000 -0.5000000 5 0.000000 -0.5000000 6 1000.000 0.000000 7 800.0000 0.000000 8 500.0000 0.000000 --------------------------------------------------------------------- Example 2: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 2000000; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 1000000. Infeasibilities: 0.000000 Total solver iterations: 0 Variable Value Reduced Cost TOT_H_KOSTNAD 1000000. 0.000000 TOT_S_INTAKT 2000000. 0.000000 S_TOT 2000000. 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 0.000000 750.0000 Q( 2) 0.000000 250.0000 Q( 3) 1000.000 0.000000 Row Slack or Surplus Dual Price 1 1000000. -1.000000 2 0.000000 -1.000000 3 0.000000 0.5000000 S_KRAV 0.000000 -0.5000000 5 0.000000 -0.5000000 6 1000.000 0.000000 7 800.0000 0.000000 8 0.000000 0.000000 ----------------------------------------------------------------------- Example 3: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 2200000; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 1200000. Infeasibilities: 0.000000 Total solver iterations: 1 Variable Value Reduced Cost TOT_H_KOSTNAD 1200000. 0.000000 TOT_S_INTAKT 2200000. 0.000000 S_TOT 2200000. 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 0.000000 500.0000 Q( 2) 400.0000 0.000000 Q( 3) 1000.000 0.000000 Row Slack or Surplus Dual Price 1 1200000. -1.000000 2 0.000000 -1.000000 3 0.000000 1.000000 S_KRAV 0.000000 -1.000000 5 0.000000 -1.000000 6 1000.000 0.000000 7 400.0000 0.000000 8 0.000000 1000.000 --------------------------------------------------------------------- Example 4: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 2400000; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 1400000. Infeasibilities: 0.000000 Total solver iterations: 0 Variable Value Reduced Cost TOT_H_KOSTNAD 1400000. 0.000000 TOT_S_INTAKT 2400000. 0.000000 S_TOT 2400000. 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 0.000000 0.000000 Q( 2) 800.0000 0.000000 Q( 3) 1000.000 0.000000 Row Slack or Surplus Dual Price 1 1400000. -1.000000 2 0.000000 -1.000000 3 0.000000 2.000000 S_KRAV 0.000000 -2.000000 5 0.000000 -2.000000 6 1000.000 0.000000 7 0.000000 500.0000 8 0.000000 3000.000 --------------------------------------------------------------------- Example 5: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 2650000; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 1900000. Infeasibilities: 0.000000 Total solver iterations: 0 Variable Value Reduced Cost TOT_H_KOSTNAD 1900000. 0.000000 TOT_S_INTAKT 2650000. 0.000000 S_TOT 2650000. 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 500.0000 0.000000 Q( 2) 800.0000 0.000000 Q( 3) 1000.000 0.000000 Row Slack or Surplus Dual Price 1 1900000. -1.000000 2 0.000000 -1.000000 3 0.000000 2.000000 S_KRAV 0.000000 -2.000000 5 0.000000 -2.000000 6 500.0000 0.000000 7 0.000000 500.0000 8 0.000000 3000.000 --------------------------------------------------------------------- Example 6: ---------- ! PL Pareto 121101; ! Peter Lohmander 121101; model: sets: Hansyn/1..3/:H_kostnad, S_Intakt, Kap, q; endsets min = Tot_H_kostnad; Tot_H_Kostnad = @sum(Hansyn(j): H_kostnad(j)*q(j)); Tot_S_Intakt = @sum(Hansyn(j): S_Intakt(j)*q(j)); [S_Krav] Tot_S_Intakt >= S_Tot; S_Tot = 2900000; @for(Hansyn(j): q(j) <= Kap(j)); data: H_kostnad = 1000 500 1000; S_Intakt = 500 500 2000; Kap = 1000 800 1000; enddata end Global optimal solution found. Objective value: 2400000. Infeasibilities: 0.000000 Total solver iterations: 0 Variable Value Reduced Cost TOT_H_KOSTNAD 2400000. 0.000000 TOT_S_INTAKT 2900000. 0.000000 S_TOT 2900000. 0.000000 H_KOSTNAD( 1) 1000.000 0.000000 H_KOSTNAD( 2) 500.0000 0.000000 H_KOSTNAD( 3) 1000.000 0.000000 S_INTAKT( 1) 500.0000 0.000000 S_INTAKT( 2) 500.0000 0.000000 S_INTAKT( 3) 2000.000 0.000000 KAP( 1) 1000.000 0.000000 KAP( 2) 800.0000 0.000000 KAP( 3) 1000.000 0.000000 Q( 1) 1000.000 0.000000 Q( 2) 800.0000 0.000000 Q( 3) 1000.000 0.000000 Row Slack or Surplus Dual Price 1 2400000. -1.000000 2 0.000000 -1.000000 3 0.000000 2.000000 S_KRAV 0.000000 -2.000000 5 0.000000 -2.000000 6 0.000000 0.000000 7 0.000000 500.0000 8 0.000000 3000.000 ---------------------------------------------------------------------