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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sssd08-04persp
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 sssd08-04.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 182022.52790000 (ANTIGONE) 182022.57010000 (BARON) 182022.57020000 (COUENNE) 182022.54710000 (GUROBI) 182022.57020000 (LINDO) 182022.57020000 (SCIP) 1464.88730300 (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ⓘ | 60 |
| #Binary Variablesⓘ | 44 |
| #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ⓘ | 48 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 40 |
| #Linear Constraintsⓘ | 28 |
| #Quadratic Constraintsⓘ | 12 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 148 |
| #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ⓘ | 5.5484e-01 |
| Maximal coefficientⓘ | 6.7692e+04 |
| Infeasibility of initial pointⓘ | 0.3333 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 41 13 0 28 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 61 17 44 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 197 161 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,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,objvar;
Positive Variables x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55,x56,x57,x58
,x59,x60;
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;
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;
e1.. - 222.395350591392*b1 - 582.786400468795*b2 - 119.753843399653*b3
- 338.549698035479*b4 - 119.783636606301*b5 - 409.374679229076*b6
- 278.20529021903*b7 - 306.426594992684*b8 - 441.233650379831*b9
- 153.049293317818*b10 - 439.090557840933*b11 - 175.155823424664*b12
- 612.328425893001*b13 - 146.717315955674*b14 - 676.916374379371*b15
- 425.643803755754*b16 - 476.000407399777*b17 - 218.667102585295*b18
- 429.494068158725*b19 - 260.065761415496*b20 - 228.081133173702*b21
- 290.916261365409*b22 - 358.983740312016*b23 - 303.078553779965*b24
- 224.102176788463*b25 - 372.279886491354*b26 - 217.090150838618*b27
- 84.469492807076*b28 - 274.179320847966*b29 - 209.61866336051*b30
- 205.445642503502*b31 - 144.701484010017*b32 - 270.520699*b33
- 100.444790162654*b34 - 64.9166596734302*b35 - 330.80933975*b36
- 110.205022516595*b37 - 67.4648851252699*b38 - 297.23545225*b39
- 96.7703053435877*b40 - 58.5635369942729*b41 - 252.028512*b42
- 91.7540307917193*b43 - 58.7189192724058*b44 - 67691.6374379371*x45
- 67691.6374379371*x46 - 67691.6374379371*x47 - 67691.6374379371*x48
+ objvar =E= 0;
e2.. 0.990828132*b1 + 0.7867768*b5 + 1.1494727*b9 + 1.090185213*b13
+ 0.861308711*b17 + 0.646379815*b21 + 1.205697202*b25 + 0.554843463*b29
- 1.730889404*x49 - 3.461778808*x50 - 5.192668212*x51 =E= 0;
e3.. 0.990828132*b2 + 0.7867768*b6 + 1.1494727*b10 + 1.090185213*b14
+ 0.861308711*b18 + 0.646379815*b22 + 1.205697202*b26 + 0.554843463*b30
- 1.528745876*x52 - 3.057491752*x53 - 4.586237628*x54 =E= 0;
e4.. 0.990828132*b3 + 0.7867768*b7 + 1.1494727*b11 + 1.090185213*b15
+ 0.861308711*b19 + 0.646379815*b23 + 1.205697202*b27 + 0.554843463*b31
- 1.282069237*x55 - 2.564138474*x56 - 3.846207711*x57 =E= 0;
e5.. 0.990828132*b4 + 0.7867768*b8 + 1.1494727*b12 + 1.090185213*b16
+ 0.861308711*b20 + 0.646379815*b24 + 1.205697202*b28 + 0.554843463*b32
- 1.520071172*x58 - 3.040142344*x59 - 4.560213516*x60 =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 =L= 1;
e15.. b36 + b37 + b38 =L= 1;
e16.. b39 + b40 + b41 =L= 1;
e17.. b42 + b43 + b44 =L= 1;
e18.. - b33 + x49 =L= 0;
e19.. - b34 + x50 =L= 0;
e20.. - b35 + x51 =L= 0;
e21.. - b36 + x52 =L= 0;
e22.. - b37 + x53 =L= 0;
e23.. - b38 + x54 =L= 0;
e24.. - b39 + x55 =L= 0;
e25.. - b40 + x56 =L= 0;
e26.. - b41 + x57 =L= 0;
e27.. - b42 + x58 =L= 0;
e28.. - b43 + x59 =L= 0;
e29.. - b44 + x60 =L= 0;
e30.. x49*b33 + x49*x45 - x45*b33 =L= 0;
e31.. x50*b34 + x50*x45 - x45*b34 =L= 0;
e32.. x51*b35 + x51*x45 - x45*b35 =L= 0;
e33.. x52*b36 + x52*x46 - x46*b36 =L= 0;
e34.. x53*b37 + x53*x46 - x46*b37 =L= 0;
e35.. x54*b38 + x54*x46 - x46*b38 =L= 0;
e36.. x55*b39 + x55*x47 - x47*b39 =L= 0;
e37.. x56*b40 + x56*x47 - x47*b40 =L= 0;
e38.. x57*b41 + x57*x47 - x47*b41 =L= 0;
e39.. x58*b42 + x58*x48 - x48*b42 =L= 0;
e40.. x59*b43 + x59*x48 - x48*b43 =L= 0;
e41.. x60*b44 + x60*x48 - x48*b44 =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 = 0.333333333333333;
b34.l = 0.333333333333333;
b35.l = 0.333333333333333;
b36.l = 0.333333333333333;
b37.l = 0.333333333333333;
b38.l = 0.333333333333333;
b39.l = 0.333333333333333;
b40.l = 0.333333333333333;
b41.l = 0.333333333333333;
b42.l = 0.333333333333333;
b43.l = 0.333333333333333;
b44.l = 0.333333333333333;
x45.l = 1.11031856270584;
x46.l = 1.47346120210071;
x47.l = 2.45215090742002;
x48.l = 1.49443619616504;
x49.l = 0.175379297755911;
x50.l = 0.175379297755911;
x51.l = 0.175379297755911;
x52.l = 0.198569411000437;
x53.l = 0.198569411000437;
x54.l = 0.198569411000437;
x55.l = 0.23677517516682;
x56.l = 0.23677517516682;
x57.l = 0.23677517516682;
x58.l = 0.199702601929659;
x59.l = 0.199702601929659;
x60.l = 0.199702601929659;
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