MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance sssd15-08
Stochastic Service System Design. Servers are modeled as M/M/1 queues, and a set of customers must be assigned to the servers which can be operated at different service levels. The objective is to minimize assignment and operating costs.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 562042.40980000 (ALPHAECP) 562617.87580000 (ANTIGONE) 562617.88180000 (AOA) 562617.88120000 (BARON) 562173.84530000 (BONMIN) 158337.97960000 (COUENNE) 550821.70250000 (LINDO) 562617.86230000 (SCIP) 562617.88120000 (SHOT) |
| Referencesⓘ | Elhedhli, Samir, Service System Design with Immobile Servers, Stochastic Demand, and Congestion, Manufacturing & Service Operations Management, 8:1, 2006, 92-97. Günlük, Oktay and Linderoth, Jeff T, Perspective reformulations of mixed integer nonlinear programs with indicator variables, Mathematical Programming, 124:1-2, 2010, 183-205. Günlük, Oktay and Linderoth, Jeff T, Perspective Reformulation and Applications. In Lee, Jon and Leyffer, Sven, Eds, Mixed Integer Nonlinear Programming, Springer, 2012, 61-89. |
| Applicationⓘ | Service System Design |
| Added to libraryⓘ | 24 Feb 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 176 |
| #Binary Variablesⓘ | 144 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 8 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 152 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 79 |
| #Linear Constraintsⓘ | 55 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 24 |
| Operands in Gen. Nonlin. Functionsⓘ | div |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 384 |
| #Nonlinear Nonzeros in Jacobianⓘ | 24 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 8 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 8 |
| #Blocks in Hessian of Lagrangianⓘ | 8 |
| 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ⓘ | 5.3649e-01 |
| Maximal coefficientⓘ | 9.3203e+04 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 80 24 0 56 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 177 33 144 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 537 513 24 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,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,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,objvar;
Positive Variables 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;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51
,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68
,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
,b86,b87,b88,b89,b90,b91,b92,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;
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;
e1.. - 403.928572687557*b1 - 152.992741540361*b2 - 267.315589205704*b3
- 401.957253171747*b4 - 239.900413376196*b5 - 172.190748942287*b6
- 242.754569605376*b7 - 206.00422281341*b8 - 175.512360171018*b9
- 12.4456890694952*b10 - 95.1129504127459*b11 - 163.523864888208*b12
- 136.749750630694*b13 - 183.460227957173*b14 - 154.161364707845*b15
- 58.2220762837777*b16 - 427.797333694278*b17 - 124.146285420687*b18
- 281.762350319908*b19 - 416.122892408842*b20 - 286.880720364618*b21
- 171.930365706852*b22 - 298.680284192437*b23 - 212.446553403468*b24
- 334.799175421099*b25 - 166.360551160919*b26 - 261.524865566971*b27
- 321.118189558705*b28 - 275.112120282415*b29 - 70.1440860194197*b30
- 281.389498973428*b31 - 225.606388157132*b32 - 321.213816864959*b33
- 71.9883302424501*b34 - 169.588450009557*b35 - 291.06773760337*b36
- 283.136668462665*b37 - 418.102856274321*b38 - 323.382162238167*b39
- 109.329676669547*b40 - 225.077476533111*b41 - 292.549188246279*b42
- 256.821062390988*b43 - 181.735382103635*b44 - 361.637553977341*b45
- 487.443715088842*b46 - 391.614198813426*b47 - 276.780369289256*b48
- 790.809160300441*b49 - 572.306788163427*b50 - 710.561007303222*b51
- 710.424717790653*b52 - 882.480677740369*b53 - 746.52609026712*b54
- 932.032155531379*b55 - 673.014016071675*b56 - 415.137891763513*b57
- 24.1331183147668*b58 - 232.723756037565*b59 - 385.530297939342*b60
- 328.99787719123*b61 - 412.551506227386*b62 - 368.4253530904*b63
- 149.097324374568*b64 - 505.111125566583*b65 - 324.408884140539*b66
- 422.192328810933*b67 - 433.424841813569*b68 - 590.521463309364*b69
- 601.187176017906*b70 - 639.549861073539*b71 - 393.266050752522*b72
- 317.266722109018*b73 - 366.343507824765*b74 - 278.701740808319*b75
- 360.414608909582*b76 - 163.468646330858*b77 - 496.33685624632*b78
- 135.080317454783*b79 - 291.219332583259*b80 - 60.7098769607628*b81
- 257.274009667912*b82 - 109.739073857234*b83 - 105.840898609517*b84
- 149.608079935928*b85 - 478.2765537338*b86 - 175.640633384092*b87
- 164.991725574781*b88 - 370.179004516539*b89 - 456.332727530502*b90
- 323.598387892417*b91 - 428.625530616724*b92 - 176.797739228846*b93
- 657.950143580026*b94 - 146.134286318179*b95 - 347.137285556827*b96
- 459.855709875116*b97 - 206.994357545204*b98 - 317.109585585788*b99
- 461.635447603175*b100 - 270.249812459436*b101 - 176.621455199898*b102
- 266.565650581812*b103 - 255.042767652375*b104 - 688.990984467753*b105
- 342.921309942336*b106 - 508.744698659858*b107 - 686.009170292228*b108
- 457.444445796545*b109 - 133.755629117181*b110 - 451.235917636358*b111
- 427.625644498357*b112 - 275.559617400364*b113 - 356.414463245256*b114
- 238.594038182377*b115 - 323.736842820792*b116 - 123.509577347529*b117
- 537.671376447504*b118 - 104.741456798329*b119 - 261.777653762851*b120
- 343.78539425*b121 - 113.508450322244*b122 - 69.177220392612*b123
- 264.047028*b124 - 87.3113122712859*b125 - 53.2512330089256*b126
- 390.47730275*b127 - 123.63305929533*b128 - 73.7850337614663*b129
- 406.29941025*b130 - 126.736316912988*b131 - 75.0745406137203*b132
- 283.160272*b133 - 95.8513476067592*b134 - 59.1487898247813*b135
- 422.01298775*b136 - 132.224826373859*b137 - 78.5002039603394*b138
- 269.10096475*b139 - 95.9362994616171*b140 - 60.754974511923*b141
- 395.712942*b142 - 123.433440930338*b143 - 73.1178281922949*b144
- 93203.2155531379*x145 - 93203.2155531379*x146 - 93203.2155531379*x147
- 93203.2155531379*x148 - 93203.2155531379*x149 - 93203.2155531379*x150
- 93203.2155531379*x151 - 93203.2155531379*x152 + objvar =E= 0;
e2.. 0.934836132*b1 + 0.594101056*b9 + 1.006108092*b17 + 0.536490725*b25
+ 1.208018103*b33 + 0.741534279*b41 + 1.434929666*b49 + 1.362989351*b57
+ 1.354757088*b65 + 0.875104896*b73 + 0.83020157*b81 + 1.181151032*b89
+ 0.985426772*b97 + 1.234184015*b105 + 0.980634977*b113
- 1.54666509375*x153 - 3.0933301875*x154 - 4.63999528125*x155 =E= 0;
e3.. 0.934836132*b2 + 0.594101056*b10 + 1.006108092*b18 + 0.536490725*b26
+ 1.208018103*b34 + 0.741534279*b42 + 1.434929666*b50 + 1.362989351*b58
+ 1.354757088*b66 + 0.875104896*b74 + 0.83020157*b82 + 1.181151032*b90
+ 0.985426772*b98 + 1.234184015*b106 + 0.980634977*b114
- 1.19326126546875*x156 - 2.3865225309375*x157 - 3.57978379640625*x158
=E= 0;
e4.. 0.934836132*b3 + 0.594101056*b11 + 1.006108092*b19 + 0.536490725*b27
+ 1.208018103*b35 + 0.741534279*b43 + 1.434929666*b51 + 1.362989351*b59
+ 1.354757088*b67 + 0.875104896*b75 + 0.83020157*b83 + 1.181151032*b91
+ 0.985426772*b99 + 1.234184015*b107 + 0.980634977*b115
- 1.54916706890625*x159 - 3.0983341378125*x160 - 4.64750120671875*x161
=E= 0;
e5.. 0.934836132*b4 + 0.594101056*b12 + 1.006108092*b20 + 0.536490725*b28
+ 1.208018103*b36 + 0.741534279*b44 + 1.434929666*b52 + 1.362989351*b60
+ 1.354757088*b68 + 0.875104896*b76 + 0.83020157*b84 + 1.181151032*b92
+ 0.985426772*b100 + 1.234184015*b108 + 0.980634977*b116
- 1.54133366953125*x162 - 3.0826673390625*x163 - 4.62400100859375*x164
=E= 0;
e6.. 0.934836132*b5 + 0.594101056*b13 + 1.006108092*b21 + 0.536490725*b29
+ 1.208018103*b37 + 0.741534279*b45 + 1.434929666*b53 + 1.362989351*b61
+ 1.354757088*b69 + 0.875104896*b77 + 0.83020157*b85 + 1.181151032*b93
+ 0.985426772*b101 + 1.234184015*b109 + 0.980634977*b117
- 1.3728304284375*x165 - 2.745660856875*x166 - 4.1184912853125*x167 =E= 0
;
e7.. 0.934836132*b6 + 0.594101056*b14 + 1.006108092*b22 + 0.536490725*b30
+ 1.208018103*b38 + 0.741534279*b46 + 1.434929666*b54 + 1.362989351*b62
+ 1.354757088*b70 + 0.875104896*b78 + 0.83020157*b86 + 1.181151032*b94
+ 0.985426772*b102 + 1.234184015*b110 + 0.980634977*b118
- 1.6224571809375*x168 - 3.244914361875*x169 - 4.8673715428125*x170 =E= 0
;
e8.. 0.934836132*b7 + 0.594101056*b15 + 1.006108092*b23 + 0.536490725*b31
+ 1.208018103*b39 + 0.741534279*b47 + 1.434929666*b55 + 1.362989351*b63
+ 1.354757088*b71 + 0.875104896*b79 + 0.83020157*b87 + 1.181151032*b95
+ 0.985426772*b103 + 1.234184015*b111 + 0.980634977*b119
- 1.52407353515625*x171 - 3.0481470703125*x172 - 4.57222060546875*x173
=E= 0;
e9.. 0.934836132*b8 + 0.594101056*b16 + 1.006108092*b24 + 0.536490725*b32
+ 1.208018103*b40 + 0.741534279*b48 + 1.434929666*b56 + 1.362989351*b64
+ 1.354757088*b72 + 0.875104896*b80 + 0.83020157*b88 + 1.181151032*b96
+ 0.985426772*b104 + 1.234184015*b112 + 0.980634977*b120
- 1.50114900421875*x174 - 3.0022980084375*x175 - 4.50344701265625*x176
=E= 0;
e10.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 =E= 1;
e11.. b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 =E= 1;
e12.. b17 + b18 + b19 + b20 + b21 + b22 + b23 + b24 =E= 1;
e13.. b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 =E= 1;
e14.. b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;
e15.. b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 =E= 1;
e16.. b49 + b50 + b51 + b52 + b53 + b54 + b55 + b56 =E= 1;
e17.. b57 + b58 + b59 + b60 + b61 + b62 + b63 + b64 =E= 1;
e18.. b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72 =E= 1;
e19.. b73 + b74 + b75 + b76 + b77 + b78 + b79 + b80 =E= 1;
e20.. b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88 =E= 1;
e21.. b89 + b90 + b91 + b92 + b93 + b94 + b95 + b96 =E= 1;
e22.. b97 + b98 + b99 + b100 + b101 + b102 + b103 + b104 =E= 1;
e23.. b105 + b106 + b107 + b108 + b109 + b110 + b111 + b112 =E= 1;
e24.. b113 + b114 + b115 + b116 + b117 + b118 + b119 + b120 =E= 1;
e25.. b121 + b122 + b123 =L= 1;
e26.. b124 + b125 + b126 =L= 1;
e27.. b127 + b128 + b129 =L= 1;
e28.. b130 + b131 + b132 =L= 1;
e29.. b133 + b134 + b135 =L= 1;
e30.. b136 + b137 + b138 =L= 1;
e31.. b139 + b140 + b141 =L= 1;
e32.. b142 + b143 + b144 =L= 1;
e33.. - b121 + x153 =L= 0;
e34.. - b122 + x154 =L= 0;
e35.. - b123 + x155 =L= 0;
e36.. - b124 + x156 =L= 0;
e37.. - b125 + x157 =L= 0;
e38.. - b126 + x158 =L= 0;
e39.. - b127 + x159 =L= 0;
e40.. - b128 + x160 =L= 0;
e41.. - b129 + x161 =L= 0;
e42.. - b130 + x162 =L= 0;
e43.. - b131 + x163 =L= 0;
e44.. - b132 + x164 =L= 0;
e45.. - b133 + x165 =L= 0;
e46.. - b134 + x166 =L= 0;
e47.. - b135 + x167 =L= 0;
e48.. - b136 + x168 =L= 0;
e49.. - b137 + x169 =L= 0;
e50.. - b138 + x170 =L= 0;
e51.. - b139 + x171 =L= 0;
e52.. - b140 + x172 =L= 0;
e53.. - b141 + x173 =L= 0;
e54.. - b142 + x174 =L= 0;
e55.. - b143 + x175 =L= 0;
e56.. - b144 + x176 =L= 0;
e57.. -x145/(1 + x145) + x153 =L= 0;
e58.. -x145/(1 + x145) + x154 =L= 0;
e59.. -x145/(1 + x145) + x155 =L= 0;
e60.. -x146/(1 + x146) + x156 =L= 0;
e61.. -x146/(1 + x146) + x157 =L= 0;
e62.. -x146/(1 + x146) + x158 =L= 0;
e63.. -x147/(1 + x147) + x159 =L= 0;
e64.. -x147/(1 + x147) + x160 =L= 0;
e65.. -x147/(1 + x147) + x161 =L= 0;
e66.. -x148/(1 + x148) + x162 =L= 0;
e67.. -x148/(1 + x148) + x163 =L= 0;
e68.. -x148/(1 + x148) + x164 =L= 0;
e69.. -x149/(1 + x149) + x165 =L= 0;
e70.. -x149/(1 + x149) + x166 =L= 0;
e71.. -x149/(1 + x149) + x167 =L= 0;
e72.. -x150/(1 + x150) + x168 =L= 0;
e73.. -x150/(1 + x150) + x169 =L= 0;
e74.. -x150/(1 + x150) + x170 =L= 0;
e75.. -x151/(1 + x151) + x171 =L= 0;
e76.. -x151/(1 + x151) + x172 =L= 0;
e77.. -x151/(1 + x151) + x173 =L= 0;
e78.. -x152/(1 + x152) + x174 =L= 0;
e79.. -x152/(1 + x152) + x175 =L= 0;
e80.. -x152/(1 + x152) + x176 =L= 0;
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: 2024-08-26 Git hash: 6cc1607f