MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


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)
205245.74300000 p1 ( gdx sol )
(infeas: 9e-16)
205054.45850000 p2 ( gdx sol )
(infeas: 1e-16)
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 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
*         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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0