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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance sssd20-04persp

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 sssd20-04.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
347856.57880000 p1 ( gdx sol )
(infeas: 2e-15)
347716.89090000 p2 ( gdx sol )
(infeas: 0)
347691.41050000 p3 ( gdx sol )
(infeas: 5e-15)
Other points (infeas > 1e-08)  
Dual Bounds
347691.29330000 (ANTIGONE)
336396.62040000 (BARON)
232138.73310000 (COUENNE)
347691.41050000 (GUROBI)
347716.89090000 (LINDO)
300793.09570000 (SCIP)
4013.68874100 (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 108
#Binary Variables 92
#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 96
#Nonlinear Nonzeros in Objective 0
#Constraints 52
#Linear Constraints 40
#Quadratic Constraints 12
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 244
#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 5.0194e-01
Maximal coefficient 1.1382e+05
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
*         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
*        341      305       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,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.. x97*b81 + x97*x93 - x93*b81 =L= 0;

e43.. x98*b82 + x98*x93 - x93*b82 =L= 0;

e44.. x99*b83 + x99*x93 - x93*b83 =L= 0;

e45.. x100*b84 + x100*x94 - x94*b84 =L= 0;

e46.. x101*b85 + x101*x94 - x94*b85 =L= 0;

e47.. x102*b86 + x102*x94 - x94*b86 =L= 0;

e48.. x103*b87 + x103*x95 - x95*b87 =L= 0;

e49.. x104*b88 + x104*x95 - x95*b88 =L= 0;

e50.. x105*b89 + x105*x95 - x95*b89 =L= 0;

e51.. x106*b90 + x106*x96 - x96*b90 =L= 0;

e52.. x107*b91 + x107*x96 - x96*b91 =L= 0;

e53.. x108*b92 + x108*x96 - x96*b92 =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 = 0.333333333333333;
b82.l = 0.333333333333333;
b83.l = 0.333333333333333;
b84.l = 0.333333333333333;
b85.l = 0.333333333333333;
b86.l = 0.333333333333333;
b87.l = 0.333333333333333;
b88.l = 0.333333333333333;
b89.l = 0.333333333333333;
b90.l = 0.333333333333333;
b91.l = 0.333333333333333;
b92.l = 0.333333333333333;
x93.l = 1.60182773798373;
x94.l = 3.05400369998218;
x95.l = 1.95673968396495;
x96.l = 1.36134435840075;
x97.l = 0.205218266964009;
x98.l = 0.205218266964009;
x99.l = 0.205218266964009;
x100.l = 0.25111008984325;
x101.l = 0.25111008984325;
x102.l = 0.25111008984325;
x103.l = 0.220596545870753;
x104.l = 0.220596545870753;
x105.l = 0.220596545870753;
x106.l = 0.192170807779844;
x107.l = 0.192170807779844;
x108.l = 0.192170807779844;

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: 2022-10-14 Git hash: 2be6d7c0
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