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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sssd15-04persp
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 sssd15-04.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 205054.38600000 (ANTIGONE) 204343.07720000 (BARON) 158721.49560000 (COUENNE) 205054.35290000 (GUROBI) 205054.45840000 (LINDO) 185611.62770000 (SCIP) 3087.83765500 (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ⓘ | MBQCP |
| #Variablesⓘ | 88 |
| #Binary Variablesⓘ | 72 |
| #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ⓘ | 76 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 47 |
| #Linear Constraintsⓘ | 35 |
| #Quadratic Constraintsⓘ | 12 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 204 |
| #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ⓘ | 5.4029e-01 |
| Maximal coefficientⓘ | 7.4750e+04 |
| Infeasibility of initial pointⓘ | 0.3333 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 48 20 0 28 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 89 17 72 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 281 245 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,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,objvar;
Positive Variables x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
,x87,x88;
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;
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;
e1.. - 53.1533839248115*b1 - 177.583181382496*b2 - 80.6428266602653*b3
- 231.95916447606*b4 - 394.432428138298*b5 - 444.974070084717*b6
- 459.794817811195*b7 - 695.629649483288*b8 - 323.203981426319*b9
- 107.360282998709*b10 - 361.859887112392*b11 - 367.306912008994*b12
- 282.872191198352*b13 - 44.0762253696262*b14 - 317.877544418109*b15
- 316.134390405973*b16 - 100.330419683223*b17 - 127.926900226391*b18
- 139.263247551061*b19 - 254.000222645919*b20 - 194.145316904472*b21
- 116.037290266393*b22 - 222.112787515659*b23 - 263.356262140469*b24
- 571.289311491824*b25 - 347.171110484916*b26 - 646.58041890394*b27
- 747.500077392939*b28 - 267.180266374013*b29 - 432.187536801291*b30
- 223.193932764969*b31 - 305.606281730255*b32 - 484.148164648118*b33
- 255.18826726263*b34 - 500.409280467716*b35 - 357.348895559311*b36
- 154.81861346409*b37 - 47.9482185242841*b38 - 178.01500365671*b39
- 197.299183634545*b40 - 110.221327583974*b41 - 276.335219124972*b42
- 66.6367550739739*b43 - 215.126920582161*b44 - 251.865680365869*b45
- 259.485555817488*b46 - 325.903992788768*b47 - 533.263861665761*b48
- 365.289467328013*b49 - 698.425848556873*b50 - 342.854784735801*b51
- 672.157315207286*b52 - 278.522996301316*b53 - 127.656852798454*b54
- 302.312726976851*b55 - 281.218053524739*b56 - 629.708028128623*b57
- 303.067014885745*b58 - 662.424721658793*b59 - 521.27200594153*b60
- 313.6973235*b61 - 136.4460104172*b62 - 95.4447793733688*b63
- 401.4402965*b64 - 160.307673981768*b65 - 107.445134115433*b66
- 456.70672375*b67 - 163.727629808624*b68 - 103.975094190251*b69
- 349.50038725*b70 - 137.744259121245*b71 - 91.7174793486262*b72
- 74750.0077392939*x73 - 74750.0077392939*x74 - 74750.0077392939*x75
- 74750.0077392939*x76 + objvar =E= 0;
e2.. 0.609376132*b1 + 1.180016336*b5 + 0.967493052*b9 + 1.004918785*b13
+ 0.698898063*b17 + 0.540292599*b21 + 1.460452986*b25 + 0.811980791*b29
+ 0.973180988*b33 + 0.544914116*b37 + 0.78515855*b41 + 1.312281472*b45
+ 1.346783152*b49 + 0.635811295*b53 + 1.327207817*b57 - 3.22664386875*x77
- 6.4532877375*x78 - 9.67993160625*x79 =E= 0;
e3.. 0.609376132*b2 + 1.180016336*b6 + 0.967493052*b10 + 1.004918785*b14
+ 0.698898063*b18 + 0.540292599*b22 + 1.460452986*b26 + 0.811980791*b30
+ 0.973180988*b34 + 0.544914116*b38 + 0.78515855*b42 + 1.312281472*b46
+ 1.346783152*b50 + 0.635811295*b54 + 1.327207817*b58
- 3.1952881621875*x80 - 6.390576324375*x81 - 9.5858644865625*x82 =E= 0;
e4.. 0.609376132*b3 + 1.180016336*b7 + 0.967493052*b11 + 1.004918785*b15
+ 0.698898063*b19 + 0.540292599*b23 + 1.460452986*b27 + 0.811980791*b31
+ 0.973180988*b35 + 0.544914116*b39 + 0.78515855*b43 + 1.312281472*b47
+ 1.346783152*b51 + 0.635811295*b55 + 1.327207817*b59
- 2.6301391753125*x83 - 5.260278350625*x84 - 7.8904175259375*x85 =E= 0;
e5.. 0.609376132*b4 + 1.180016336*b8 + 0.967493052*b12 + 1.004918785*b16
+ 0.698898063*b20 + 0.540292599*b24 + 1.460452986*b28 + 0.811980791*b32
+ 0.973180988*b36 + 0.544914116*b40 + 0.78515855*b44 + 1.312281472*b48
+ 1.346783152*b52 + 0.635811295*b56 + 1.327207817*b60
- 2.6743241765625*x86 - 5.348648353125*x87 - 8.0229725296875*x88 =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 =L= 1;
e22.. b64 + b65 + b66 =L= 1;
e23.. b67 + b68 + b69 =L= 1;
e24.. b70 + b71 + b72 =L= 1;
e25.. - b61 + x77 =L= 0;
e26.. - b62 + x78 =L= 0;
e27.. - b63 + x79 =L= 0;
e28.. - b64 + x80 =L= 0;
e29.. - b65 + x81 =L= 0;
e30.. - b66 + x82 =L= 0;
e31.. - b67 + x83 =L= 0;
e32.. - b68 + x84 =L= 0;
e33.. - b69 + x85 =L= 0;
e34.. - b70 + x86 =L= 0;
e35.. - b71 + x87 =L= 0;
e36.. - b72 + x88 =L= 0;
e37.. x77*b61 + x77*x73 - x73*b61 =L= 0;
e38.. x78*b62 + x78*x73 - x73*b62 =L= 0;
e39.. x79*b63 + x79*x73 - x73*b63 =L= 0;
e40.. x80*b64 + x80*x74 - x74*b64 =L= 0;
e41.. x81*b65 + x81*x74 - x74*b65 =L= 0;
e42.. x82*b66 + x82*x74 - x74*b66 =L= 0;
e43.. x83*b67 + x83*x75 - x75*b67 =L= 0;
e44.. x84*b68 + x84*x75 - x75*b68 =L= 0;
e45.. x85*b69 + x85*x75 - x75*b69 =L= 0;
e46.. x86*b70 + x86*x76 - x76*b70 =L= 0;
e47.. x87*b71 + x87*x76 - x76*b71 =L= 0;
e48.. x88*b72 + x88*x76 - x76*b72 =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 = 0.333333333333333;
b62.l = 0.333333333333333;
b63.l = 0.333333333333333;
b64.l = 0.333333333333333;
b65.l = 0.333333333333333;
b66.l = 0.333333333333333;
b67.l = 0.333333333333333;
b68.l = 0.333333333333333;
b69.l = 0.333333333333333;
b70.l = 0.333333333333333;
b71.l = 0.333333333333333;
b72.l = 0.333333333333333;
x73.l = 1.22251555798631;
x74.l = 1.24950210754822;
x75.l = 2.07513088371977;
x76.l = 1.97319440621145;
x77.l = 0.183353130884111;
x78.l = 0.183353130884111;
x79.l = 0.183353130884111;
x80.l = 0.185152394887074;
x81.l = 0.185152394887074;
x82.l = 0.185152394887074;
x83.l = 0.224936863089399;
x84.l = 0.224936863089399;
x85.l = 0.224936863089399;
x86.l = 0.2212204716123;
x87.l = 0.2212204716123;
x88.l = 0.2212204716123;
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