MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sssd25-04persp
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. Perspective reformulation of sssd25-04.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 291708.16370000 (ANTIGONE) 300176.56370000 (BARON) 180772.44700000 (COUENNE) 300176.55110000 (GUROBI) 300186.80480000 (LINDO) 248446.30120000 (SCIP) 5314.19879300 (SHOT) 300176.26370000 (XPRESS) |
| 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ⓘ | MBQCP |
| #Variablesⓘ | 128 |
| #Binary Variablesⓘ | 112 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 28 |
| #Nonlinear Binary Variablesⓘ | 12 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 116 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 57 |
| #Linear Constraintsⓘ | 45 |
| #Quadratic Constraintsⓘ | 12 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 284 |
| #Nonlinear Nonzeros in Jacobianⓘ | 36 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 72 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 7 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.5819e-01 |
| Maximal coefficientⓘ | 8.3309e+04 |
| Infeasibility of initial pointⓘ | 0.3333 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 58 30 0 28 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 129 17 112 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 401 365 36 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,x113,x114,x115,x116
,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,objvar;
Positive Variables x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123
,x124,x125,x126,x127,x128;
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;
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;
e1.. - 476.627680186915*b1 - 149.653586784487*b2 - 213.186384418957*b3
- 43.7888464292729*b4 - 474.830868219332*b5 - 804.41120755867*b6
- 584.914840194532*b7 - 661.646071204307*b8 - 392.259337390379*b9
- 142.80919923228*b10 - 218.980029277262*b11 - 104.519355726959*b12
- 314.988665746119*b13 - 501.761182472619*b14 - 416.807578457382*b15
- 524.390259195122*b16 - 362.341095830922*b17 - 441.362501912098*b18
- 402.716752066181*b19 - 492.339440818786*b20 - 290.964161684016*b21
- 116.368122158017*b22 - 173.712811065166*b23 - 95.9656692808925*b24
- 443.684333533333*b25 - 176.081128582949*b26 - 302.39173954457*b27
- 293.29371225224*b28 - 476.763266014932*b29 - 183.917148897559*b30
- 272.205185020914*b31 - 136.278105402226*b32 - 101.35843572405*b33
- 193.942699651262*b34 - 141.921469465657*b35 - 201.173648709993*b36
- 132.921832386141*b37 - 421.655945550644*b38 - 281.212652600547*b39
- 407.005327357163*b40 - 202.365762241646*b41 - 137.219422282215*b42
- 132.146952277583*b43 - 179.383015135974*b44 - 123.618453957013*b45
- 297.215252315231*b46 - 218.762870620071*b47 - 282.961164098487*b48
- 20.13413882933*b49 - 497.103669118494*b50 - 268.341006965987*b51
- 427.522422721593*b52 - 210.032834185575*b53 - 434.311463333895*b54
- 298.270736776993*b55 - 444.612005461353*b56 - 211.951029854733*b57
- 447.318981178372*b58 - 332.208676638743*b59 - 453.095321147229*b60
- 435.628401127826*b61 - 771.659835894158*b62 - 623.845701115879*b63
- 775.557667039354*b64 - 424.738471081496*b65 - 833.085816488132*b66
- 592.460027321246*b67 - 700.942808077211*b68 - 229.947132383408*b69
- 586.218425366478*b70 - 424.710208954907*b71 - 555.528795297853*b72
- 327.711607414859*b73 - 238.953801669268*b74 - 251.293372908654*b75
- 313.742954288217*b76 - 478.24585803249*b77 - 80.7823868731141*b78
- 266.940737208009*b79 - 164.458228751629*b80 - 332.729569180138*b81
- 388.723389119461*b82 - 237.094588860685*b83 - 245.459595758858*b84
- 170.849806397817*b85 - 170.734963967704*b86 - 30.8907942571205*b87
- 104.086188009457*b88 - 66.4196868291459*b89 - 312.344045852442*b90
- 151.766233459965*b91 - 278.677297797007*b92 - 205.289077931114*b93
- 86.9146012652412*b94 - 127.990999929026*b95 - 141.658946009938*b96
- 588.039796501339*b97 - 363.309460856624*b98 - 476.707321955199*b99
- 487.438573778052*b100 - 489.84367475*b101 - 216.633855557639*b102
- 152.801343309708*b103 - 384.081627*b104 - 178.524432787122*b105
- 129.092639672378*b106 - 311.0588205*b107 - 156.215197085809*b108
- 117.416983804282*b109 - 300.51551825*b110 - 147.887674474043*b111
- 110.035201882344*b112 - 83308.5816488132*x113 - 83308.5816488132*x114
- 83308.5816488132*x115 - 83308.5816488132*x116 + objvar =E= 0;
e2.. 1.493016132*b1 + 1.456072816*b5 + 0.993236412*b9 + 1.025966745*b13
+ 1.038311423*b17 + 0.674453719*b21 + 1.110104106*b25 + 1.179319831*b29
+ 0.560898388*b33 + 1.098374636*b37 + 0.81518723*b41 + 0.558194512*b45
+ 1.439212232*b49 + 1.368059775*b53 + 1.096159257*b57 + 1.34695262*b61
+ 1.499851813*b65 + 1.138420427*b69 + 1.142989815*b73 + 1.204066374*b77
+ 1.342748386*b81 + 0.943180215*b85 + 1.100967989*b89 + 0.659153757*b93
+ 1.197148552*b97 - 5.2960774859375*x117 - 10.592154971875*x118
- 15.8882324578125*x119 =E= 0;
e3.. 1.493016132*b2 + 1.456072816*b6 + 0.993236412*b10 + 1.025966745*b14
+ 1.038311423*b18 + 0.674453719*b22 + 1.110104106*b26 + 1.179319831*b30
+ 0.560898388*b34 + 1.098374636*b38 + 0.81518723*b42 + 0.558194512*b46
+ 1.439212232*b50 + 1.368059775*b54 + 1.096159257*b58 + 1.34695262*b62
+ 1.499851813*b66 + 1.138420427*b70 + 1.142989815*b74 + 1.204066374*b78
+ 1.342748386*b82 + 0.943180215*b86 + 1.100967989*b90 + 0.659153757*b94
+ 1.197148552*b98 - 4.8209976578125*x120 - 9.641995315625*x121
- 14.4629929734375*x122 =E= 0;
e4.. 1.493016132*b3 + 1.456072816*b7 + 0.993236412*b11 + 1.025966745*b15
+ 1.038311423*b19 + 0.674453719*b23 + 1.110104106*b27 + 1.179319831*b31
+ 0.560898388*b35 + 1.098374636*b39 + 0.81518723*b43 + 0.558194512*b47
+ 1.439212232*b51 + 1.368059775*b55 + 1.096159257*b59 + 1.34695262*b63
+ 1.499851813*b67 + 1.138420427*b71 + 1.142989815*b75 + 1.204066374*b79
+ 1.342748386*b83 + 0.943180215*b87 + 1.100967989*b91 + 0.659153757*b95
+ 1.197148552*b99 - 4.924666325*x123 - 9.84933265*x124
- 14.773998975*x125 =E= 0;
e5.. 1.493016132*b4 + 1.456072816*b8 + 0.993236412*b12 + 1.025966745*b16
+ 1.038311423*b20 + 0.674453719*b24 + 1.110104106*b28 + 1.179319831*b32
+ 0.560898388*b36 + 1.098374636*b40 + 0.81518723*b44 + 0.558194512*b48
+ 1.439212232*b52 + 1.368059775*b56 + 1.096159257*b60 + 1.34695262*b64
+ 1.499851813*b68 + 1.138420427*b72 + 1.142989815*b76 + 1.204066374*b80
+ 1.342748386*b84 + 0.943180215*b88 + 1.100967989*b92 + 0.659153757*b96
+ 1.197148552*b100 - 4.4766575796875*x126 - 8.953315159375*x127
- 13.4299727390625*x128 =E= 0;
e6.. b1 + b2 + b3 + b4 =E= 1;
e7.. b5 + b6 + b7 + b8 =E= 1;
e8.. b9 + b10 + b11 + b12 =E= 1;
e9.. b13 + b14 + b15 + b16 =E= 1;
e10.. b17 + b18 + b19 + b20 =E= 1;
e11.. b21 + b22 + b23 + b24 =E= 1;
e12.. b25 + b26 + b27 + b28 =E= 1;
e13.. b29 + b30 + b31 + b32 =E= 1;
e14.. b33 + b34 + b35 + b36 =E= 1;
e15.. b37 + b38 + b39 + b40 =E= 1;
e16.. b41 + b42 + b43 + b44 =E= 1;
e17.. b45 + b46 + b47 + b48 =E= 1;
e18.. b49 + b50 + b51 + b52 =E= 1;
e19.. b53 + b54 + b55 + b56 =E= 1;
e20.. b57 + b58 + b59 + b60 =E= 1;
e21.. b61 + b62 + b63 + b64 =E= 1;
e22.. b65 + b66 + b67 + b68 =E= 1;
e23.. b69 + b70 + b71 + b72 =E= 1;
e24.. b73 + b74 + b75 + b76 =E= 1;
e25.. b77 + b78 + b79 + b80 =E= 1;
e26.. b81 + b82 + b83 + b84 =E= 1;
e27.. b85 + b86 + b87 + b88 =E= 1;
e28.. b89 + b90 + b91 + b92 =E= 1;
e29.. b93 + b94 + b95 + b96 =E= 1;
e30.. b97 + b98 + b99 + b100 =E= 1;
e31.. b101 + b102 + b103 =L= 1;
e32.. b104 + b105 + b106 =L= 1;
e33.. b107 + b108 + b109 =L= 1;
e34.. b110 + b111 + b112 =L= 1;
e35.. - b101 + x117 =L= 0;
e36.. - b102 + x118 =L= 0;
e37.. - b103 + x119 =L= 0;
e38.. - b104 + x120 =L= 0;
e39.. - b105 + x121 =L= 0;
e40.. - b106 + x122 =L= 0;
e41.. - b107 + x123 =L= 0;
e42.. - b108 + x124 =L= 0;
e43.. - b109 + x125 =L= 0;
e44.. - b110 + x126 =L= 0;
e45.. - b111 + x127 =L= 0;
e46.. - b112 + x128 =L= 0;
e47.. x117*b101 + x117*x113 - x113*b101 =L= 0;
e48.. x118*b102 + x118*x113 - x113*b102 =L= 0;
e49.. x119*b103 + x119*x113 - x113*b103 =L= 0;
e50.. x120*b104 + x120*x114 - x114*b104 =L= 0;
e51.. x121*b105 + x121*x114 - x114*b105 =L= 0;
e52.. x122*b106 + x122*x114 - x114*b106 =L= 0;
e53.. x123*b107 + x123*x115 - x115*b107 =L= 0;
e54.. x124*b108 + x124*x115 - x115*b108 =L= 0;
e55.. x125*b109 + x125*x115 - x115*b109 =L= 0;
e56.. x126*b110 + x126*x116 - x116*b110 =L= 0;
e57.. x127*b111 + x127*x116 - x116*b111 =L= 0;
e58.. x128*b112 + x128*x116 - x116*b112 =L= 0;
* set non-default levels
b1.l = 0.25;
b2.l = 0.25;
b3.l = 0.25;
b4.l = 0.25;
b5.l = 0.25;
b6.l = 0.25;
b7.l = 0.25;
b8.l = 0.25;
b9.l = 0.25;
b10.l = 0.25;
b11.l = 0.25;
b12.l = 0.25;
b13.l = 0.25;
b14.l = 0.25;
b15.l = 0.25;
b16.l = 0.25;
b17.l = 0.25;
b18.l = 0.25;
b19.l = 0.25;
b20.l = 0.25;
b21.l = 0.25;
b22.l = 0.25;
b23.l = 0.25;
b24.l = 0.25;
b25.l = 0.25;
b26.l = 0.25;
b27.l = 0.25;
b28.l = 0.25;
b29.l = 0.25;
b30.l = 0.25;
b31.l = 0.25;
b32.l = 0.25;
b33.l = 0.25;
b34.l = 0.25;
b35.l = 0.25;
b36.l = 0.25;
b37.l = 0.25;
b38.l = 0.25;
b39.l = 0.25;
b40.l = 0.25;
b41.l = 0.25;
b42.l = 0.25;
b43.l = 0.25;
b44.l = 0.25;
b45.l = 0.25;
b46.l = 0.25;
b47.l = 0.25;
b48.l = 0.25;
b49.l = 0.25;
b50.l = 0.25;
b51.l = 0.25;
b52.l = 0.25;
b53.l = 0.25;
b54.l = 0.25;
b55.l = 0.25;
b56.l = 0.25;
b57.l = 0.25;
b58.l = 0.25;
b59.l = 0.25;
b60.l = 0.25;
b61.l = 0.25;
b62.l = 0.25;
b63.l = 0.25;
b64.l = 0.25;
b65.l = 0.25;
b66.l = 0.25;
b67.l = 0.25;
b68.l = 0.25;
b69.l = 0.25;
b70.l = 0.25;
b71.l = 0.25;
b72.l = 0.25;
b73.l = 0.25;
b74.l = 0.25;
b75.l = 0.25;
b76.l = 0.25;
b77.l = 0.25;
b78.l = 0.25;
b79.l = 0.25;
b80.l = 0.25;
b81.l = 0.25;
b82.l = 0.25;
b83.l = 0.25;
b84.l = 0.25;
b85.l = 0.25;
b86.l = 0.25;
b87.l = 0.25;
b88.l = 0.25;
b89.l = 0.25;
b90.l = 0.25;
b91.l = 0.25;
b92.l = 0.25;
b93.l = 0.25;
b94.l = 0.25;
b95.l = 0.25;
b96.l = 0.25;
b97.l = 0.25;
b98.l = 0.25;
b99.l = 0.25;
b100.l = 0.25;
b101.l = 0.333333333333333;
b102.l = 0.333333333333333;
b103.l = 0.333333333333333;
b104.l = 0.333333333333333;
b105.l = 0.333333333333333;
b106.l = 0.333333333333333;
b107.l = 0.333333333333333;
b108.l = 0.333333333333333;
b109.l = 0.333333333333333;
b110.l = 0.333333333333333;
b111.l = 0.333333333333333;
b112.l = 0.333333333333333;
x113.l = 1.84609632242111;
x114.l = 2.47900149079549;
x115.l = 2.30645349772837;
x116.l = 3.29868478857466;
x117.l = 0.216213849109492;
x118.l = 0.216213849109492;
x119.l = 0.216213849109492;
x120.l = 0.237520401313832;
x121.l = 0.237520401313832;
x122.l = 0.237520401313832;
x123.l = 0.232520382671138;
x124.l = 0.232520382671138;
x125.l = 0.232520382671138;
x126.l = 0.255790235914493;
x127.l = 0.255790235914493;
x128.l = 0.255790235914493;
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