MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sssd20-04
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ⓘ | 347583.01130000 (ALPHAECP) 347691.32570000 (ANTIGONE) 347691.41010000 (BARON) 347691.41010000 (BONMIN) 228871.95830000 (COUENNE) 347691.41040000 (LINDO) 347691.19730000 (SCIP) 347691.40820000 (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ⓘ | 108 |
| #Binary Variablesⓘ | 92 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 4 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 96 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 52 |
| #Linear Constraintsⓘ | 40 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 12 |
| Operands in Gen. Nonlin. Functionsⓘ | div |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 232 |
| #Nonlinear Nonzeros in Jacobianⓘ | 12 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 4 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 4 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| 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ⓘ | 5.0194e-01 |
| Maximal coefficientⓘ | 1.1382e+05 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 53 25 0 28 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 109 17 92 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 329 317 12 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,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103
,x104,x105,x106,x107,x108,objvar;
Positive Variables x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103,x104,x105
,x106,x107,x108;
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;
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;
e1.. - 605.279840123728*b1 - 272.608555855308*b2 - 211.960656393875*b3
- 135.715048070326*b4 - 522.241469316371*b5 - 523.563443912583*b6
- 619.396068733614*b7 - 682.855110454901*b8 - 114.621684843966*b9
- 261.173379139252*b10 - 513.947181134071*b11 - 358.827151019868*b12
- 52.6956363514181*b13 - 220.516589731527*b14 - 345.528110071738*b15
- 282.457316020068*b16 - 164.693392296952*b17 - 399.53784188835*b18
- 579.783225922065*b19 - 516.220792703845*b20 - 141.747533297772*b21
- 335.99629563561*b22 - 476.041671993639*b23 - 412.41709048995*b24
- 249.021288299155*b25 - 32.6643717959122*b26 - 199.880519193262*b27
- 133.876249431799*b28 - 728.457456178222*b29 - 404.601461725878*b30
- 192.078907281649*b31 - 305.768394889279*b32 - 221.337276729365*b33
- 192.029949456353*b34 - 290.444487065555*b35 - 290.589607684046*b36
- 51.4630955019675*b37 - 378.97714206935*b38 - 703.676326841317*b39
- 539.35222186517*b40 - 204.068863192141*b41 - 463.922884836254*b42
- 653.596824664278*b43 - 561.360926563887*b44 - 266.946572387463*b45
- 560.351177303554*b46 - 769.136225452049*b47 - 680.608731917532*b48
- 63.9346010099856*b49 - 279.007631632013*b50 - 482.164187877198*b51
- 396.080242012788*b52 - 220.027468271858*b53 - 241.243800922173*b54
- 278.137335265831*b55 - 303.106288586679*b56 - 422.202307395423*b57
- 190.792583868763*b58 - 305.391726831552*b59 - 321.417518470348*b60
- 658.941366540719*b61 - 257.620909868047*b62 - 150.646514025985*b63
- 290.969639301944*b64 - 505.285454816257*b65 - 51.8926025973049*b66
- 331.503998535252*b67 - 203.933628440855*b68 - 342.132118599327*b69
- 368.956004133481*b70 - 594.305258519636*b71 - 387.086094157069*b72
- 159.012285419563*b73 - 466.830163547866*b74 - 692.307419918051*b75
- 595.529758838679*b76 - 367.398716653205*b77 - 816.295996604146*b78
- 1138.18899052505*b79 - 1010.10082815226*b80 - 334.527248*b81
- 153.380628575016*b82 - 110.155626976693*b83 - 304.26749275*b84
- 134.618265608558*b85 - 94.9717940075149*b86 - 386.41984025*b87
- 164.839722634043*b88 - 114.190322638477*b89 - 292.732952*b90
- 143.429945907125*b91 - 106.48563964612*b92 - 113818.899052505*x93
- 113818.899052505*x94 - 113818.899052505*x95 - 113818.899052505*x96
+ objvar =E= 0;
e2.. 1.051196132*b1 + 1.318044576*b5 + 0.980364732*b9 + 0.515442765*b13
+ 0.868604743*b17 + 0.607373159*b21 + 0.785278546*b25 + 0.995650311*b29
+ 0.767039688*b33 + 1.321644376*b37 + 0.80017289*b41 + 0.935237992*b45
+ 0.892997692*b49 + 0.501935535*b53 + 1.211683537*b57 + 1.39435304*b61
+ 1.454079593*b65 + 0.971951107*b69 + 0.997801135*b73 + 1.479427834*b77
- 4.0303184825*x97 - 8.060636965*x98 - 12.0909554475*x99 =E= 0;
e3.. 1.051196132*b2 + 1.318044576*b6 + 0.980364732*b10 + 0.515442765*b14
+ 0.868604743*b18 + 0.607373159*b22 + 0.785278546*b26 + 0.995650311*b30
+ 0.767039688*b34 + 1.321644376*b38 + 0.80017289*b42 + 0.935237992*b46
+ 0.892997692*b50 + 0.501935535*b54 + 1.211683537*b58 + 1.39435304*b62
+ 1.454079593*b66 + 0.971951107*b70 + 0.997801135*b74 + 1.479427834*b78
- 3.29375444375*x100 - 6.5875088875*x101 - 9.88126333125*x102 =E= 0;
e4.. 1.051196132*b3 + 1.318044576*b7 + 0.980364732*b11 + 0.515442765*b15
+ 0.868604743*b19 + 0.607373159*b23 + 0.785278546*b27 + 0.995650311*b31
+ 0.767039688*b35 + 1.321644376*b39 + 0.80017289*b43 + 0.935237992*b47
+ 0.892997692*b51 + 0.501935535*b55 + 1.211683537*b59 + 1.39435304*b63
+ 1.454079593*b67 + 0.971951107*b71 + 0.997801135*b75 + 1.479427834*b79
- 3.74935596125*x103 - 7.4987119225*x104 - 11.24806788375*x105 =E= 0;
e5.. 1.051196132*b4 + 1.318044576*b8 + 0.980364732*b12 + 0.515442765*b16
+ 0.868604743*b20 + 0.607373159*b24 + 0.785278546*b28 + 0.995650311*b32
+ 0.767039688*b36 + 1.321644376*b40 + 0.80017289*b44 + 0.935237992*b48
+ 0.892997692*b52 + 0.501935535*b56 + 1.211683537*b60 + 1.39435304*b64
+ 1.454079593*b68 + 0.971951107*b72 + 0.997801135*b76 + 1.479427834*b80
- 4.30395742125*x106 - 8.6079148425*x107 - 12.91187226375*x108 =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 =L= 1;
e27.. b84 + b85 + b86 =L= 1;
e28.. b87 + b88 + b89 =L= 1;
e29.. b90 + b91 + b92 =L= 1;
e30.. - b81 + x97 =L= 0;
e31.. - b82 + x98 =L= 0;
e32.. - b83 + x99 =L= 0;
e33.. - b84 + x100 =L= 0;
e34.. - b85 + x101 =L= 0;
e35.. - b86 + x102 =L= 0;
e36.. - b87 + x103 =L= 0;
e37.. - b88 + x104 =L= 0;
e38.. - b89 + x105 =L= 0;
e39.. - b90 + x106 =L= 0;
e40.. - b91 + x107 =L= 0;
e41.. - b92 + x108 =L= 0;
e42.. -x93/(1 + x93) + x97 =L= 0;
e43.. -x93/(1 + x93) + x98 =L= 0;
e44.. -x93/(1 + x93) + x99 =L= 0;
e45.. -x94/(1 + x94) + x100 =L= 0;
e46.. -x94/(1 + x94) + x101 =L= 0;
e47.. -x94/(1 + x94) + x102 =L= 0;
e48.. -x95/(1 + x95) + x103 =L= 0;
e49.. -x95/(1 + x95) + x104 =L= 0;
e50.. -x95/(1 + x95) + x105 =L= 0;
e51.. -x96/(1 + x96) + x106 =L= 0;
e52.. -x96/(1 + x96) + x107 =L= 0;
e53.. -x96/(1 + x96) + x108 =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: 2024-04-02 Git hash: 1dd5fb9b