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Instance fo9_ar4_1
Optimization of block layout design problems with unequal areas
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 23.46428571 (ALPHAECP) 23.46428569 (ANTIGONE) 23.46428448 (BARON) 23.46428571 (BONMIN) 10.06527121 (COUENNE) 18.45387615 (LINDO) 23.46428571 (SCIP) 23.46427763 (SHOT) |
| Referencesⓘ | Castillo, Ignacio, Westerlund, Joakim, Emet, Stefan, and Westerlund, Tapio, Optimization of block layout design problems with unequal areas: A comparison of MILP and MINLP optimization methods, Computers and Chemical Engineering, 30:1, 2005, 54-69. |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 19 Dec 2005 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 180 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 72 |
| #Nonlinear Variablesⓘ | 18 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 16 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 435 |
| #Linear Constraintsⓘ | 417 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 18 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 1734 |
| #Nonlinear Nonzeros in Jacobianⓘ | 18 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 18 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 18 |
| #Blocks in Hessian of Lagrangianⓘ | 18 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 8.3333e-02 |
| Maximal coefficientⓘ | 3.6000e+01 |
| Infeasibility of initial pointⓘ | 9 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 436 2 2 432 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 181 109 0 72 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1751 1733 18 0
*
* Solve m using MINLP minimizing objvar;
Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36
,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53
,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68,i69,i70
,i71,i72,objvar,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128
,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141
,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154
,x155,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167
,x168,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180
,x181;
Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
,i18,i19,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34
,i35,i36,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51
,i52,i53,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68
,i69,i70,i71,i72;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295,e296,e297,e298
,e299,e300,e301,e302,e303,e304,e305,e306,e307,e308,e309,e310,e311
,e312,e313,e314,e315,e316,e317,e318,e319,e320,e321,e322,e323,e324
,e325,e326,e327,e328,e329,e330,e331,e332,e333,e334,e335,e336,e337
,e338,e339,e340,e341,e342,e343,e344,e345,e346,e347,e348,e349,e350
,e351,e352,e353,e354,e355,e356,e357,e358,e359,e360,e361,e362,e363
,e364,e365,e366,e367,e368,e369,e370,e371,e372,e373,e374,e375,e376
,e377,e378,e379,e380,e381,e382,e383,e384,e385,e386,e387,e388,e389
,e390,e391,e392,e393,e394,e395,e396,e397,e398,e399,e400,e401,e402
,e403,e404,e405,e406,e407,e408,e409,e410,e411,e412,e413,e414,e415
,e416,e417,e418,e419,e420,e421,e422,e423,e424,e425,e426,e427,e428
,e429,e430,e431,e432,e433,e434,e435,e436;
e1.. objvar - x74 - x75 - x76 - x77 - x78 - x79 - x80 - x81 - x82 - x83
- x84 - x85 - x86 - x87 - x88 - x89 =E= 0;
e2.. x90 - x91 =G= 0;
e3.. x92 - x93 =G= 0;
e4.. i1 - i2 =E= 0;
e5.. - 12*i1 - x74 + 0.5*x94 + 0.5*x95 =L= 0;
e6.. 13*i1 - x75 + 0.5*x96 + 0.5*x97 =L= 13;
e7.. - 12*i3 + 0.5*x94 + 0.5*x98 - x99 =L= 0;
e8.. 13*i3 + 0.5*x96 + 0.5*x100 - x101 =L= 13;
e9.. - 12*i5 + 0.5*x94 + 0.5*x102 - x103 =L= 0;
e10.. 13*i5 + 0.5*x96 + 0.5*x104 - x105 =L= 13;
e11.. - 12*i7 + 0.5*x94 + 0.5*x106 - x107 =L= 0;
e12.. 13*i7 + 0.5*x96 + 0.5*x108 - x109 =L= 13;
e13.. - 12*i9 + 0.5*x94 + 0.5*x110 - x111 =L= 0;
e14.. 13*i9 + 0.5*x96 + 0.5*x112 - x113 =L= 13;
e15.. - 12*i11 + 0.5*x94 + 0.5*x114 - x115 =L= 0;
e16.. 13*i11 + 0.5*x96 + 0.5*x116 - x117 =L= 13;
e17.. - 12*i13 + 0.5*x94 + 0.5*x118 - x119 =L= 0;
e18.. 13*i13 + 0.5*x96 + 0.5*x120 - x121 =L= 13;
e19.. - 12*i15 + 0.5*x94 + 0.5*x122 - x123 =L= 0;
e20.. 13*i15 + 0.5*x96 + 0.5*x124 - x125 =L= 13;
e21.. - 12*i17 - x76 + 0.5*x95 + 0.5*x98 =L= 0;
e22.. 13*i17 - x77 + 0.5*x97 + 0.5*x100 =L= 13;
e23.. - 12*i19 + 0.5*x95 + 0.5*x102 - x126 =L= 0;
e24.. 13*i19 + 0.5*x97 + 0.5*x104 - x127 =L= 13;
e25.. - 12*i21 + 0.5*x95 + 0.5*x106 - x128 =L= 0;
e26.. 13*i21 + 0.5*x97 + 0.5*x108 - x129 =L= 13;
e27.. - 12*i23 + 0.5*x95 + 0.5*x110 - x130 =L= 0;
e28.. 13*i23 + 0.5*x97 + 0.5*x112 - x131 =L= 13;
e29.. - 12*i25 + 0.5*x95 + 0.5*x114 - x132 =L= 0;
e30.. 13*i25 + 0.5*x97 + 0.5*x116 - x133 =L= 13;
e31.. - 12*i27 + 0.5*x95 + 0.5*x118 - x134 =L= 0;
e32.. 13*i27 + 0.5*x97 + 0.5*x120 - x135 =L= 13;
e33.. - 12*i29 + 0.5*x95 + 0.5*x122 - x136 =L= 0;
e34.. 13*i29 + 0.5*x97 + 0.5*x124 - x137 =L= 13;
e35.. - 12*i31 - x78 + 0.5*x98 + 0.5*x102 =L= 0;
e36.. 13*i31 - x79 + 0.5*x100 + 0.5*x104 =L= 13;
e37.. - 12*i33 + 0.5*x98 + 0.5*x106 - x138 =L= 0;
e38.. 13*i33 + 0.5*x100 + 0.5*x108 - x139 =L= 13;
e39.. - 12*i35 + 0.5*x98 + 0.5*x110 - x140 =L= 0;
e40.. 13*i35 + 0.5*x100 + 0.5*x112 - x141 =L= 13;
e41.. - 12*i37 + 0.5*x98 + 0.5*x114 - x142 =L= 0;
e42.. 13*i37 + 0.5*x100 + 0.5*x116 - x143 =L= 13;
e43.. - 12*i39 + 0.5*x98 + 0.5*x118 - x144 =L= 0;
e44.. 13*i39 + 0.5*x100 + 0.5*x120 - x145 =L= 13;
e45.. - 12*i41 + 0.5*x98 + 0.5*x122 - x146 =L= 0;
e46.. 13*i41 + 0.5*x100 + 0.5*x124 - x147 =L= 13;
e47.. - 12*i43 - x80 + 0.5*x102 + 0.5*x106 =L= 0;
e48.. 13*i43 - x81 + 0.5*x104 + 0.5*x108 =L= 13;
e49.. - 12*i45 + 0.5*x102 + 0.5*x110 - x148 =L= 0;
e50.. 13*i45 + 0.5*x104 + 0.5*x112 - x149 =L= 13;
e51.. - 12*i47 + 0.5*x102 + 0.5*x114 - x150 =L= 0;
e52.. 13*i47 + 0.5*x104 + 0.5*x116 - x151 =L= 13;
e53.. - 12*i49 + 0.5*x102 + 0.5*x118 - x152 =L= 0;
e54.. 13*i49 + 0.5*x104 + 0.5*x120 - x153 =L= 13;
e55.. - 12*i51 + 0.5*x102 + 0.5*x122 - x154 =L= 0;
e56.. 13*i51 + 0.5*x104 + 0.5*x124 - x155 =L= 13;
e57.. - 12*i53 - x82 + 0.5*x106 + 0.5*x110 =L= 0;
e58.. 13*i53 - x83 + 0.5*x108 + 0.5*x112 =L= 13;
e59.. - 12*i55 + 0.5*x106 + 0.5*x114 - x156 =L= 0;
e60.. 13*i55 + 0.5*x108 + 0.5*x116 - x157 =L= 13;
e61.. - 12*i57 + 0.5*x106 + 0.5*x118 - x158 =L= 0;
e62.. 13*i57 + 0.5*x108 + 0.5*x120 - x159 =L= 13;
e63.. - 12*i59 + 0.5*x106 + 0.5*x122 - x160 =L= 0;
e64.. 13*i59 + 0.5*x108 + 0.5*x124 - x161 =L= 13;
e65.. - 12*i61 - x84 + 0.5*x110 + 0.5*x114 =L= 0;
e66.. 13*i61 - x85 + 0.5*x112 + 0.5*x116 =L= 13;
e67.. - 12*i63 + 0.5*x110 + 0.5*x118 - x162 =L= 0;
e68.. 13*i63 + 0.5*x112 + 0.5*x120 - x163 =L= 13;
e69.. - 12*i65 + 0.5*x110 + 0.5*x122 - x164 =L= 0;
e70.. 13*i65 + 0.5*x112 + 0.5*x124 - x165 =L= 13;
e71.. - 12*i67 - x86 + 0.5*x114 + 0.5*x118 =L= 0;
e72.. 13*i67 - x87 + 0.5*x116 + 0.5*x120 =L= 13;
e73.. - 12*i69 + 0.5*x114 + 0.5*x122 - x166 =L= 0;
e74.. 13*i69 + 0.5*x116 + 0.5*x124 - x167 =L= 13;
e75.. - 12*i71 - x88 + 0.5*x118 + 0.5*x122 =L= 0;
e76.. 13*i71 - x89 + 0.5*x120 + 0.5*x124 =L= 13;
e77.. - 0.5*x94 - 0.125*x96 =L= -2;
e78.. - 0.125*x94 - 0.5*x96 =L= -2;
e79.. - 0.5*x95 - 0.125*x97 =L= -2;
e80.. - 0.125*x95 - 0.5*x97 =L= -2;
e81.. - 0.5*x98 - 0.125*x100 =L= -2;
e82.. - 0.125*x98 - 0.5*x100 =L= -2;
e83.. - 0.333333*x102 - 0.083333*x104 =L= -2;
e84.. - 0.083333*x102 - 0.333333*x104 =L= -2;
e85.. - 0.333333*x106 - 0.083333*x108 =L= -2;
e86.. - 0.083333*x106 - 0.333333*x108 =L= -2;
e87.. - 0.666667*x110 - 0.166667*x112 =L= -2;
e88.. - 0.166667*x110 - 0.666667*x112 =L= -2;
e89.. - 0.666667*x114 - 0.166667*x116 =L= -2;
e90.. - 0.166667*x114 - 0.666667*x116 =L= -2;
e91.. - 0.666667*x118 - 0.166667*x120 =L= -2;
e92.. - 0.166667*x118 - 0.666667*x120 =L= -2;
e93.. - 0.666667*x122 - 0.166667*x124 =L= -2;
e94.. - 0.166667*x122 - 0.666667*x124 =L= -2;
e95.. x90 + 0.5*x94 =L= 12;
e96.. - x90 + 0.5*x94 =L= 0;
e97.. x93 + 0.5*x96 =L= 13;
e98.. - x93 + 0.5*x96 =L= 0;
e99.. x91 + 0.5*x95 =L= 12;
e100.. - x91 + 0.5*x95 =L= 0;
e101.. x92 + 0.5*x97 =L= 13;
e102.. - x92 + 0.5*x97 =L= 0;
e103.. 0.5*x98 + x168 =L= 12;
e104.. 0.5*x98 - x168 =L= 0;
e105.. 0.5*x100 + x169 =L= 13;
e106.. 0.5*x100 - x169 =L= 0;
e107.. 0.5*x102 + x170 =L= 12;
e108.. 0.5*x102 - x170 =L= 0;
e109.. 0.5*x104 + x171 =L= 13;
e110.. 0.5*x104 - x171 =L= 0;
e111.. 0.5*x106 + x172 =L= 12;
e112.. 0.5*x106 - x172 =L= 0;
e113.. 0.5*x108 + x173 =L= 13;
e114.. 0.5*x108 - x173 =L= 0;
e115.. 0.5*x110 + x174 =L= 12;
e116.. 0.5*x110 - x174 =L= 0;
e117.. 0.5*x112 + x175 =L= 13;
e118.. 0.5*x112 - x175 =L= 0;
e119.. 0.5*x114 + x176 =L= 12;
e120.. 0.5*x114 - x176 =L= 0;
e121.. 0.5*x116 + x177 =L= 13;
e122.. 0.5*x116 - x177 =L= 0;
e123.. 0.5*x118 + x178 =L= 12;
e124.. 0.5*x118 - x178 =L= 0;
e125.. 0.5*x120 + x179 =L= 13;
e126.. 0.5*x120 - x179 =L= 0;
e127.. 0.5*x122 + x180 =L= 12;
e128.. 0.5*x122 - x180 =L= 0;
e129.. 0.5*x124 + x181 =L= 13;
e130.. 0.5*x124 - x181 =L= 0;
e131.. - x74 + x90 - x91 =L= 0;
e132.. - x74 - x90 + x91 =L= 0;
e133.. - x75 - x92 + x93 =L= 0;
e134.. - x75 + x92 - x93 =L= 0;
e135.. - 12*i1 - 12*i2 - x90 + x91 + 0.5*x94 + 0.5*x95 =L= 0;
e136.. - 12*i1 + 12*i2 + x90 - x91 + 0.5*x94 + 0.5*x95 =L= 12;
e137.. 13*i1 - 13*i2 + x92 - x93 + 0.5*x96 + 0.5*x97 =L= 13;
e138.. 13*i1 + 13*i2 - x92 + x93 + 0.5*x96 + 0.5*x97 =L= 26;
e139.. x90 - x99 - x168 =L= 0;
e140.. - x90 - x99 + x168 =L= 0;
e141.. x93 - x101 - x169 =L= 0;
e142.. - x93 - x101 + x169 =L= 0;
e143.. - 12*i3 - 12*i4 - x90 + 0.5*x94 + 0.5*x98 + x168 =L= 0;
e144.. - 12*i3 + 12*i4 + x90 + 0.5*x94 + 0.5*x98 - x168 =L= 12;
e145.. 13*i3 - 13*i4 - x93 + 0.5*x96 + 0.5*x100 + x169 =L= 13;
e146.. 13*i3 + 13*i4 + x93 + 0.5*x96 + 0.5*x100 - x169 =L= 26;
e147.. x90 - x103 - x170 =L= 0;
e148.. - x90 - x103 + x170 =L= 0;
e149.. x93 - x105 - x171 =L= 0;
e150.. - x93 - x105 + x171 =L= 0;
e151.. - 12*i5 - 12*i6 - x90 + 0.5*x94 + 0.5*x102 + x170 =L= 0;
e152.. - 12*i5 + 12*i6 + x90 + 0.5*x94 + 0.5*x102 - x170 =L= 12;
e153.. 13*i5 - 13*i6 - x93 + 0.5*x96 + 0.5*x104 + x171 =L= 13;
e154.. 13*i5 + 13*i6 + x93 + 0.5*x96 + 0.5*x104 - x171 =L= 26;
e155.. x90 - x107 - x172 =L= 0;
e156.. - x90 - x107 + x172 =L= 0;
e157.. x93 - x109 - x173 =L= 0;
e158.. - x93 - x109 + x173 =L= 0;
e159.. - 12*i7 - 12*i8 - x90 + 0.5*x94 + 0.5*x106 + x172 =L= 0;
e160.. - 12*i7 + 12*i8 + x90 + 0.5*x94 + 0.5*x106 - x172 =L= 12;
e161.. 13*i7 - 13*i8 - x93 + 0.5*x96 + 0.5*x108 + x173 =L= 13;
e162.. 13*i7 + 13*i8 + x93 + 0.5*x96 + 0.5*x108 - x173 =L= 26;
e163.. x90 - x111 - x174 =L= 0;
e164.. - x90 - x111 + x174 =L= 0;
e165.. x93 - x113 - x175 =L= 0;
e166.. - x93 - x113 + x175 =L= 0;
e167.. - 12*i9 - 12*i10 - x90 + 0.5*x94 + 0.5*x110 + x174 =L= 0;
e168.. - 12*i9 + 12*i10 + x90 + 0.5*x94 + 0.5*x110 - x174 =L= 12;
e169.. 13*i9 - 13*i10 - x93 + 0.5*x96 + 0.5*x112 + x175 =L= 13;
e170.. 13*i9 + 13*i10 + x93 + 0.5*x96 + 0.5*x112 - x175 =L= 26;
e171.. x90 - x115 - x176 =L= 0;
e172.. - x90 - x115 + x176 =L= 0;
e173.. x93 - x117 - x177 =L= 0;
e174.. - x93 - x117 + x177 =L= 0;
e175.. - 12*i11 - 12*i12 - x90 + 0.5*x94 + 0.5*x114 + x176 =L= 0;
e176.. - 12*i11 + 12*i12 + x90 + 0.5*x94 + 0.5*x114 - x176 =L= 12;
e177.. 13*i11 - 13*i12 - x93 + 0.5*x96 + 0.5*x116 + x177 =L= 13;
e178.. 13*i11 + 13*i12 + x93 + 0.5*x96 + 0.5*x116 - x177 =L= 26;
e179.. x90 - x119 - x178 =L= 0;
e180.. - x90 - x119 + x178 =L= 0;
e181.. x93 - x121 - x179 =L= 0;
e182.. - x93 - x121 + x179 =L= 0;
e183.. - 12*i13 - 12*i14 - x90 + 0.5*x94 + 0.5*x118 + x178 =L= 0;
e184.. - 12*i13 + 12*i14 + x90 + 0.5*x94 + 0.5*x118 - x178 =L= 12;
e185.. 13*i13 - 13*i14 - x93 + 0.5*x96 + 0.5*x120 + x179 =L= 13;
e186.. 13*i13 + 13*i14 + x93 + 0.5*x96 + 0.5*x120 - x179 =L= 26;
e187.. x90 - x123 - x180 =L= 0;
e188.. - x90 - x123 + x180 =L= 0;
e189.. x93 - x125 - x181 =L= 0;
e190.. - x93 - x125 + x181 =L= 0;
e191.. - 12*i15 - 12*i16 - x90 + 0.5*x94 + 0.5*x122 + x180 =L= 0;
e192.. - 12*i15 + 12*i16 + x90 + 0.5*x94 + 0.5*x122 - x180 =L= 12;
e193.. 13*i15 - 13*i16 - x93 + 0.5*x96 + 0.5*x124 + x181 =L= 13;
e194.. 13*i15 + 13*i16 + x93 + 0.5*x96 + 0.5*x124 - x181 =L= 26;
e195.. - x76 + x91 - x168 =L= 0;
e196.. - x76 - x91 + x168 =L= 0;
e197.. - x77 + x92 - x169 =L= 0;
e198.. - x77 - x92 + x169 =L= 0;
e199.. - 12*i17 - 12*i18 - x91 + 0.5*x95 + 0.5*x98 + x168 =L= 0;
e200.. - 12*i17 + 12*i18 + x91 + 0.5*x95 + 0.5*x98 - x168 =L= 12;
e201.. 13*i17 - 13*i18 - x92 + 0.5*x97 + 0.5*x100 + x169 =L= 13;
e202.. 13*i17 + 13*i18 + x92 + 0.5*x97 + 0.5*x100 - x169 =L= 26;
e203.. x91 - x126 - x170 =L= 0;
e204.. - x91 - x126 + x170 =L= 0;
e205.. x92 - x127 - x171 =L= 0;
e206.. - x92 - x127 + x171 =L= 0;
e207.. - 12*i19 - 12*i20 - x91 + 0.5*x95 + 0.5*x102 + x170 =L= 0;
e208.. - 12*i19 + 12*i20 + x91 + 0.5*x95 + 0.5*x102 - x170 =L= 12;
e209.. 13*i19 - 13*i20 - x92 + 0.5*x97 + 0.5*x104 + x171 =L= 13;
e210.. 13*i19 + 13*i20 + x92 + 0.5*x97 + 0.5*x104 - x171 =L= 26;
e211.. x91 - x128 - x172 =L= 0;
e212.. - x91 - x128 + x172 =L= 0;
e213.. x92 - x129 - x173 =L= 0;
e214.. - x92 - x129 + x173 =L= 0;
e215.. - 12*i21 - 12*i22 - x91 + 0.5*x95 + 0.5*x106 + x172 =L= 0;
e216.. - 12*i21 + 12*i22 + x91 + 0.5*x95 + 0.5*x106 - x172 =L= 12;
e217.. 13*i21 - 13*i22 - x92 + 0.5*x97 + 0.5*x108 + x173 =L= 13;
e218.. 13*i21 + 13*i22 + x92 + 0.5*x97 + 0.5*x108 - x173 =L= 26;
e219.. x91 - x130 - x174 =L= 0;
e220.. - x91 - x130 + x174 =L= 0;
e221.. x92 - x131 - x175 =L= 0;
e222.. - x92 - x131 + x175 =L= 0;
e223.. - 12*i23 - 12*i24 - x91 + 0.5*x95 + 0.5*x110 + x174 =L= 0;
e224.. - 12*i23 + 12*i24 + x91 + 0.5*x95 + 0.5*x110 - x174 =L= 12;
e225.. 13*i23 - 13*i24 - x92 + 0.5*x97 + 0.5*x112 + x175 =L= 13;
e226.. 13*i23 + 13*i24 + x92 + 0.5*x97 + 0.5*x112 - x175 =L= 26;
e227.. x91 - x132 - x176 =L= 0;
e228.. - x91 - x132 + x176 =L= 0;
e229.. x92 - x133 - x177 =L= 0;
e230.. - x92 - x133 + x177 =L= 0;
e231.. - 12*i25 - 12*i26 - x91 + 0.5*x95 + 0.5*x114 + x176 =L= 0;
e232.. - 12*i25 + 12*i26 + x91 + 0.5*x95 + 0.5*x114 - x176 =L= 12;
e233.. 13*i25 - 13*i26 - x92 + 0.5*x97 + 0.5*x116 + x177 =L= 13;
e234.. 13*i25 + 13*i26 + x92 + 0.5*x97 + 0.5*x116 - x177 =L= 26;
e235.. x91 - x134 - x178 =L= 0;
e236.. - x91 - x134 + x178 =L= 0;
e237.. x92 - x135 - x179 =L= 0;
e238.. - x92 - x135 + x179 =L= 0;
e239.. - 12*i27 - 12*i28 - x91 + 0.5*x95 + 0.5*x118 + x178 =L= 0;
e240.. - 12*i27 + 12*i28 + x91 + 0.5*x95 + 0.5*x118 - x178 =L= 12;
e241.. 13*i27 - 13*i28 - x92 + 0.5*x97 + 0.5*x120 + x179 =L= 13;
e242.. 13*i27 + 13*i28 + x92 + 0.5*x97 + 0.5*x120 - x179 =L= 26;
e243.. x91 - x136 - x180 =L= 0;
e244.. - x91 - x136 + x180 =L= 0;
e245.. x92 - x137 - x181 =L= 0;
e246.. - x92 - x137 + x181 =L= 0;
e247.. - 12*i29 - 12*i30 - x91 + 0.5*x95 + 0.5*x122 + x180 =L= 0;
e248.. - 12*i29 + 12*i30 + x91 + 0.5*x95 + 0.5*x122 - x180 =L= 12;
e249.. 13*i29 - 13*i30 - x92 + 0.5*x97 + 0.5*x124 + x181 =L= 13;
e250.. 13*i29 + 13*i30 + x92 + 0.5*x97 + 0.5*x124 - x181 =L= 26;
e251.. - x78 + x168 - x170 =L= 0;
e252.. - x78 - x168 + x170 =L= 0;
e253.. - x79 + x169 - x171 =L= 0;
e254.. - x79 - x169 + x171 =L= 0;
e255.. - 12*i31 - 12*i32 + 0.5*x98 + 0.5*x102 - x168 + x170 =L= 0;
e256.. - 12*i31 + 12*i32 + 0.5*x98 + 0.5*x102 + x168 - x170 =L= 12;
e257.. 13*i31 - 13*i32 + 0.5*x100 + 0.5*x104 - x169 + x171 =L= 13;
e258.. 13*i31 + 13*i32 + 0.5*x100 + 0.5*x104 + x169 - x171 =L= 26;
e259.. - x138 + x168 - x172 =L= 0;
e260.. - x138 - x168 + x172 =L= 0;
e261.. - x139 + x169 - x173 =L= 0;
e262.. - x139 - x169 + x173 =L= 0;
e263.. - 12*i33 - 12*i34 + 0.5*x98 + 0.5*x106 - x168 + x172 =L= 0;
e264.. - 12*i33 + 12*i34 + 0.5*x98 + 0.5*x106 + x168 - x172 =L= 12;
e265.. 13*i33 - 13*i34 + 0.5*x100 + 0.5*x108 - x169 + x173 =L= 13;
e266.. 13*i33 + 13*i34 + 0.5*x100 + 0.5*x108 + x169 - x173 =L= 26;
e267.. - x140 + x168 - x174 =L= 0;
e268.. - x140 - x168 + x174 =L= 0;
e269.. - x141 + x169 - x175 =L= 0;
e270.. - x141 - x169 + x175 =L= 0;
e271.. - 12*i35 - 12*i36 + 0.5*x98 + 0.5*x110 - x168 + x174 =L= 0;
e272.. - 12*i35 + 12*i36 + 0.5*x98 + 0.5*x110 + x168 - x174 =L= 12;
e273.. 13*i35 - 13*i36 + 0.5*x100 + 0.5*x112 - x169 + x175 =L= 13;
e274.. 13*i35 + 13*i36 + 0.5*x100 + 0.5*x112 + x169 - x175 =L= 26;
e275.. - x142 + x168 - x176 =L= 0;
e276.. - x142 - x168 + x176 =L= 0;
e277.. - x143 + x169 - x177 =L= 0;
e278.. - x143 - x169 + x177 =L= 0;
e279.. - 12*i37 - 12*i38 + 0.5*x98 + 0.5*x114 - x168 + x176 =L= 0;
e280.. - 12*i37 + 12*i38 + 0.5*x98 + 0.5*x114 + x168 - x176 =L= 12;
e281.. 13*i37 - 13*i38 + 0.5*x100 + 0.5*x116 - x169 + x177 =L= 13;
e282.. 13*i37 + 13*i38 + 0.5*x100 + 0.5*x116 + x169 - x177 =L= 26;
e283.. - x144 + x168 - x178 =L= 0;
e284.. - x144 - x168 + x178 =L= 0;
e285.. - x145 + x169 - x179 =L= 0;
e286.. - x145 - x169 + x179 =L= 0;
e287.. - 12*i39 - 12*i40 + 0.5*x98 + 0.5*x118 - x168 + x178 =L= 0;
e288.. - 12*i39 + 12*i40 + 0.5*x98 + 0.5*x118 + x168 - x178 =L= 12;
e289.. 13*i39 - 13*i40 + 0.5*x100 + 0.5*x120 - x169 + x179 =L= 13;
e290.. 13*i39 + 13*i40 + 0.5*x100 + 0.5*x120 + x169 - x179 =L= 26;
e291.. - x146 + x168 - x180 =L= 0;
e292.. - x146 - x168 + x180 =L= 0;
e293.. - x147 + x169 - x181 =L= 0;
e294.. - x147 - x169 + x181 =L= 0;
e295.. - 12*i41 - 12*i42 + 0.5*x98 + 0.5*x122 - x168 + x180 =L= 0;
e296.. - 12*i41 + 12*i42 + 0.5*x98 + 0.5*x122 + x168 - x180 =L= 12;
e297.. 13*i41 - 13*i42 + 0.5*x100 + 0.5*x124 - x169 + x181 =L= 13;
e298.. 13*i41 + 13*i42 + 0.5*x100 + 0.5*x124 + x169 - x181 =L= 26;
e299.. - x80 + x170 - x172 =L= 0;
e300.. - x80 - x170 + x172 =L= 0;
e301.. - x81 + x171 - x173 =L= 0;
e302.. - x81 - x171 + x173 =L= 0;
e303.. - 12*i43 - 12*i44 + 0.5*x102 + 0.5*x106 - x170 + x172 =L= 0;
e304.. - 12*i43 + 12*i44 + 0.5*x102 + 0.5*x106 + x170 - x172 =L= 12;
e305.. 13*i43 - 13*i44 + 0.5*x104 + 0.5*x108 - x171 + x173 =L= 13;
e306.. 13*i43 + 13*i44 + 0.5*x104 + 0.5*x108 + x171 - x173 =L= 26;
e307.. - x148 + x170 - x174 =L= 0;
e308.. - x148 - x170 + x174 =L= 0;
e309.. - x149 + x171 - x175 =L= 0;
e310.. - x149 - x171 + x175 =L= 0;
e311.. - 12*i45 - 12*i46 + 0.5*x102 + 0.5*x110 - x170 + x174 =L= 0;
e312.. - 12*i45 + 12*i46 + 0.5*x102 + 0.5*x110 + x170 - x174 =L= 12;
e313.. 13*i45 - 13*i46 + 0.5*x104 + 0.5*x112 - x171 + x175 =L= 13;
e314.. 13*i45 + 13*i46 + 0.5*x104 + 0.5*x112 + x171 - x175 =L= 26;
e315.. - x150 + x170 - x176 =L= 0;
e316.. - x150 - x170 + x176 =L= 0;
e317.. - x151 + x171 - x177 =L= 0;
e318.. - x151 - x171 + x177 =L= 0;
e319.. - 12*i47 - 12*i48 + 0.5*x102 + 0.5*x114 - x170 + x176 =L= 0;
e320.. - 12*i47 + 12*i48 + 0.5*x102 + 0.5*x114 + x170 - x176 =L= 12;
e321.. 13*i47 - 13*i48 + 0.5*x104 + 0.5*x116 - x171 + x177 =L= 13;
e322.. 13*i47 + 13*i48 + 0.5*x104 + 0.5*x116 + x171 - x177 =L= 26;
e323.. - x152 + x170 - x178 =L= 0;
e324.. - x152 - x170 + x178 =L= 0;
e325.. - x153 + x171 - x179 =L= 0;
e326.. - x153 - x171 + x179 =L= 0;
e327.. - 12*i49 - 12*i50 + 0.5*x102 + 0.5*x118 - x170 + x178 =L= 0;
e328.. - 12*i49 + 12*i50 + 0.5*x102 + 0.5*x118 + x170 - x178 =L= 12;
e329.. 13*i49 - 13*i50 + 0.5*x104 + 0.5*x120 - x171 + x179 =L= 13;
e330.. 13*i49 + 13*i50 + 0.5*x104 + 0.5*x120 + x171 - x179 =L= 26;
e331.. - x154 + x170 - x180 =L= 0;
e332.. - x154 - x170 + x180 =L= 0;
e333.. - x155 + x171 - x181 =L= 0;
e334.. - x155 - x171 + x181 =L= 0;
e335.. - 12*i51 - 12*i52 + 0.5*x102 + 0.5*x122 - x170 + x180 =L= 0;
e336.. - 12*i51 + 12*i52 + 0.5*x102 + 0.5*x122 + x170 - x180 =L= 12;
e337.. 13*i51 - 13*i52 + 0.5*x104 + 0.5*x124 - x171 + x181 =L= 13;
e338.. 13*i51 + 13*i52 + 0.5*x104 + 0.5*x124 + x171 - x181 =L= 26;
e339.. - x82 + x172 - x174 =L= 0;
e340.. - x82 - x172 + x174 =L= 0;
e341.. - x83 + x173 - x175 =L= 0;
e342.. - x83 - x173 + x175 =L= 0;
e343.. - 12*i53 - 12*i54 + 0.5*x106 + 0.5*x110 - x172 + x174 =L= 0;
e344.. - 12*i53 + 12*i54 + 0.5*x106 + 0.5*x110 + x172 - x174 =L= 12;
e345.. 13*i53 - 13*i54 + 0.5*x108 + 0.5*x112 - x173 + x175 =L= 13;
e346.. 13*i53 + 13*i54 + 0.5*x108 + 0.5*x112 + x173 - x175 =L= 26;
e347.. - x156 + x172 - x176 =L= 0;
e348.. - x156 - x172 + x176 =L= 0;
e349.. - x157 + x173 - x177 =L= 0;
e350.. - x157 - x173 + x177 =L= 0;
e351.. - 12*i55 - 12*i56 + 0.5*x106 + 0.5*x114 - x172 + x176 =L= 0;
e352.. - 12*i55 + 12*i56 + 0.5*x106 + 0.5*x114 + x172 - x176 =L= 12;
e353.. 13*i55 - 13*i56 + 0.5*x108 + 0.5*x116 - x173 + x177 =L= 13;
e354.. 13*i55 + 13*i56 + 0.5*x108 + 0.5*x116 + x173 - x177 =L= 26;
e355.. - x158 + x172 - x178 =L= 0;
e356.. - x158 - x172 + x178 =L= 0;
e357.. - x159 + x173 - x179 =L= 0;
e358.. - x159 - x173 + x179 =L= 0;
e359.. - 12*i57 - 12*i58 + 0.5*x106 + 0.5*x118 - x172 + x178 =L= 0;
e360.. - 12*i57 + 12*i58 + 0.5*x106 + 0.5*x118 + x172 - x178 =L= 12;
e361.. 13*i57 - 13*i58 + 0.5*x108 + 0.5*x120 - x173 + x179 =L= 13;
e362.. 13*i57 + 13*i58 + 0.5*x108 + 0.5*x120 + x173 - x179 =L= 26;
e363.. - x160 + x172 - x180 =L= 0;
e364.. - x160 - x172 + x180 =L= 0;
e365.. - x161 + x173 - x181 =L= 0;
e366.. - x161 - x173 + x181 =L= 0;
e367.. - 12*i59 - 12*i60 + 0.5*x106 + 0.5*x122 - x172 + x180 =L= 0;
e368.. - 12*i59 + 12*i60 + 0.5*x106 + 0.5*x122 + x172 - x180 =L= 12;
e369.. 13*i59 - 13*i60 + 0.5*x108 + 0.5*x124 - x173 + x181 =L= 13;
e370.. 13*i59 + 13*i60 + 0.5*x108 + 0.5*x124 + x173 - x181 =L= 26;
e371.. - x84 + x174 - x176 =L= 0;
e372.. - x84 - x174 + x176 =L= 0;
e373.. - x85 + x175 - x177 =L= 0;
e374.. - x85 - x175 + x177 =L= 0;
e375.. - 12*i61 - 12*i62 + 0.5*x110 + 0.5*x114 - x174 + x176 =L= 0;
e376.. - 12*i61 + 12*i62 + 0.5*x110 + 0.5*x114 + x174 - x176 =L= 12;
e377.. 13*i61 - 13*i62 + 0.5*x112 + 0.5*x116 - x175 + x177 =L= 13;
e378.. 13*i61 + 13*i62 + 0.5*x112 + 0.5*x116 + x175 - x177 =L= 26;
e379.. - x162 + x174 - x178 =L= 0;
e380.. - x162 - x174 + x178 =L= 0;
e381.. - x163 + x175 - x179 =L= 0;
e382.. - x163 - x175 + x179 =L= 0;
e383.. - 12*i63 - 12*i64 + 0.5*x110 + 0.5*x118 - x174 + x178 =L= 0;
e384.. - 12*i63 + 12*i64 + 0.5*x110 + 0.5*x118 + x174 - x178 =L= 12;
e385.. 13*i63 - 13*i64 + 0.5*x112 + 0.5*x120 - x175 + x179 =L= 13;
e386.. 13*i63 + 13*i64 + 0.5*x112 + 0.5*x120 + x175 - x179 =L= 26;
e387.. - x164 + x174 - x180 =L= 0;
e388.. - x164 - x174 + x180 =L= 0;
e389.. - x165 + x175 - x181 =L= 0;
e390.. - x165 - x175 + x181 =L= 0;
e391.. - 12*i65 - 12*i66 + 0.5*x110 + 0.5*x122 - x174 + x180 =L= 0;
e392.. - 12*i65 + 12*i66 + 0.5*x110 + 0.5*x122 + x174 - x180 =L= 12;
e393.. 13*i65 - 13*i66 + 0.5*x112 + 0.5*x124 - x175 + x181 =L= 13;
e394.. 13*i65 + 13*i66 + 0.5*x112 + 0.5*x124 + x175 - x181 =L= 26;
e395.. - x86 + x176 - x178 =L= 0;
e396.. - x86 - x176 + x178 =L= 0;
e397.. - x87 + x177 - x179 =L= 0;
e398.. - x87 - x177 + x179 =L= 0;
e399.. - 12*i67 - 12*i68 + 0.5*x114 + 0.5*x118 - x176 + x178 =L= 0;
e400.. - 12*i67 + 12*i68 + 0.5*x114 + 0.5*x118 + x176 - x178 =L= 12;
e401.. 13*i67 - 13*i68 + 0.5*x116 + 0.5*x120 - x177 + x179 =L= 13;
e402.. 13*i67 + 13*i68 + 0.5*x116 + 0.5*x120 + x177 - x179 =L= 26;
e403.. - x166 + x176 - x180 =L= 0;
e404.. - x166 - x176 + x180 =L= 0;
e405.. - x167 + x177 - x181 =L= 0;
e406.. - x167 - x177 + x181 =L= 0;
e407.. - 12*i69 - 12*i70 + 0.5*x114 + 0.5*x122 - x176 + x180 =L= 0;
e408.. - 12*i69 + 12*i70 + 0.5*x114 + 0.5*x122 + x176 - x180 =L= 12;
e409.. 13*i69 - 13*i70 + 0.5*x116 + 0.5*x124 - x177 + x181 =L= 13;
e410.. 13*i69 + 13*i70 + 0.5*x116 + 0.5*x124 + x177 - x181 =L= 26;
e411.. - x88 + x178 - x180 =L= 0;
e412.. - x88 - x178 + x180 =L= 0;
e413.. - x89 + x179 - x181 =L= 0;
e414.. - x89 - x179 + x181 =L= 0;
e415.. - 12*i71 - 12*i72 + 0.5*x118 + 0.5*x122 - x178 + x180 =L= 0;
e416.. - 12*i71 + 12*i72 + 0.5*x118 + 0.5*x122 + x178 - x180 =L= 12;
e417.. 13*i71 - 13*i72 + 0.5*x120 + 0.5*x124 - x179 + x181 =L= 13;
e418.. 13*i71 + 13*i72 + 0.5*x120 + 0.5*x124 + x179 - x181 =L= 26;
e419.. 16/x94 - x96 =L= 0;
e420.. 16/x96 - x94 =L= 0;
e421.. 16/x95 - x97 =L= 0;
e422.. 16/x97 - x95 =L= 0;
e423.. 16/x98 - x100 =L= 0;
e424.. 16/x100 - x98 =L= 0;
e425.. 36/x102 - x104 =L= 0;
e426.. 36/x104 - x102 =L= 0;
e427.. 36/x106 - x108 =L= 0;
e428.. 36/x108 - x106 =L= 0;
e429.. 9/x110 - x112 =L= 0;
e430.. 9/x112 - x110 =L= 0;
e431.. 9/x114 - x116 =L= 0;
e432.. 9/x116 - x114 =L= 0;
e433.. 9/x118 - x120 =L= 0;
e434.. 9/x120 - x118 =L= 0;
e435.. 9/x122 - x124 =L= 0;
e436.. 9/x124 - x122 =L= 0;
* set non-default bounds
i1.up = 100;
i2.up = 100;
i3.up = 100;
i4.up = 100;
i5.up = 100;
i6.up = 100;
i7.up = 100;
i8.up = 100;
i9.up = 100;
i10.up = 100;
i11.up = 100;
i12.up = 100;
i13.up = 100;
i14.up = 100;
i15.up = 100;
i16.up = 100;
i17.up = 100;
i18.up = 100;
i19.up = 100;
i20.up = 100;
i21.up = 100;
i22.up = 100;
i23.up = 100;
i24.up = 100;
i25.up = 100;
i26.up = 100;
i27.up = 100;
i28.up = 100;
i29.up = 100;
i30.up = 100;
i31.up = 100;
i32.up = 100;
i33.up = 100;
i34.up = 100;
i35.up = 100;
i36.up = 100;
i37.up = 100;
i38.up = 100;
i39.up = 100;
i40.up = 100;
i41.up = 100;
i42.up = 100;
i43.up = 100;
i44.up = 100;
i45.up = 100;
i46.up = 100;
i47.up = 100;
i48.up = 100;
i49.up = 100;
i50.up = 100;
i51.up = 100;
i52.up = 100;
i53.up = 100;
i54.up = 100;
i55.up = 100;
i56.up = 100;
i57.up = 100;
i58.up = 100;
i59.up = 100;
i60.up = 100;
i61.up = 100;
i62.up = 100;
i63.up = 100;
i64.up = 100;
i65.up = 100;
i66.up = 100;
i67.up = 100;
i68.up = 100;
i69.up = 100;
i70.up = 100;
i71.up = 100;
i72.up = 100;
x94.lo = 2; x94.up = 8;
x95.lo = 2; x95.up = 8;
x96.lo = 2; x96.up = 8;
x97.lo = 2; x97.up = 8;
x98.lo = 2; x98.up = 8;
x100.lo = 2; x100.up = 8;
x102.lo = 3; x102.up = 12;
x104.lo = 3; x104.up = 12;
x106.lo = 3; x106.up = 12;
x108.lo = 3; x108.up = 12;
x110.lo = 1.5; x110.up = 6;
x112.lo = 1.5; x112.up = 6;
x114.lo = 1.5; x114.up = 6;
x116.lo = 1.5; x116.up = 6;
x118.lo = 1.5; x118.up = 6;
x120.lo = 1.5; x120.up = 6;
x122.lo = 1.5; x122.up = 6;
x124.lo = 1.5; x124.up = 6;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc