The inventory constraint makes our model infeasible, we are unable to identify exactly why.
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sindre Eriksen
Mar 3, 2021, 5:47:37 AM3/3/21
to AMPL Modeling Language
The model works as intended as long as q0, q2 and q3 is commented out. q0 and q3 works as intended as long as q2 is commented out. When q2 is included, it calcluates the initial inventory as intended, but q0 returns either 0 or negative values. That is, it returns the negative values of D, indicating that
"I[p,k,t-1] + A[p,k,t]" is not taken into account at all.
This is the code:
reset;
param P;
set J ordered;
set K ordered;
param T;
param VC{J,K,1..T};
param FC{J,K,1..T};
param D{1..P,K, 1..T};
param value {1..P,K};
param Zmax {J,K};
param Zmin{J};
param InventMax {1..P,K};
param Init{1..P,K};
var Y{J,K,1..T} binary;
var Z{1..P,J,K,1..T} >=0;
var I{1..P,K,1..T} >=0;
var A{1..P, K, 1..T} >=0;
maximize TotalCosts: sum{p in 1..P, j in J,k in K, t in 1..T} value[p,k]*Z[p,j,k,t]- sum{j in J, k in K,t in 1..T} (VC[j,k,t]+FC[j,k,t])*Y[j,k,t];#-sum{p in 1..P,t in 1..T,k in K} H[p,k]*I[p,k,t];
#s.t. q0 {p in 1..P,k in K,t in 2..T}:
# I[p,k,t]=I[p,k,t-1] + A[p,k,t] - D[p,k,t];
#s.t. q2 {p in 1..P,k in K}:
# I[p,k,1]=Init[p,k] + A[p,k,1] - D[p,k,1];
#s.t. q3 {p in 1..P,k in K, t in 1..T}:
# I[p,k,t]<=InventMax[p,k];
s.t. con90{p in 1..P, k in K, t in 1..T}: A[p,k,t] = sum{j in J} Z[p,j,k,t];
s.t. q4 {j in J, k in K, t in 1..T}:
sum{p in 1..P} Z[p,j,k,t] <= Zmax[j,k]*Y[j,k,t];
s.t. q5 {j in J, k in K,t in 1..T}:
sum{p in 1..P} Z[p,j,k,t] >= Zmin[j]*Y[j,k,t];
s.t. q51 {p in 1..P, j in J, k in K,t in 1..T}:
Z[p,j,k,t] <= D[p,k,t]*Y[j,k,t];
s.t. q12 {k in K, t in 1..T}:
sum {j in J} Y[j,k,t] <= 1;
s.t. q74 {t in 1..T}:
sum {k in K} Y["ALPHA",k,t] <= 2;
s.t. q89 {t in 1..T}:
sum {k in K} Y["BETA",k,t] <= 2;
s.t. q99 {t in 1..T}:
sum {k in K} Y["GAMMA",k,t] <= 2;
data;
param P := 3;
set J := ALPHA BETA GAMMA;
set K := Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin;
param T:= 52;
param value:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
1 0 122 126 130 0 131 129 112
2 129 129 133 136 145 138 136 0
3 0 0 151 154 163 156 154 0;
#Variable cost
param VC:=
[ALPHA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491
Aabenraa 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888
Copenhagen 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453
Oslo 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513
Bergen 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854
Stockholm 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799
Gothenburg 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870
Stettin 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437
[BETA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853
Aabenraa 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199
Copenhagen 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821
Oslo 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361
Bergen 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402
Stockholm 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971
Gothenburg 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928
Stettin 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295
[GAMMA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330
Aabenraa 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631
Copenhagen 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301
Oslo 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385
Bergen 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164
Stockholm 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401
Gothenburg 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137
Stettin 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328;
# Fixed costs
param FC:=
[ALPHA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320
Aabenraa 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300
Copenhagen 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100
Oslo 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
Bergen 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850
Stockholm 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000
Gothenburg 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600
Stettin 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250
[BETA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130
Aabenraa 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
Copenhagen 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250
Oslo 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800
Bergen 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850
Stockholm 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400
Gothenburg 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
Stettin 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650
[GAMMA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130
Aabenraa 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
Copenhagen 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250
Oslo 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800
Bergen 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850
Stockholm 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400
Gothenburg 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900
Stettin 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650;
# Demand
param D:=
[1,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Aabenraa 183 103 342 163 253 230 221 229 153 316 155 262 153 102 132 327 221 635 218 318 292 259 256 373 498 304 427 227 79 210 392 479 214 466 188 379 419 375 260 74 0 712 868 937 0 0 53 343 474 677 355 104
Copenhagen 292 950 705 1210 1449 1575 878 1085 1022 1221 1591 1468 303 473 958 890 2024 2081 1243 1379 1219 2007 2051 1374 1356 2591 1254 2757 447 445 614 1131 1215 1236 995 1044 292 2254 1353 1744 2457 1741 1014 1812 3437 2355 2605 942 1599 1116 2165 151
Oslo 475 430 433 976 626 1171 948 1054 1234 921 837 1270 375 352 1323 1034 820 885 925 1715 1180 981 1941 1043 1096 2567 1622 902 126 286 927 1031 1157 1205 1666 1356 1886 1422 1453 891 1755 1852 1600 2147 1329 1538 1403 580 682 1049 1815 118
Bergen 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Stockholm 322 380 475 590 703 602 907 864 715 671 708 491 201 400 1055 740 845 688 1226 1111 275 1020 395 1133 2270 1296 1047 1907 277 452 743 1265 382 567 431 1172 984 843 1251 0 1346 1595 1580 1280 952 1254 594 863 746 718 436 30
Gothenburg 600 530 922 612 847 830 1152 1056 1246 1218 1860 1538 479 550 1252 1475 1438 1274 887 1838 1027 2005 1167 1519 1512 1850 2011 1776 208 267 1205 1794 207 2111 1458 1209 1712 2036 1914 1358 2391 2009 1848 1402 2012 1837 1167 1012 1003 1545 883 213
Stettin 205 207 522 586 719 891 673 810 664 644 849 673 146 349 570 1106 929 595 633 1408 719 1204 1355 590 1102 579 807 1002 775 227 546 1256 634 636 397 961 851 509 1318 1248 1077 952 852 968 1288 2169 0 194 873 1543 885 85
[2,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 177 295 351 298 427 386 81 354 402 178 0 265 190 158 571 596 529 110 543 845 332 444 522 568 248 0 639 469 214 292 217 187 0 547 577 0 674 363 463 587 310 440 538 399 500 411 416 294 600 368 524 137
Aabenraa 97 118 118 175 216 120 117 116 97 158 158 306 80 177 40 437 149 117 76 339 225 203 216 179 140 308 329 358 216 199 178 230 250 58 182 251 179 77 130 98 133 237 256 258 198 122 135 254 257 192 121 40
Copenhagen 205 187 282 120 218 405 167 0 279 325 47 219 319 214 140 254 334 546 743 147 261 338 306 305 342 292 368 241 315 187 143 284 235 495 117 266 302 421 528 230 497 272 357 347 307 355 308 454 167 250 233 98
Oslo 106 263 195 194 88 85 237 153 108 234 198 265 88 133 283 158 0 107 228 243 109 299 282 281 195 250 263 156 193 237 133 152 240 0 0 0 123 196 216 235 148 150 263 0 359 510 63 148 333 0 154 65
Bergen 240 276 147 148 611 298 529 233 456 395 0 328 124 311 269 260 273 149 350 320 271 530 437 712 558 664 386 175 333 329 389 650 258 344 501 493 408 442 676 379 294 514 563 0 423 269 486 410 486 448 173 785
Stockholm 195 246 198 265 97 382 100 96 430 368 513 202 187 286 265 119 145 321 199 515 254 299 174 556 164 437 445 432 319 213 308 341 310 334 222 299 196 73 501 215 445 362 315 366 433 266 378 912 233 198 121 0
Gothenburg 149 94 216 332 455 123 237 138 276 322 94 165 191 232 23 263 176 163 226 557 289 516 380 360 298 426 434 241 221 212 259 317 204 476 287 367 359 306 531 317 436 486 264 125 667 120 361 535 409 345 234 22
Stettin 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[3,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Aabenraa 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Copenhagen 181 448 840 682 476 638 402 675 482 475 584 730 172 294 359 404 528 569 267 511 331 579 457 385 320 396 393 351 241 209 245 376 146 202 301 248 519 491 559 1173 377 389 475 0 906 462 452 574 531 82 1024 61
Oslo 133 159 424 508 509 572 469 376 369 459 517 388 237 429 301 208 507 473 242 271 231 269 298 404 263 184 271 259 208 214 368 350 163 131 0 321 347 496 409 314 500 328 0 534 282 641 488 435 459 548 691 102
Bergen 535 557 1340 941 1446 1575 945 1573 1374 641 1800 1420 396 437 1003 1192 991 655 434 1354 613 1237 1393 675 1048 836 1305 484 632 555 853 350 531 792 809 522 1354 684 1163 828 571 1435 960 630 617 632 632 382 1470 1689 847 29
Stockholm 316 399 279 411 216 380 395 427 508 524 549 536 194 138 372 498 447 203 263 200 248 375 318 855 777 121 251 610 345 253 335 395 296 317 261 128 650 225 277 183 0 446 368 442 413 591 319 809 347 476 335 86
Gothenburg 352 480 613 930 964 603 724 710 936 962 860 656 329 160 678 792 1105 950 439 710 569 995 433 805 797 277 668 376 215 125 308 595 193 679 354 162 518 480 779 496 515 515 371 502 461 934 747 697 615 951 925 127
Stettin 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
param Zmax:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
ALPHA 2800 2200 4100 4100 3400 2900 4100 600
BETA 2400 2200 2900 2900 2700 2500 2900 2800
GAMMA 2300 2000 2300 2300 2300 2300 2300 2300;
param Zmin:=
ALPHA 500
BETA 400
GAMMA 300;
param InventMax:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
1 0 1200 2100 1800 0 1600 2100 2700
2 2100 700 1050 1000 900 800 1000 0
3 0 0 1050 1300 1800 700 1000 0;
param Init:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
1 0 1026 1292 543 0 1057 1492 1798
2 1736 571 1038 747 830 745 753 0
3 0 0 1022 1014 1793 568 844 0;
option solver gurobi;
solve;
param P;
set J ordered;
set K ordered;
param T;
param VC{J,K,1..T};
param FC{J,K,1..T};
param D{1..P,K, 1..T};
param value {1..P,K};
param Zmax {J,K};
param Zmin{J};
param InventMax {1..P,K};
param Init{1..P,K};
var Y{J,K,1..T} binary;
var Z{1..P,J,K,1..T} >=0;
var I{1..P,K,1..T} >=0;
var A{1..P, K, 1..T} >=0;
maximize TotalCosts: sum{p in 1..P, j in J,k in K, t in 1..T} value[p,k]*Z[p,j,k,t]- sum{j in J, k in K,t in 1..T} (VC[j,k,t]+FC[j,k,t])*Y[j,k,t];#-sum{p in 1..P,t in 1..T,k in K} H[p,k]*I[p,k,t];
#s.t. q0 {p in 1..P,k in K,t in 2..T}:
# I[p,k,t]=I[p,k,t-1] + A[p,k,t] - D[p,k,t];
#s.t. q2 {p in 1..P,k in K}:
# I[p,k,1]=Init[p,k] + A[p,k,1] - D[p,k,1];
#s.t. q3 {p in 1..P,k in K, t in 1..T}:
# I[p,k,t]<=InventMax[p,k];
s.t. con90{p in 1..P, k in K, t in 1..T}: A[p,k,t] = sum{j in J} Z[p,j,k,t];
s.t. q4 {j in J, k in K, t in 1..T}:
sum{p in 1..P} Z[p,j,k,t] <= Zmax[j,k]*Y[j,k,t];
s.t. q5 {j in J, k in K,t in 1..T}:
sum{p in 1..P} Z[p,j,k,t] >= Zmin[j]*Y[j,k,t];
s.t. q51 {p in 1..P, j in J, k in K,t in 1..T}:
Z[p,j,k,t] <= D[p,k,t]*Y[j,k,t];
s.t. q12 {k in K, t in 1..T}:
sum {j in J} Y[j,k,t] <= 1;
s.t. q74 {t in 1..T}:
sum {k in K} Y["ALPHA",k,t] <= 2;
s.t. q89 {t in 1..T}:
sum {k in K} Y["BETA",k,t] <= 2;
s.t. q99 {t in 1..T}:
sum {k in K} Y["GAMMA",k,t] <= 2;
data;
param P := 3;
set J := ALPHA BETA GAMMA;
set K := Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin;
param T:= 52;
param value:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
1 0 122 126 130 0 131 129 112
2 129 129 133 136 145 138 136 0
3 0 0 151 154 163 156 154 0;
#Variable cost
param VC:=
[ALPHA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491 4491
Aabenraa 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888 4888
Copenhagen 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453 4453
Oslo 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513 8513
Bergen 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854 10854
Stockholm 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799 13799
Gothenburg 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870 6870
Stettin 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437 8437
[BETA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853 3853
Aabenraa 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199 4199
Copenhagen 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821 3821
Oslo 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361 7361
Bergen 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402 9402
Stockholm 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971 11971
Gothenburg 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928 5928
Stettin 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295 7295
[GAMMA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330 3330
Aabenraa 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631 3631
Copenhagen 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301 3301
Oslo 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385 6385
Bergen 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164 8164
Stockholm 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401 10401
Gothenburg 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137 5137
Stettin 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328 6328;
# Fixed costs
param FC:=
[ALPHA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320 1320
Aabenraa 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300 1300
Copenhagen 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100
Oslo 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
Bergen 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850
Stockholm 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000
Gothenburg 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600 2600
Stettin 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250 2250
[BETA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130
Aabenraa 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
Copenhagen 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250
Oslo 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800
Bergen 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850
Stockholm 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400
Gothenburg 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
Stettin 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650
[GAMMA,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130 1130
Aabenraa 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100
Copenhagen 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250 3250
Oslo 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800 1800
Bergen 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850 850
Stockholm 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400 2400
Gothenburg 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900 1900
Stettin 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650 1650;
# Demand
param D:=
[1,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Aabenraa 183 103 342 163 253 230 221 229 153 316 155 262 153 102 132 327 221 635 218 318 292 259 256 373 498 304 427 227 79 210 392 479 214 466 188 379 419 375 260 74 0 712 868 937 0 0 53 343 474 677 355 104
Copenhagen 292 950 705 1210 1449 1575 878 1085 1022 1221 1591 1468 303 473 958 890 2024 2081 1243 1379 1219 2007 2051 1374 1356 2591 1254 2757 447 445 614 1131 1215 1236 995 1044 292 2254 1353 1744 2457 1741 1014 1812 3437 2355 2605 942 1599 1116 2165 151
Oslo 475 430 433 976 626 1171 948 1054 1234 921 837 1270 375 352 1323 1034 820 885 925 1715 1180 981 1941 1043 1096 2567 1622 902 126 286 927 1031 1157 1205 1666 1356 1886 1422 1453 891 1755 1852 1600 2147 1329 1538 1403 580 682 1049 1815 118
Bergen 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Stockholm 322 380 475 590 703 602 907 864 715 671 708 491 201 400 1055 740 845 688 1226 1111 275 1020 395 1133 2270 1296 1047 1907 277 452 743 1265 382 567 431 1172 984 843 1251 0 1346 1595 1580 1280 952 1254 594 863 746 718 436 30
Gothenburg 600 530 922 612 847 830 1152 1056 1246 1218 1860 1538 479 550 1252 1475 1438 1274 887 1838 1027 2005 1167 1519 1512 1850 2011 1776 208 267 1205 1794 207 2111 1458 1209 1712 2036 1914 1358 2391 2009 1848 1402 2012 1837 1167 1012 1003 1545 883 213
Stettin 205 207 522 586 719 891 673 810 664 644 849 673 146 349 570 1106 929 595 633 1408 719 1204 1355 590 1102 579 807 1002 775 227 546 1256 634 636 397 961 851 509 1318 1248 1077 952 852 968 1288 2169 0 194 873 1543 885 85
[2,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 177 295 351 298 427 386 81 354 402 178 0 265 190 158 571 596 529 110 543 845 332 444 522 568 248 0 639 469 214 292 217 187 0 547 577 0 674 363 463 587 310 440 538 399 500 411 416 294 600 368 524 137
Aabenraa 97 118 118 175 216 120 117 116 97 158 158 306 80 177 40 437 149 117 76 339 225 203 216 179 140 308 329 358 216 199 178 230 250 58 182 251 179 77 130 98 133 237 256 258 198 122 135 254 257 192 121 40
Copenhagen 205 187 282 120 218 405 167 0 279 325 47 219 319 214 140 254 334 546 743 147 261 338 306 305 342 292 368 241 315 187 143 284 235 495 117 266 302 421 528 230 497 272 357 347 307 355 308 454 167 250 233 98
Oslo 106 263 195 194 88 85 237 153 108 234 198 265 88 133 283 158 0 107 228 243 109 299 282 281 195 250 263 156 193 237 133 152 240 0 0 0 123 196 216 235 148 150 263 0 359 510 63 148 333 0 154 65
Bergen 240 276 147 148 611 298 529 233 456 395 0 328 124 311 269 260 273 149 350 320 271 530 437 712 558 664 386 175 333 329 389 650 258 344 501 493 408 442 676 379 294 514 563 0 423 269 486 410 486 448 173 785
Stockholm 195 246 198 265 97 382 100 96 430 368 513 202 187 286 265 119 145 321 199 515 254 299 174 556 164 437 445 432 319 213 308 341 310 334 222 299 196 73 501 215 445 362 315 366 433 266 378 912 233 198 121 0
Gothenburg 149 94 216 332 455 123 237 138 276 322 94 165 191 232 23 263 176 163 226 557 289 516 380 360 298 426 434 241 221 212 259 317 204 476 287 367 359 306 531 317 436 486 264 125 667 120 361 535 409 345 234 22
Stettin 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[3,*,*] :
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52:=
Aalborg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Aabenraa 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Copenhagen 181 448 840 682 476 638 402 675 482 475 584 730 172 294 359 404 528 569 267 511 331 579 457 385 320 396 393 351 241 209 245 376 146 202 301 248 519 491 559 1173 377 389 475 0 906 462 452 574 531 82 1024 61
Oslo 133 159 424 508 509 572 469 376 369 459 517 388 237 429 301 208 507 473 242 271 231 269 298 404 263 184 271 259 208 214 368 350 163 131 0 321 347 496 409 314 500 328 0 534 282 641 488 435 459 548 691 102
Bergen 535 557 1340 941 1446 1575 945 1573 1374 641 1800 1420 396 437 1003 1192 991 655 434 1354 613 1237 1393 675 1048 836 1305 484 632 555 853 350 531 792 809 522 1354 684 1163 828 571 1435 960 630 617 632 632 382 1470 1689 847 29
Stockholm 316 399 279 411 216 380 395 427 508 524 549 536 194 138 372 498 447 203 263 200 248 375 318 855 777 121 251 610 345 253 335 395 296 317 261 128 650 225 277 183 0 446 368 442 413 591 319 809 347 476 335 86
Gothenburg 352 480 613 930 964 603 724 710 936 962 860 656 329 160 678 792 1105 950 439 710 569 995 433 805 797 277 668 376 215 125 308 595 193 679 354 162 518 480 779 496 515 515 371 502 461 934 747 697 615 951 925 127
Stettin 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
param Zmax:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
ALPHA 2800 2200 4100 4100 3400 2900 4100 600
BETA 2400 2200 2900 2900 2700 2500 2900 2800
GAMMA 2300 2000 2300 2300 2300 2300 2300 2300;
param Zmin:=
ALPHA 500
BETA 400
GAMMA 300;
param InventMax:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
1 0 1200 2100 1800 0 1600 2100 2700
2 2100 700 1050 1000 900 800 1000 0
3 0 0 1050 1300 1800 700 1000 0;
param Init:
Aalborg Aabenraa Copenhagen Oslo Bergen Stockholm Gothenburg Stettin:=
1 0 1026 1292 543 0 1057 1492 1798
2 1736 571 1038 747 830 745 753 0
3 0 0 1022 1014 1793 568 844 0;
option solver gurobi;
solve;
AMPL Google Group
Mar 4, 2021, 12:34:03 PM3/4/21
to AMPL Modeling Language
I confirmed that your problem is infeasible, and that it becomes feasible when the q0 constraints are dropped.
There is no single easy way to troubleshoot infeasibility. Determining and fixing the cause of infeasibility will probably require some more study of the model. Also, even if the model is correct, there may be no feasible solution for the particular data that is given. Examining the solution after the "solve" does not help, since solvers do not return a valid solution when the problem infeasible. It is possible to suggest some good ways to start looking for the cause of infeasibility, however.
As an initial step, it is often helpful to use AMPL's expand command to see see whether AMPL generated the constraints that you expected. By itself, expand; shows all of the constraints. If there are many of them, you can use, for example, expand C1; to expand all of the constraints that have a particular name. Also you can write, for instance, expand >listing.txt; or expand C1 >listing.txt; to send all of the output to the file listing.txt.
You can also continue using AMPL's drop and restore commands to narrow your search for the cause of the infeasibility. If you drop some constraints and the resulting problem is still infeasible, then you don't need to consider the dropped constraints in looking for the cause of infeasibility. By trying a series of drops, you may be able to determine that the infeasibility is being caused by only a small subset of the constraints.
To get more help with diagnosing the infeasibility, you can ask any of the popular MIP solvers (CPLEX, Gurobi, Xpress) to compute an irreducible infeasible subset. For more on this topic, search "IIS" at https://groups.google.com/group/ampl, and also see the discussion of "infeasibility diagnosis" in chapter 14 of the AMPL book (https://ampl.com/BOOK/CHAPTERS/17-solvers.pdf#page=25).
There is no single easy way to troubleshoot infeasibility. Determining and fixing the cause of infeasibility will probably require some more study of the model. Also, even if the model is correct, there may be no feasible solution for the particular data that is given. Examining the solution after the "solve" does not help, since solvers do not return a valid solution when the problem infeasible. It is possible to suggest some good ways to start looking for the cause of infeasibility, however.
As an initial step, it is often helpful to use AMPL's expand command to see see whether AMPL generated the constraints that you expected. By itself, expand; shows all of the constraints. If there are many of them, you can use, for example, expand C1; to expand all of the constraints that have a particular name. Also you can write, for instance, expand >listing.txt; or expand C1 >listing.txt; to send all of the output to the file listing.txt.
You can also continue using AMPL's drop and restore commands to narrow your search for the cause of the infeasibility. If you drop some constraints and the resulting problem is still infeasible, then you don't need to consider the dropped constraints in looking for the cause of infeasibility. By trying a series of drops, you may be able to determine that the infeasibility is being caused by only a small subset of the constraints.
To get more help with diagnosing the infeasibility, you can ask any of the popular MIP solvers (CPLEX, Gurobi, Xpress) to compute an irreducible infeasible subset. For more on this topic, search "IIS" at https://groups.google.com/group/ampl, and also see the discussion of "infeasibility diagnosis" in chapter 14 of the AMPL book (https://ampl.com/BOOK/CHAPTERS/17-solvers.pdf#page=25).
--
Robert Fourer
am...@googlegroups.com
sindre Eriksen
Mar 5, 2021, 5:07:56 AM3/5/21
to AMPL Modeling Language
Thank you for the answer Robert.
We concluded that the infeasibility must lie in "q0", since the model becomes feasible when we drop it. Is this the correct way of thought, or can the infeasibility lie elsewhere?
AMPL Google Group
Mar 6, 2021, 10:42:43 AM3/6/21
to AMPL Modeling Language
You can conclude that the q0 constraints are helping to make the problem infeasible. But the cause of infeasibility also involves other constraints. You can see that by running the following test, which drops the objective and all of the constraints except q0, then uses the solver to find a solution that is feasible for the q0 constraints:
ampl: drop all;
ampl: restore q0;
ampl: solve;
Gurobi 9.1.1: optimal solution; objective 0
Objective = find a feasible point.
What you want to do is to find a small subset of constraints that are infeasible. This subset will include q0, but also some others. See my previous suggestion for two ways to do this: by using the drop and restore commands, or by using the "irreducible infeasible subset" feature of Gurobi.
ampl: drop all;
ampl: restore q0;
ampl: solve;
Gurobi 9.1.1: optimal solution; objective 0
Objective = find a feasible point.
What you want to do is to find a small subset of constraints that are infeasible. This subset will include q0, but also some others. See my previous suggestion for two ways to do this: by using the drop and restore commands, or by using the "irreducible infeasible subset" feature of Gurobi.
--
Robert Fourer
am...@googlegroups.com
On Fri, Mar 5, 2021 at 10:08 AM UTC, AMPL Modeling Language <am...@googlegroups.com> wrote:
Thank you for the answer Robert.
We concluded that the infeasibility must lie in "q0", since the model becomes feasible when we drop it. Is this the correct way of thought, or can the infeasibility lie elsewhere?
On Thu, Mar 4, 2021 at 5:33 PM UTC, AMPL Google Group <am...@googlegroups.com> wrote:
I confirmed that your problem is infeasible, and that it becomes feasible when the q0 constraints are dropped.
There is no single easy way to troubleshoot infeasibility. Determining and fixing the cause of infeasibility will probably require some more study of the model. Also, even if the model is correct, there may be no feasible solution for the particular data that is given. Examining the solution after the "solve" does not help, since solvers do not return a valid solution when the problem infeasible. It is possible to suggest some good ways to start looking for the cause of infeasibility, however.
As an initial step, it is often helpful to use AMPL's expand command to see see whether AMPL generated the constraints that you expected. By itself, expand; shows all of the constraints. If there are many of them, you can use, for example, expand C1; to expand all of the constraints that have a particular name. Also you can write, for instance, expand >listing.txt; or expand C1 >listing.txt; to send all of the output to the file listing.txt.
You can also continue using AMPL's drop and restore commands to narrow your search for the cause of the infeasibility. If you drop some constraints and the resulting problem is still infeasible, then you don't need to consider the dropped constraints in looking for the cause of infeasibility. By trying a series of drops, you may be able to determine that the infeasibility is being caused by only a small subset of the constraints.
To get more help with diagnosing the infeasibility, you can ask any of the popular MIP solvers (CPLEX, Gurobi, Xpress) to compute an irreducible infeasible subset. For more on this topic, search "IIS" at https://groups.google.com/group/ampl, and also see the discussion of "infeasibility diagnosis" in chapter 14 of the AMPL book (https://ampl.com/BOOK/CHAPTERS/17-solvers.pdf#page=25).
--
Robert Fourer
am...@googlegroups.com
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