MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sssd20-08
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ⓘ | 460520.71760000 (ALPHAECP) 469619.52260000 (ANTIGONE) 469619.83720000 (BARON) 469439.85370000 (BONMIN) 141875.06860000 (COUENNE) 463988.44480000 (LINDO) 469619.70780000 (SCIP) 469619.56790000 (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ⓘ | 216 |
| #Binary Variablesⓘ | 184 |
| #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ⓘ | 192 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 84 |
| #Linear Constraintsⓘ | 60 |
| #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ⓘ | 464 |
| #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ⓘ | 5.4743e-01 |
| Maximal coefficientⓘ | 8.8729e+04 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 85 29 0 56 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 217 33 184 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 657 633 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,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,x185,x186,x187,x188,x189,x190,x191,x192,x193,x194
,x195,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205,x206,x207
,x208,x209,x210,x211,x212,x213,x214,x215,x216,objvar;
Positive Variables x185,x186,x187,x188,x189,x190,x191,x192,x193,x194,x195
,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205,x206,x207,x208
,x209,x210,x211,x212,x213,x214,x215,x216;
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,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;
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;
e1.. - 111.366069033018*b1 - 173.736682895127*b2 - 206.584137827711*b3
- 311.192639215759*b4 - 391.096663187392*b5 - 412.724041015689*b6
- 362.90703724183*b7 - 412.238377551605*b8 - 202.33239914492*b9
- 206.873035263351*b10 - 459.424203486646*b11 - 436.382257935297*b12
- 595.212791352102*b13 - 554.589535228908*b14 - 561.749361850176*b15
- 581.529277658138*b16 - 530.881632918085*b17 - 536.948983658504*b18
- 325.467953593857*b19 - 315.525067375426*b20 - 76.225942040435*b21
- 254.905793105451*b22 - 113.004738070171*b23 - 177.189040572114*b24
- 173.894920684095*b25 - 152.600290074966*b26 - 204.409857240935*b27
- 16.5055441265287*b28 - 138.719762707452*b29 - 72.1288414712326*b30
- 120.847015325226*b31 - 99.571165171974*b32 - 151.849080781614*b33
- 145.681002740026*b34 - 319.104683215451*b35 - 286.753801045421*b36
- 393.925160475677*b37 - 359.934057246776*b38 - 372.757367428863*b39
- 380.320704273821*b40 - 209.897358368756*b41 - 176.903014825797*b42
- 484.441224042163*b43 - 386.398700662687*b44 - 569.816540558016*b45
- 500.146929279378*b46 - 536.081866783575*b47 - 538.164119624621*b48
- 472.75417976903*b49 - 394.671861667082*b50 - 661.778650400896*b51
- 311.233594837076*b52 - 537.233382862136*b53 - 352.610164566948*b54
- 508.430479292237*b55 - 433.246268236365*b56 - 240.434688571414*b57
- 247.573379889676*b58 - 140.125745864737*b59 - 129.619586841229*b60
- 95.259779915922*b61 - 157.318586867059*b62 - 70.3512639139942*b63
- 129.990055093272*b64 - 243.357134921591*b65 - 304.003791259259*b66
- 387.22826595551*b67 - 513.078195638243*b68 - 616.876803085642*b69
- 635.234357536375*b70 - 584.514585206566*b71 - 639.355553242285*b72
- 471.729855743646*b73 - 557.923885983252*b74 - 106.468143550206*b75
- 576.327451798806*b76 - 526.167479727853*b77 - 684.640492332848*b78
- 496.847481320222*b79 - 632.720138765642*b80 - 349.132941483343*b81
- 328.586110112758*b82 - 615.607044330971*b83 - 537.140113127724*b84
- 717.322415523131*b85 - 647.481188136546*b86 - 684.12778533852*b87
- 686.401242893627*b88 - 506.816284666641*b89 - 398.035848133399*b90
- 855.431776792172*b91 - 471.606942587939*b92 - 801.214873020304*b93
- 596.722224078614*b94 - 753.768882151975*b95 - 691.333659314473*b96
- 85.3675502274446*b97 - 158.379394593169*b98 - 257.300026361108*b99
- 320.704543355031*b100 - 448.126320657674*b101 - 457.763772256702*b102
- 408.83386135894*b103 - 463.255868286668*b104 - 237.144352702819*b105
- 177.481389098916*b106 - 528.418902427793*b107 - 367.481249017807*b108
- 581.69455257316*b109 - 486.218458446561*b110 - 545.202814571382*b111
- 534.842653535173*b112 - 273.315651326331*b113 - 294.736877404174*b114
- 91.5634612712189*b115 - 207.431742416254*b116 - 131.445214576321*b117
- 232.45283126314*b118 - 119.004267377741*b119 - 195.036716336294*b120
- 382.803613122328*b121 - 467.001607601617*b122 - 186.213458590968*b123
- 547.081668156355*b124 - 541.160249117729*b125 - 656.49566392312*b126
- 512.884098066802*b127 - 621.549425681682*b128 - 181.371452020713*b129
- 175.492124453316*b130 - 162.248252595624*b131 - 55.0280789945633*b132
- 114.798088119326*b133 - 107.382697687723*b134 - 90.3342797608636*b135
- 106.314336443356*b136 - 221.180367269329*b137 - 200.830918650843*b138
- 420.854797821172*b139 - 351.4013073243*b140 - 486.967847106279*b141
- 432.551908850222*b142 - 462.429481904519*b143 - 462.157040602356*b144
- 181.09388190356*b145 - 223.750754907429*b146 - 118.11570891131*b147
- 279.735432351987*b148 - 287.185185564983*b149 - 336.883342353846*b150
- 272.594688961982*b151 - 322.770119748047*b152 - 326.795248361408*b153
- 271.173036007453*b154 - 758.353052369709*b155 - 597.043789091874*b156
- 887.286114762329*b157 - 775.415492640821*b158 - 834.258761011951*b159
- 836.015790081594*b160 - 333.50853775*b161 - 114.488510347914*b162
- 71.1466014342705*b163 - 327.61554475*b164 - 115.456652447649*b165
- 72.6961052063678*b166 - 418.975572*b167 - 144.050104531568*b168
- 89.5861361571157*b169 - 441.6481805*b170 - 147.751509681552*b171
- 90.6409148587658*b172 - 284.85345325*b173 - 109.929987849219*b174
- 72.4317650925971*b175 - 364.98681475*b176 - 131.410153066893*b177
- 83.6314997177532*b178 - 261.83219775*b179 - 103.183186592188*b180
- 68.7017117455899*b181 - 481.55377575*b182 - 144.356933487536*b183
- 83.8297118343163*b184 - 88728.6114762329*x185 - 88728.6114762329*x186
- 88728.6114762329*x187 - 88728.6114762329*x188 - 88728.6114762329*x189
- 88728.6114762329*x190 - 88728.6114762329*x191 - 88728.6114762329*x192
+ objvar =E= 0;
e2.. 0.818476132*b1 + 0.870157536*b9 + 1.031851452*b17 + 0.557538685*b25
+ 0.547431463*b33 + 0.875695399*b41 + 1.084580786*b49 + 0.730328391*b57
+ 0.942474488*b65 + 1.428565416*b73 + 0.86023025*b81 + 1.427064072*b89
+ 1.077855852*b97 + 0.966432495*b105 + 0.749586417*b113 + 1.20475136*b121
+ 0.637168473*b129 + 0.637828387*b137 + 0.578555855*b145
+ 1.377981994*b153 - 1.68639324125*x193 - 3.3727864825*x194
- 5.05917972375*x195 =E= 0;
e3.. 0.818476132*b2 + 0.870157536*b10 + 1.031851452*b18 + 0.557538685*b26
+ 0.547431463*b34 + 0.875695399*b42 + 1.084580786*b50 + 0.730328391*b58
+ 0.942474488*b66 + 1.428565416*b74 + 0.86023025*b82 + 1.427064072*b90
+ 1.077855852*b98 + 0.966432495*b106 + 0.749586417*b114 + 1.20475136*b122
+ 0.637168473*b130 + 0.637828387*b138 + 0.578555855*b146
+ 1.377981994*b154 - 1.792318871875*x196 - 3.58463774375*x197
- 5.376956615625*x198 =E= 0;
e4.. 0.818476132*b3 + 0.870157536*b11 + 1.031851452*b19 + 0.557538685*b27
+ 0.547431463*b35 + 0.875695399*b43 + 1.084580786*b51 + 0.730328391*b59
+ 0.942474488*b67 + 1.428565416*b75 + 0.86023025*b83 + 1.427064072*b91
+ 1.077855852*b99 + 0.966432495*b107 + 0.749586417*b115 + 1.20475136*b123
+ 0.637168473*b131 + 0.637828387*b139 + 0.578555855*b147
+ 1.377981994*b155 - 2.128386030625*x199 - 4.25677206125*x200
- 6.385158091875*x201 =E= 0;
e5.. 0.818476132*b4 + 0.870157536*b12 + 1.031851452*b20 + 0.557538685*b28
+ 0.547431463*b36 + 0.875695399*b44 + 1.084580786*b52 + 0.730328391*b60
+ 0.942474488*b68 + 1.428565416*b76 + 0.86023025*b84 + 1.427064072*b92
+ 1.077855852*b100 + 0.966432495*b108 + 0.749586417*b116
+ 1.20475136*b124 + 0.637168473*b132 + 0.637828387*b140
+ 0.578555855*b148 + 1.377981994*b156 - 2.066948260625*x202
- 4.13389652125*x203 - 6.200844781875*x204 =E= 0;
e6.. 0.818476132*b5 + 0.870157536*b13 + 1.031851452*b21 + 0.557538685*b29
+ 0.547431463*b37 + 0.875695399*b45 + 1.084580786*b53 + 0.730328391*b61
+ 0.942474488*b69 + 1.428565416*b77 + 0.86023025*b85 + 1.427064072*b93
+ 1.077855852*b101 + 0.966432495*b109 + 0.749586417*b117
+ 1.20475136*b125 + 0.637168473*b133 + 0.637828387*b141
+ 0.578555855*b149 + 1.377981994*b157 - 2.04641702*x205 - 4.09283404*x206
- 6.13925106*x207 =E= 0;
e7.. 0.818476132*b6 + 0.870157536*b14 + 1.031851452*b22 + 0.557538685*b30
+ 0.547431463*b38 + 0.875695399*b46 + 1.084580786*b54 + 0.730328391*b62
+ 0.942474488*b70 + 1.428565416*b78 + 0.86023025*b86 + 1.427064072*b94
+ 1.077855852*b102 + 0.966432495*b110 + 0.749586417*b118
+ 1.20475136*b126 + 0.637168473*b134 + 0.637828387*b142
+ 0.578555855*b150 + 1.377981994*b158 - 2.129217781875*x208
- 4.25843556375*x209 - 6.387653345625*x210 =E= 0;
e8.. 0.818476132*b7 + 0.870157536*b15 + 1.031851452*b23 + 0.557538685*b31
+ 0.547431463*b39 + 0.875695399*b47 + 1.084580786*b55 + 0.730328391*b63
+ 0.942474488*b71 + 1.428565416*b79 + 0.86023025*b87 + 1.427064072*b95
+ 1.077855852*b103 + 0.966432495*b111 + 0.749586417*b119
+ 1.20475136*b127 + 0.637168473*b135 + 0.637828387*b143
+ 0.578555855*b151 + 1.377981994*b159 - 2.002947450625*x211
- 4.00589490125*x212 - 6.008842351875*x213 =E= 0;
e9.. 0.818476132*b8 + 0.870157536*b16 + 1.031851452*b24 + 0.557538685*b32
+ 0.547431463*b40 + 0.875695399*b48 + 1.084580786*b56 + 0.730328391*b64
+ 0.942474488*b72 + 1.428565416*b80 + 0.86023025*b88 + 1.427064072*b96
+ 1.077855852*b104 + 0.966432495*b112 + 0.749586417*b120
+ 1.20475136*b128 + 0.637168473*b136 + 0.637828387*b144
+ 0.578555855*b152 + 1.377981994*b160 - 1.62146898*x214 - 3.24293796*x215
- 4.86440694*x216 =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 + b124 + b125 + b126 + b127 + b128 =E= 1;
e26.. b129 + b130 + b131 + b132 + b133 + b134 + b135 + b136 =E= 1;
e27.. b137 + b138 + b139 + b140 + b141 + b142 + b143 + b144 =E= 1;
e28.. b145 + b146 + b147 + b148 + b149 + b150 + b151 + b152 =E= 1;
e29.. b153 + b154 + b155 + b156 + b157 + b158 + b159 + b160 =E= 1;
e30.. b161 + b162 + b163 =L= 1;
e31.. b164 + b165 + b166 =L= 1;
e32.. b167 + b168 + b169 =L= 1;
e33.. b170 + b171 + b172 =L= 1;
e34.. b173 + b174 + b175 =L= 1;
e35.. b176 + b177 + b178 =L= 1;
e36.. b179 + b180 + b181 =L= 1;
e37.. b182 + b183 + b184 =L= 1;
e38.. - b161 + x193 =L= 0;
e39.. - b162 + x194 =L= 0;
e40.. - b163 + x195 =L= 0;
e41.. - b164 + x196 =L= 0;
e42.. - b165 + x197 =L= 0;
e43.. - b166 + x198 =L= 0;
e44.. - b167 + x199 =L= 0;
e45.. - b168 + x200 =L= 0;
e46.. - b169 + x201 =L= 0;
e47.. - b170 + x202 =L= 0;
e48.. - b171 + x203 =L= 0;
e49.. - b172 + x204 =L= 0;
e50.. - b173 + x205 =L= 0;
e51.. - b174 + x206 =L= 0;
e52.. - b175 + x207 =L= 0;
e53.. - b176 + x208 =L= 0;
e54.. - b177 + x209 =L= 0;
e55.. - b178 + x210 =L= 0;
e56.. - b179 + x211 =L= 0;
e57.. - b180 + x212 =L= 0;
e58.. - b181 + x213 =L= 0;
e59.. - b182 + x214 =L= 0;
e60.. - b183 + x215 =L= 0;
e61.. - b184 + x216 =L= 0;
e62.. -x185/(1 + x185) + x193 =L= 0;
e63.. -x185/(1 + x185) + x194 =L= 0;
e64.. -x185/(1 + x185) + x195 =L= 0;
e65.. -x186/(1 + x186) + x196 =L= 0;
e66.. -x186/(1 + x186) + x197 =L= 0;
e67.. -x186/(1 + x186) + x198 =L= 0;
e68.. -x187/(1 + x187) + x199 =L= 0;
e69.. -x187/(1 + x187) + x200 =L= 0;
e70.. -x187/(1 + x187) + x201 =L= 0;
e71.. -x188/(1 + x188) + x202 =L= 0;
e72.. -x188/(1 + x188) + x203 =L= 0;
e73.. -x188/(1 + x188) + x204 =L= 0;
e74.. -x189/(1 + x189) + x205 =L= 0;
e75.. -x189/(1 + x189) + x206 =L= 0;
e76.. -x189/(1 + x189) + x207 =L= 0;
e77.. -x190/(1 + x190) + x208 =L= 0;
e78.. -x190/(1 + x190) + x209 =L= 0;
e79.. -x190/(1 + x190) + x210 =L= 0;
e80.. -x191/(1 + x191) + x211 =L= 0;
e81.. -x191/(1 + x191) + x212 =L= 0;
e82.. -x191/(1 + x191) + x213 =L= 0;
e83.. -x192/(1 + x192) + x214 =L= 0;
e84.. -x192/(1 + x192) + x215 =L= 0;
e85.. -x192/(1 + x192) + x216 =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