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Instance csched2a
Corrected version of csched2. The printed version of the paper had some data inconsistencies. The objective of the models also has been reformulated.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -527723.11250000 (ANTIGONE) -165398.70130000 (BARON) -1763030.63900000 (COUENNE) -190823.58970000 (GUROBI) -4960890.00000000 (LINDO) -5036693.92200000 (SCIP) -303731.32720000 (XPRESS) |
| Referencesⓘ | And, Vipul J and Grossmann, I E, Cyclic Scheduling of Continuous Parallel Units with Decaying Performance, American Institute of Chemical Engineers Journal, 44:7, 1998, 1623-1636. |
| Sourceⓘ | modified MacMINLP model c-sched.mod with c-sched2.dat, GAMS Model Library model csched |
| Applicationⓘ | Cyclic Scheduling of Continuous Parallel Units |
| Added to libraryⓘ | 14 Jun 2007 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 232 |
| #Binary Variablesⓘ | 140 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 57 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 57 |
| #Nonlinear Nonzeros in Objectiveⓘ | 57 |
| #Constraintsⓘ | 137 |
| #Linear Constraintsⓘ | 137 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp mul |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 564 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 225 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 57 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 57 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 57 |
| Average blocksize in Hessian of Lagrangianⓘ | 57.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-02 |
| Maximal coefficientⓘ | 5.2668e+05 |
| Infeasibility of initial pointⓘ | 6e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 138 92 7 39 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 233 93 140 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 622 565 57 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,x91,x92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,b181
,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192,b193,b194
,b195,b196,b197,b198,b199,b200,b201,b202,b203,b204,b205,b206,b207
,b208,b209,b210,b211,b212,b213,b214,b215,b216,b217,b218,b219,b220
,b221,b222,b223,b224,b225,b226,b227,b228,b229,b230,b231,b232,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x57,x58,x59,x60,x61,x62
,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79
,x80,x81,x82,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92;
Binary Variables b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103,b104,b105
,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116,b117,b118
,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129,b130,b131
,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142,b143,b144
,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155,b156,b157
,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168,b169,b170
,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,b181,b182,b183
,b184,b185,b186,b187,b188,b189,b190,b191,b192,b193,b194,b195,b196
,b197,b198,b199,b200,b201,b202,b203,b204,b205,b206,b207,b208,b209
,b210,b211,b212,b213,b214,b215,b216,b217,b218,b219,b220,b221,b222
,b223,b224,b225,b226,b227,b228,b229,b230,b231,b232;
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;
e1.. ((479700 - 479700*exp(-0.1*x1/x29))*x29 + 31980*x1 - 100*x29 + (252000 -
252000*exp(-0.2*x2/x30))*x30 + 22680*x2 - 90*x30 + (423500 - 423500*exp(-
0.1*x3/x31))*x31 + 25410*x3 - 80*x31 + (157440 - 157440*exp(-0.2*x4/x32))*
x32 + 19680*x4 - 75*x32 + (172108.695652174 - 172108.695652174*exp(-0.23*
x5/x33))*x33 + 40950*x5 - 90*x33 + (33970.5882352941 - 33970.5882352941*
exp(-0.34*x6/x34))*x34 + 8580*x6 - 93*x34 + (130200 - 130200*exp(-0.2*x7/
x35))*x35 + 13440*x7 - 78*x35 + (200640 - 200640*exp(-0.2*x8/x36))*x36 +
26334*x8 - 80*x36 + (526680 - 526680*exp(-0.1*x9/x37))*x37 + 26334*x9 - 85
*x37 + (212850 - 212850*exp(-0.2*x10/x38))*x38 + 29670*x10 - 75*x38 + (
141360 - 141360*exp(-0.25*x11/x39))*x39 + 28500*x11 - 90*x39 + (
152937.931034483 - 152937.931034483*exp(-0.29*x12/x40))*x40 + 49104*x12 -
94*x40 + (76444.4444444444 - 76444.4444444444*exp(-0.27*x13/x41))*x41 +
13932*x13 - 78*x41 + (76840 - 76840*exp(-0.3*x14/x42))*x42 + 11526*x14 -
70*x42 + (102300 - 102300*exp(-0.3*x15/x43))*x43 + 18810*x15 - 90*x43 + (
170800 - 170800*exp(-0.2*x16/x44))*x44 + 17568*x16 - 90*x44 + (115200 -
115200*exp(-0.3*x17/x45))*x45 + 20160*x17 - 90*x45 + (176000 - 176000*exp(
-0.27*x18/x46))*x46 + 30360*x18 - 85*x46 + (126357.142857143 -
126357.142857143*exp(-0.28*x19/x47))*x47 + 36600*x19 - 93*x47 + (
45931.0344827586 - 45931.0344827586*exp(-0.29*x20/x48))*x48 + 9000*x20 -
92*x48 + (123318 - 123318*exp(-0.25*x21/x49))*x49 + 17901*x21 - 75*x49 + (
223200 - 223200*exp(-0.2*x22/x50))*x50 + 28800*x22 - 80*x50 + (225000 -
225000*exp(-0.2*x23/x51))*x51 + 23750*x23 - 90*x51 + (240800 - 240800*exp(
-0.15*x24/x52))*x52 + 21672*x24 - 85*x52 + (115920 - 115920*exp(-0.25*x25/
x53))*x53 + 19320*x25 - 80*x53 + (133241.379310345 - 133241.379310345*exp(
-0.29*x26/x54))*x54 + 42780*x26 - 92*x54 + (90763.6363636364 -
90763.6363636364*exp(-0.22*x27/x55))*x55 + 13312*x27 - 85*x55 + (
78857.1428571429 - 78857.1428571429*exp(-0.28*x28/x56))*x56 + 11730*x28 -
72*x56)/x92 + objvar =E= 0;
e2.. - 1300*x1 - 1100*x8 - 900*x15 - 1200*x22 + x57 + 300*x92 =E= 0;
e3.. - 1200*x2 - 1050*x9 - 800*x16 - 1000*x23 + x58 + 400*x92 =E= 0;
e4.. - 1100*x3 - 1000*x10 - 800*x17 - 800*x24 + x59 + 300*x92 =E= 0;
e5.. - 800*x4 - 1000*x11 - 1200*x18 - 700*x25 + x60 + 500*x92 =E= 0;
e6.. - 1300*x5 - 1200*x12 - 1000*x19 - 1200*x26 + x61 + 500*x92 =E= 0;
e7.. - 300*x6 - 400*x13 - 300*x20 - 400*x27 + x62 + 100*x92 =E= 0;
e8.. - 700*x7 - 600*x14 - 850*x21 - 600*x28 + x63 + 600*x92 =E= 0;
e9.. x57 - 300*x92 =L= 0;
e10.. x58 - 300*x92 =L= 0;
e11.. x59 - 300*x92 =L= 0;
e12.. x60 - 300*x92 =L= 0;
e13.. x61 - 300*x92 =L= 0;
e14.. x62 - 300*x92 =L= 0;
e15.. x63 - 300*x92 =L= 0;
e16.. x29 - 0.01*b93 - b94 - 2*b95 - 3*b96 - 4*b97 =E= 0;
e17.. x30 - 0.01*b98 - b99 - 2*b100 - 3*b101 - 4*b102 =E= 0;
e18.. x31 - 0.01*b103 - b104 - 2*b105 - 3*b106 - 4*b107 =E= 0;
e19.. x32 - 0.01*b108 - b109 - 2*b110 - 3*b111 - 4*b112 =E= 0;
e20.. x33 - 0.01*b113 - b114 - 2*b115 - 3*b116 - 4*b117 =E= 0;
e21.. x34 - 0.01*b118 - b119 - 2*b120 - 3*b121 - 4*b122 =E= 0;
e22.. x35 - 0.01*b123 - b124 - 2*b125 - 3*b126 - 4*b127 =E= 0;
e23.. x36 - 0.01*b128 - b129 - 2*b130 - 3*b131 - 4*b132 =E= 0;
e24.. x37 - 0.01*b133 - b134 - 2*b135 - 3*b136 - 4*b137 =E= 0;
e25.. x38 - 0.01*b138 - b139 - 2*b140 - 3*b141 - 4*b142 =E= 0;
e26.. x39 - 0.01*b143 - b144 - 2*b145 - 3*b146 - 4*b147 =E= 0;
e27.. x40 - 0.01*b148 - b149 - 2*b150 - 3*b151 - 4*b152 =E= 0;
e28.. x41 - 0.01*b153 - b154 - 2*b155 - 3*b156 - 4*b157 =E= 0;
e29.. x42 - 0.01*b158 - b159 - 2*b160 - 3*b161 - 4*b162 =E= 0;
e30.. x43 - 0.01*b163 - b164 - 2*b165 - 3*b166 - 4*b167 =E= 0;
e31.. x44 - 0.01*b168 - b169 - 2*b170 - 3*b171 - 4*b172 =E= 0;
e32.. x45 - 0.01*b173 - b174 - 2*b175 - 3*b176 - 4*b177 =E= 0;
e33.. x46 - 0.01*b178 - b179 - 2*b180 - 3*b181 - 4*b182 =E= 0;
e34.. x47 - 0.01*b183 - b184 - 2*b185 - 3*b186 - 4*b187 =E= 0;
e35.. x48 - 0.01*b188 - b189 - 2*b190 - 3*b191 - 4*b192 =E= 0;
e36.. x49 - 0.01*b193 - b194 - 2*b195 - 3*b196 - 4*b197 =E= 0;
e37.. x50 - 0.01*b198 - b199 - 2*b200 - 3*b201 - 4*b202 =E= 0;
e38.. x51 - 0.01*b203 - b204 - 2*b205 - 3*b206 - 4*b207 =E= 0;
e39.. x52 - 0.01*b208 - b209 - 2*b210 - 3*b211 - 4*b212 =E= 0;
e40.. x53 - 0.01*b213 - b214 - 2*b215 - 3*b216 - 4*b217 =E= 0;
e41.. x54 - 0.01*b218 - b219 - 2*b220 - 3*b221 - 4*b222 =E= 0;
e42.. x55 - 0.01*b223 - b224 - 2*b225 - 3*b226 - 4*b227 =E= 0;
e43.. x56 - 0.01*b228 - b229 - 2*b230 - 3*b231 - 4*b232 =E= 0;
e44.. - b93 - b94 - b95 - b96 - b97 =E= -1;
e45.. - b98 - b99 - b100 - b101 - b102 =E= -1;
e46.. - b103 - b104 - b105 - b106 - b107 =E= -1;
e47.. - b108 - b109 - b110 - b111 - b112 =E= -1;
e48.. - b113 - b114 - b115 - b116 - b117 =E= -1;
e49.. - b118 - b119 - b120 - b121 - b122 =E= -1;
e50.. - b123 - b124 - b125 - b126 - b127 =E= -1;
e51.. - b128 - b129 - b130 - b131 - b132 =E= -1;
e52.. - b133 - b134 - b135 - b136 - b137 =E= -1;
e53.. - b138 - b139 - b140 - b141 - b142 =E= -1;
e54.. - b143 - b144 - b145 - b146 - b147 =E= -1;
e55.. - b148 - b149 - b150 - b151 - b152 =E= -1;
e56.. - b153 - b154 - b155 - b156 - b157 =E= -1;
e57.. - b158 - b159 - b160 - b161 - b162 =E= -1;
e58.. - b163 - b164 - b165 - b166 - b167 =E= -1;
e59.. - b168 - b169 - b170 - b171 - b172 =E= -1;
e60.. - b173 - b174 - b175 - b176 - b177 =E= -1;
e61.. - b178 - b179 - b180 - b181 - b182 =E= -1;
e62.. - b183 - b184 - b185 - b186 - b187 =E= -1;
e63.. - b188 - b189 - b190 - b191 - b192 =E= -1;
e64.. - b193 - b194 - b195 - b196 - b197 =E= -1;
e65.. - b198 - b199 - b200 - b201 - b202 =E= -1;
e66.. - b203 - b204 - b205 - b206 - b207 =E= -1;
e67.. - b208 - b209 - b210 - b211 - b212 =E= -1;
e68.. - b213 - b214 - b215 - b216 - b217 =E= -1;
e69.. - b218 - b219 - b220 - b221 - b222 =E= -1;
e70.. - b223 - b224 - b225 - b226 - b227 =E= -1;
e71.. - b228 - b229 - b230 - b231 - b232 =E= -1;
e72.. - x1 - 2*x29 + x64 =E= 0;
e73.. - x2 - 3*x30 + x65 =E= 0;
e74.. - x3 - 3*x31 + x66 =E= 0;
e75.. - x4 - 3*x32 + x67 =E= 0;
e76.. - x5 - x33 + x68 =E= 0;
e77.. - x6 - 2*x34 + x69 =E= 0;
e78.. - x7 - 3*x35 + x70 =E= 0;
e79.. - x8 - 3*x36 + x71 =E= 0;
e80.. - x9 - x37 + x72 =E= 0;
e81.. - x10 - 2*x38 + x73 =E= 0;
e82.. - x11 - 2*x39 + x74 =E= 0;
e83.. - x12 - 2*x40 + x75 =E= 0;
e84.. - x13 - x41 + x76 =E= 0;
e85.. - x14 - x42 + x77 =E= 0;
e86.. - x15 - x43 + x78 =E= 0;
e87.. - x16 - 3*x44 + x79 =E= 0;
e88.. - x17 - x45 + x80 =E= 0;
e89.. - x18 - x46 + x81 =E= 0;
e90.. - x19 - 2*x47 + x82 =E= 0;
e91.. - x20 - x48 + x83 =E= 0;
e92.. - x21 - 2*x49 + x84 =E= 0;
e93.. - x22 - 2*x50 + x85 =E= 0;
e94.. - x23 - x51 + x86 =E= 0;
e95.. - x24 - 3*x52 + x87 =E= 0;
e96.. - x25 - 2*x53 + x88 =E= 0;
e97.. - x26 - 2*x54 + x89 =E= 0;
e98.. - x27 - x55 + x90 =E= 0;
e99.. - x28 - x56 + x91 =E= 0;
e100.. x64 + x65 + x66 + x67 + x68 + x69 + x70 - x92 =L= 0;
e101.. x71 + x72 + x73 + x74 + x75 + x76 + x77 - x92 =L= 0;
e102.. x78 + x79 + x80 + x81 + x82 + x83 + x84 - x92 =L= 0;
e103.. x85 + x86 + x87 + x88 + x89 + x90 + x91 - x92 =L= 0;
e104.. x1 + 100*b93 =L= 100;
e105.. x2 + 100*b98 =L= 100;
e106.. x3 + 100*b103 =L= 100;
e107.. x4 + 100*b108 =L= 100;
e108.. x5 + 100*b113 =L= 100;
e109.. x6 + 100*b118 =L= 100;
e110.. x7 + 100*b123 =L= 100;
e111.. x8 + 100*b128 =L= 100;
e112.. x9 + 100*b133 =L= 100;
e113.. x10 + 100*b138 =L= 100;
e114.. x11 + 100*b143 =L= 100;
e115.. x12 + 100*b148 =L= 100;
e116.. x13 + 100*b153 =L= 100;
e117.. x14 + 100*b158 =L= 100;
e118.. x15 + 100*b163 =L= 100;
e119.. x16 + 100*b168 =L= 100;
e120.. x17 + 100*b173 =L= 100;
e121.. x18 + 100*b178 =L= 100;
e122.. x19 + 100*b183 =L= 100;
e123.. x20 + 100*b188 =L= 100;
e124.. x21 + 100*b193 =L= 100;
e125.. x22 + 100*b198 =L= 100;
e126.. x23 + 100*b203 =L= 100;
e127.. x24 + 100*b208 =L= 100;
e128.. x25 + 100*b213 =L= 100;
e129.. x26 + 100*b218 =L= 100;
e130.. x27 + 100*b223 =L= 100;
e131.. x28 + 100*b228 =L= 100;
e132.. x29 + x36 + x43 + x50 =G= 1;
e133.. x30 + x37 + x44 + x51 =G= 1;
e134.. x31 + x38 + x45 + x52 =G= 1;
e135.. x32 + x39 + x46 + x53 =G= 1;
e136.. x33 + x40 + x47 + x54 =G= 1;
e137.. x34 + x41 + x48 + x55 =G= 1;
e138.. x35 + x42 + x49 + x56 =G= 1;
* set non-default bounds
x29.lo = 0.01; x29.up = 4;
x30.lo = 0.01; x30.up = 4;
x31.lo = 0.01; x31.up = 4;
x32.lo = 0.01; x32.up = 4;
x33.lo = 0.01; x33.up = 4;
x34.lo = 0.01; x34.up = 4;
x35.lo = 0.01; x35.up = 4;
x36.lo = 0.01; x36.up = 4;
x37.lo = 0.01; x37.up = 4;
x38.lo = 0.01; x38.up = 4;
x39.lo = 0.01; x39.up = 4;
x40.lo = 0.01; x40.up = 4;
x41.lo = 0.01; x41.up = 4;
x42.lo = 0.01; x42.up = 4;
x43.lo = 0.01; x43.up = 4;
x44.lo = 0.01; x44.up = 4;
x45.lo = 0.01; x45.up = 4;
x46.lo = 0.01; x46.up = 4;
x47.lo = 0.01; x47.up = 4;
x48.lo = 0.01; x48.up = 4;
x49.lo = 0.01; x49.up = 4;
x50.lo = 0.01; x50.up = 4;
x51.lo = 0.01; x51.up = 4;
x52.lo = 0.01; x52.up = 4;
x53.lo = 0.01; x53.up = 4;
x54.lo = 0.01; x54.up = 4;
x55.lo = 0.01; x55.up = 4;
x56.lo = 0.01; x56.up = 4;
* set non-default levels
x29.l = 1;
x30.l = 1;
x31.l = 1;
x32.l = 1;
x33.l = 1;
x34.l = 1;
x35.l = 1;
x36.l = 1;
x37.l = 1;
x38.l = 1;
x39.l = 1;
x40.l = 1;
x41.l = 1;
x42.l = 1;
x43.l = 1;
x44.l = 1;
x45.l = 1;
x46.l = 1;
x47.l = 1;
x48.l = 1;
x49.l = 1;
x50.l = 1;
x51.l = 1;
x52.l = 1;
x53.l = 1;
x54.l = 1;
x55.l = 1;
x56.l = 1;
x92.l = 100;
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