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)
300591.01460000 p1 ( gdx sol )
(infeas: 6e-15)
300186.80480000 p2 ( gdx sol )
(infeas: 0)
300176.56370000 p3 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
291708.16370000 (ANTIGONE)
287231.58570000 (BARON)
180772.44700000 (COUENNE)
300176.55110000 (GUROBI)
300186.80480000 (LINDO)
248446.30120000 (SCIP)
5314.19879300 (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 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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-08-11 Git hash: f176bd52
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