Zadanie 5
param m := 6;
param n :=10;
set M :=1..m;
set N := 1..n;
param b {j in N};
param p {i in M, j in N};
param T {i in N};
var x {i in M, j in N}>= 0 integer;
var Cmax>=0;
minimize czas : Cmax;
subject to ilosc_sztuk{j in N}: sum {i in M}x[i,j]=b[j];
subject to czas_dysponowany{i in M}: sum {j in N}p[i,j]*x[i,j]<= T[i];
subject to czas_wykonania {i in M}: sum{j in N}p[i,j]*x[i,j]<=Cmax;
end;
data;
param b:= 1 30 2 180 3 60 4 90 5 100 6 75 7 30 8 125 9 125 10 42;
param T := 1 300 2 50 3 120 4 50 5 120 6 150;
param p : 1 2 3 4 5 6 7 8 9 10:=
1 1000 0.250 1000 0.500 0.250 1000 0.750 0.355 1000 0.425
2 1000 0.166 0.250 0.333 1000 0.550 1000 1000 1000 0.950
3 0.125 1000 0.500 0.250 0.166 1000 1000 0.959 0.450 0.255
4 0.250 1000 1000 1000 1000 0.025 0.325 1000 0.650 1000
5 0.459 0.560 0.457 1000 0.543 1000 0.623 1000 0.750 0.220
6 0.367 0.214 0.324 0.789 1000 0.458 0.560 0.759 0.325 1000;
end;
Problem: lab5
Rows: 23
Columns: 61 (60 integer, 0 binary)
Non-zeros: 187
Status: INTEGER OPTIMAL
Objective: czas = 38.296 (MINimum) 38.16309116 (LP)
No. Row name Activity Lower bound Upper bound
------ ------------ ------------- ------------- -------------
1 czas 38.296
2 ilosc_sztuk[1]
30 30 =
3 ilosc_sztuk[2]
180 180 =
4 ilosc_sztuk[3]
60 60 =
5 ilosc_sztuk[4]
90 90 =
6 ilosc_sztuk[5]
100 100 =
7 ilosc_sztuk[6]
75 75 =
8 ilosc_sztuk[7]
30 30 =
9 ilosc_sztuk[8]
125 125 =
10 ilosc_sztuk[9]
125 125 =
11 ilosc_sztuk[10]
42 42 =
12 czas_dysponowany[1]
38.235 300
13 czas_dysponowany[2]
38.296 50
14 czas_dysponowany[3]
38.268 120
15 czas_dysponowany[4]
38.275 50
16 czas_dysponowany[5]
38.2 120
17 czas_dysponowany[6]
38.251 150
18 czas_wykonania[1]
-0.061 0
19 czas_wykonania[2]
0 0
20 czas_wykonania[3]
-0.028 0
21 czas_wykonania[4]
-0.021 0
22 czas_wykonania[5]
-0.096 0
23 czas_wykonania[6]
-0.045 0
No. Column name Activity Lower bound Upper bound
------ ------------ ------------- ------------- -------------
1 x[1,1] * 0 0
2 x[2,1] * 0 0
3 x[3,1] * 4 0
4 x[4,1] * 26 0
5 x[5,1] * 0 0
6 x[6,1] * 0 0
7 x[1,2] * 0 0
8 x[2,2] * 179 0
9 x[3,2] * 0 0
10 x[4,2] * 0 0
11 x[5,2] * 0 0
12 x[6,2] * 1 0
13 x[1,3] * 0 0
14 x[2,3] * 29 0
15 x[3,3] * 0 0
16 x[4,3] * 0 0
17 x[5,3] * 31 0
18 x[6,3] * 0 0
19 x[1,4] * 0 0
20 x[2,4] * 4 0
21 x[3,4] * 86 0
22 x[4,4] * 0 0
23 x[5,4] * 0 0
24 x[6,4] * 0 0
25 x[1,5] * 1 0
26 x[2,5] * 0 0
27 x[3,5] * 98 0
28 x[4,5] * 0 0
29 x[5,5] * 1 0
30 x[6,5] * 0 0
31 x[1,6] * 0 0
32 x[2,6] * 0 0
33 x[3,6] * 0 0
34 x[4,6] * 75 0
35 x[5,6] * 0 0
36 x[6,6] * 0 0
37 x[1,7] * 0 0
38 x[2,7] * 0 0
39 x[3,7] * 0 0
40 x[4,7] * 30 0
41 x[5,7] * 0 0
42 x[6,7] * 0 0
43 x[1,8] * 107 0
44 x[2,8] * 0 0
45 x[3,8] * 0 0
46 x[4,8] * 0 0
47 x[5,8] * 0 0
48 x[6,8] * 18 0
49 x[1,9] * 0 0
50 x[2,9] * 0 0
51 x[3,9] * 0 0
52 x[4,9] * 31 0
53 x[5,9] * 19 0
54 x[6,9] * 75 0
55 x[1,10] * 0 0
56 x[2,10] * 0 0
57 x[3,10] * 0 0
58 x[4,10] * 0 0
59 x[5,10] * 42 0
60 x[6,10] * 0 0
61 Cmax 38.296 0
Integer feasibility conditions:
INT.PE: max.abs.err. = 5.00e-015 on row 15
max.rel.err. = 1.27e-016 on row 15
High quality
INT.PB: max.abs.err. = 0.00e+000 on row 0
max.rel.err. = 0.00e+000 on row 0
High quality
End of output
Zadanie 6
Wariant a
set N:=1..n;
set P within N;
set Q within N;
param a {j in N};
param b {j in N};
param c {j in N};
param d {j in N};
param nmin;
param W;
var x {j in N}>=0;
var y {j in N}>=0;
var u {j in N} >=0 integer;
var z {j in N} binary;
maximize zysk: sum {j in N} (b[j]*x[j]-d[j]*y[j]);
subject to OGR1: sum {j in N} x[j]<=W;
subject to OGR2 {j in N}: x[j]<=W*z[j];
subject to OGR3 {j in N}:a[j]*u[j]=x[j];
subject to OGR4 {j in N}:x[j]<=c[j]+y[j];
subject to OGR5: sum {j in N} z[j]>=nmin;
subject to OGR6 {p in P,q in Q}: z[p]+z[q]<=1;
subject to OGR7a:
0.75*sum {j in N:j<=k} x[j] <= sum {j in N: j>=k+1} x[j];
subject to OGR8a:
1.25*sum {j in N:j<=k} x[j] >= sum {j in N: j>=k+1} x[j];
end;
data;
set P:= 2 3 6 7;
set Q:= 5 10 12 14;
param nmin:= 3;
param W:= 3600000;
param a:= 1 60 2 90 3 42 4 30 5 30 6 25 7 50 8 36 9 100 10 60 11 205 12 75 13 90 14 120;
param b:= 1 0.30 2 0.33 3 0.21 4 0.15 5 0.45 6 0.06 7 0.42 8 0.51 9 0.57 10 0.27 11 0.39 12 0.39 13 0.45 14 0.60;
param c:= 1 6600 2 6900 3 1020 4 900 5 900 6 1250 7 1500 8 4500 9 11000 10 6600 11 12050 12 1750 13 6900 14 7200;
param d:= 1 0.10 2 0.11 3 0.07 4 0.05 5 0.15 6 0.02 7 0.14 8 0.17 9 0.19 10 0.09 11 0.13 12 0.09 13 0.15 14 0.20;
end;
Problem: lab6
Rows: 63
Columns: 56 (28 integer, 14 binary)
Non-zeros: 200
Status: INTEGER OPTIMAL
Objective: zysk = 1284277.2 (MAXimum) 1284672 (LP)
No. Row name Activity Lower bound Upper bound
------ ------------ ------------- ------------- -------------
1 zysk 1.28428e+006
2 OGR1 3.6e+006 3.6e+006
3 OGR2[1] -3.5934e+006 0
4 OGR2[2] 0 0
5 OGR2[3] 0 0
6 OGR2[4] 0 0
7 OGR2[5] -2.00658e+006 0
8 OGR2[6] 0 0
9 OGR2[7] 0 0
10 OGR2[8] -3.5955e+006 0
11 OGR2[9] -3.589e+006 0
12 OGR2[10] 0 0
13 OGR2[11] -3.5998e+006 0
14 OGR2[12] -3.59993e+006 0
15 OGR2[13] -3.59316e+006 0
16 OGR2[14] -1.62264e+006 0
17 OGR3[1] 0 0 =
18 OGR3[2] 0 0 =
19 OGR3[3] 0 0 =
20 OGR3[4] 0 0 =
21 OGR3[5] 0 0 =
22 OGR3[6] 0 0 =
23 OGR3[7] 0 0 =
24 OGR3[8] 0 0 =
25 OGR3[9] 0 0 =
26 OGR3[10] 0 0 =
27 OGR3[11] 0 0 =
28 OGR3[12] 0 0 =
29 OGR3[13] 0 0 =
30 OGR3[14] 0 0 =
31 OGR4[1] 6600 6600
32 OGR4[2] 0 6900
33 OGR4[3] 0 1020
34 OGR4[4] 0 900
35 OGR4[5] 900 900
36 OGR4[6] 0 1250
37 OGR4[7] 0 1500
38 OGR4[8] 4500 4500
39 OGR4[9] 11000 11000
40 OGR4[10] 0 6600
41 OGR4[11] 205 12050
42 OGR4[12] 75 1750
43 OGR4[13] 6840 6900
44 OGR4[14] 7200 7200
45 OGR5 8 3
46 OGR6[2,5] 1 1
47 OGR6[2,10] 0 1
48 OGR6[2,12] 1 1
49 OGR6[2,14] 1 1
50 OGR6[3,5] 1 1
51 OGR6[3,10] 0 1
52 OGR6[3,12] 1 1
53 OGR6[3,14] 1 1
54 OGR6[6,5] 1 1
55 OGR6[6,10] 0 1
56 OGR6[6,12] 1 1
57 OGR6[6,14] 1 1
58 OGR6[7,5] 1 1
59 OGR6[7,10] 0 1
60 OGR6[7,12] 1 1
61 OGR6[7,14] 1 1
62 OGR7a -799965 0
63 OGR8a 45 0
No. Column name Activity Lower bound Upper bound
------ ------------ ------------- ------------- -------------
1 x[1] 6600 0
2 x[2] 0 0
3 x[3] 0 0
4 x[4] 0 0
5 x[5] 1.59342e+006 0
6 x[6] 0 0
7 x[7] 0 0
8 x[8] 4500 0
9 x[9] 11000 0
10 x[10] 0 0
11 x[11] 205 0
12 x[12] 75 0
13 x[13] 6840 0
14 x[14] 1.97736e+006 0
15 y[1] 0 0
16 y[2] 0 0
17 y[3] 0 0
18 y[4] 0 0
19 y[5] 1.59252e+006 0
20 y[6] 0 0
21 y[7] 0 0
22 y[8] 0 0
23 y[9] 0 0
24 y[10] 0 0
25 y[11] 0 0
26 y[12] 0 0
27 y[13] 0 0
28 y[14] 1.97016e+006 0
29 u[1] * 110 0
30 u[2] * 0 0
31 u[3] * 0 0
32 u[4] * 0 0
33 u[5] * 53114 0
34 u[6] * 0 0
35 u[7] * 0 0
36 u[8] * 125 0
37 u[9] * 110 0
38 u[10] * 0 0
39 u[11] * 1 0
40 u[12] * 1 0
41 u[13] * 76 0
42 u[14] * 16478 0
43 z[1] * 1 0 1
44 z[2] * 0 0 1
45 z[3] * 0 0 1
46 z[4] * 0 0 1
47 z[5] * 1 0 1
48 z[6] * 0 0 1
49 z[7] * 0 0 1
50 z[8] * 1 0 1
51 z[9] * 1 0 1
52 z[10] * 0 0 1
53 z[11] * 1 0 1
54 z[12] * 1 0 1
55 z[13] * 1 0 1
56 z[14] * 1 0 1
Integer feasibility conditions:
INT.PE: max.abs.err. = 2.19e-011 on row 1
max.rel.err. = 1.70e-017 on row 1
High quality
INT.PB: max.abs.err. = 0.00e+000 on row 0
max.rel.err. = 0.00e+000 on row 0
High quality
End of output