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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sssd12-05persp
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 sssd12-05.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 281408.46520000 (ANTIGONE) 277551.29510000 (BARON) 223966.36540000 (COUENNE) 281408.60930000 (GUROBI) 281408.63530000 (LINDO) 281408.35670000 (SCIP) 2403.82567600 (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ⓘ | 95 |
| #Binary Variablesⓘ | 75 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 35 |
| #Nonlinear Binary Variablesⓘ | 15 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 80 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 52 |
| #Linear Constraintsⓘ | 37 |
| #Quadratic Constraintsⓘ | 15 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 225 |
| #Nonlinear Nonzeros in Jacobianⓘ | 45 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 90 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 5 |
| 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ⓘ | 9.3617e+04 |
| Infeasibility of initial pointⓘ | 0.3333 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 53 18 0 35 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 96 21 75 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 306 261 45 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,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,x91,x92,x93,x94,x95,objvar;
Positive Variables x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87,x88,x89
,x90,x91,x92,x93,x94,x95;
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;
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.. - 301.899928098152*b1 - 282.051473607022*b2 - 151.594044960674*b3
- 114.784185877557*b4 - 213.364530716922*b5 - 772.653148294131*b6
- 697.676211791334*b7 - 146.306371684975*b8 - 390.583393857486*b9
- 208.147527440482*b10 - 662.892902187869*b11 - 577.461337631217*b12
- 221.10047354739*b13 - 425.919826737657*b14 - 123.074770812851*b15
- 333.28129673946*b16 - 248.380746723092*b17 - 249.162942146638*b18
- 164.598799150643*b19 - 280.957171099846*b20 - 308.552481034871*b21
- 270.059605282374*b22 - 104.633483616243*b23 - 79.6631898566695*b24
- 170.696237801571*b25 - 237.754076296143*b26 - 189.862911729786*b27
- 107.217531395173*b28 - 131.358715293396*b29 - 103.406777059692*b30
- 626.417763832299*b31 - 487.184730842973*b32 - 502.300580630229*b33
- 506.426352475088*b34 - 463.185748318154*b35 - 358.178221555384*b36
- 281.629247221142*b37 - 230.4203839171*b38 - 251.915433121165*b39
- 209.261088879339*b40 - 303.899003044044*b41 - 243.197489456663*b42
- 237.390965850675*b43 - 57.1385835039462*b44 - 301.733744039334*b45
- 30.6123768510861*b46 - 21.3396948414106*b47 - 278.520865043453*b48
- 162.122145724483*b49 - 304.508803157003*b50 - 252.516206195527*b51
- 178.796029580139*b52 - 319.145634893211*b53 - 257.755103285795*b54
- 317.996864520235*b55 - 936.171150833806*b56 - 887.611963724196*b57
- 419.760722838682*b58 - 519.981401235063*b59 - 524.621957902125*b60
- 326.37044675*b61 - 119.610927362864*b62 - 76.800859418795*b63
- 338.15311375*b64 - 113.101546866718*b65 - 69.3762358590679*b66
- 313.6973235*b67 - 116.266585440261*b68 - 75.0744657614982*b69
- 401.4402965*b70 - 138.599587312691*b71 - 86.376825937843*b72
- 456.70672375*b73 - 150.554161322115*b74 - 91.6821859840903*b75
- 93617.1150833806*x76 - 93617.1150833806*x77 - 93617.1150833806*x78
- 93617.1150833806*x79 - 93617.1150833806*x80 + objvar =E= 0;
e2.. 0.609376132*b1 + 1.180016336*b6 + 0.967493052*b11 + 1.004918785*b16
+ 0.698898063*b21 + 0.540292599*b26 + 1.460452986*b31 + 0.811980791*b36
+ 0.973180988*b41 + 0.544914116*b46 + 0.78515855*b51 + 1.312281472*b56
- 2.0080698912*x81 - 4.0161397824*x82 - 6.0242096736*x83 =E= 0;
e3.. 0.609376132*b2 + 1.180016336*b7 + 0.967493052*b12 + 1.004918785*b17
+ 0.698898063*b22 + 0.540292599*b27 + 1.460452986*b32 + 0.811980791*b37
+ 0.973180988*b42 + 0.544914116*b47 + 0.78515855*b52 + 1.312281472*b57
- 1.581486777*x84 - 3.162973554*x85 - 4.744460331*x86 =E= 0;
e4.. 0.609376132*b3 + 1.180016336*b8 + 0.967493052*b13 + 1.004918785*b18
+ 0.698898063*b23 + 0.540292599*b28 + 1.460452986*b33 + 0.811980791*b38
+ 0.973180988*b43 + 0.544914116*b48 + 0.78515855*b53 + 1.312281472*b58
- 1.9963246902*x87 - 3.9926493804*x88 - 5.9889740706*x89 =E= 0;
e5.. 0.609376132*b4 + 1.180016336*b9 + 0.967493052*b14 + 1.004918785*b19
+ 0.698898063*b24 + 0.540292599*b29 + 1.460452986*b34 + 0.811980791*b39
+ 0.973180988*b44 + 0.544914116*b49 + 0.78515855*b54 + 1.312281472*b59
- 2.065052076*x90 - 4.130104152*x91 - 6.195156228*x92 =E= 0;
e6.. 0.609376132*b5 + 1.180016336*b10 + 0.967493052*b15 + 1.004918785*b20
+ 0.698898063*b25 + 0.540292599*b30 + 1.460452986*b35 + 0.811980791*b40
+ 0.973180988*b45 + 0.544914116*b50 + 0.78515855*b55 + 1.312281472*b60
- 2.0449844238*x93 - 4.0899688476*x94 - 6.1349532714*x95 =E= 0;
e7.. b1 + b2 + b3 + b4 + b5 =E= 1;
e8.. b6 + b7 + b8 + b9 + b10 =E= 1;
e9.. b11 + b12 + b13 + b14 + b15 =E= 1;
e10.. b16 + b17 + b18 + b19 + b20 =E= 1;
e11.. b21 + b22 + b23 + b24 + b25 =E= 1;
e12.. b26 + b27 + b28 + b29 + b30 =E= 1;
e13.. b31 + b32 + b33 + b34 + b35 =E= 1;
e14.. b36 + b37 + b38 + b39 + b40 =E= 1;
e15.. b41 + b42 + b43 + b44 + b45 =E= 1;
e16.. b46 + b47 + b48 + b49 + b50 =E= 1;
e17.. b51 + b52 + b53 + b54 + b55 =E= 1;
e18.. b56 + b57 + b58 + b59 + b60 =E= 1;
e19.. b61 + b62 + b63 =L= 1;
e20.. b64 + b65 + b66 =L= 1;
e21.. b67 + b68 + b69 =L= 1;
e22.. b70 + b71 + b72 =L= 1;
e23.. b73 + b74 + b75 =L= 1;
e24.. - b61 + x81 =L= 0;
e25.. - b62 + x82 =L= 0;
e26.. - b63 + x83 =L= 0;
e27.. - b64 + x84 =L= 0;
e28.. - b65 + x85 =L= 0;
e29.. - b66 + x86 =L= 0;
e30.. - b67 + x87 =L= 0;
e31.. - b68 + x88 =L= 0;
e32.. - b69 + x89 =L= 0;
e33.. - b70 + x90 =L= 0;
e34.. - b71 + x91 =L= 0;
e35.. - b72 + x92 =L= 0;
e36.. - b73 + x93 =L= 0;
e37.. - b74 + x94 =L= 0;
e38.. - b75 + x95 =L= 0;
e39.. x81*b61 + x81*x76 - x76*b61 =L= 0;
e40.. x82*b62 + x82*x76 - x76*b62 =L= 0;
e41.. x83*b63 + x83*x76 - x76*b63 =L= 0;
e42.. x84*b64 + x84*x77 - x77*b64 =L= 0;
e43.. x85*b65 + x85*x77 - x77*b65 =L= 0;
e44.. x86*b66 + x86*x77 - x77*b66 =L= 0;
e45.. x87*b67 + x87*x78 - x78*b67 =L= 0;
e46.. x88*b68 + x88*x78 - x78*b68 =L= 0;
e47.. x89*b69 + x89*x78 - x78*b69 =L= 0;
e48.. x90*b70 + x90*x79 - x79*b70 =L= 0;
e49.. x91*b71 + x91*x79 - x79*b71 =L= 0;
e50.. x92*b72 + x92*x79 - x79*b72 =L= 0;
e51.. x93*b73 + x93*x80 - x80*b73 =L= 0;
e52.. x94*b74 + x94*x80 - x80*b74 =L= 0;
e53.. x95*b75 + x95*x80 - x80*b75 =L= 0;
* set non-default levels
b1.l = 0.2;
b2.l = 0.2;
b3.l = 0.2;
b4.l = 0.2;
b5.l = 0.2;
b6.l = 0.2;
b7.l = 0.2;
b8.l = 0.2;
b9.l = 0.2;
b10.l = 0.2;
b11.l = 0.2;
b12.l = 0.2;
b13.l = 0.2;
b14.l = 0.2;
b15.l = 0.2;
b16.l = 0.2;
b17.l = 0.2;
b18.l = 0.2;
b19.l = 0.2;
b20.l = 0.2;
b21.l = 0.2;
b22.l = 0.2;
b23.l = 0.2;
b24.l = 0.2;
b25.l = 0.2;
b26.l = 0.2;
b27.l = 0.2;
b28.l = 0.2;
b29.l = 0.2;
b30.l = 0.2;
b31.l = 0.2;
b32.l = 0.2;
b33.l = 0.2;
b34.l = 0.2;
b35.l = 0.2;
b36.l = 0.2;
b37.l = 0.2;
b38.l = 0.2;
b39.l = 0.2;
b40.l = 0.2;
b41.l = 0.2;
b42.l = 0.2;
b43.l = 0.2;
b44.l = 0.2;
b45.l = 0.2;
b46.l = 0.2;
b47.l = 0.2;
b48.l = 0.2;
b49.l = 0.2;
b50.l = 0.2;
b51.l = 0.2;
b52.l = 0.2;
b53.l = 0.2;
b54.l = 0.2;
b55.l = 0.2;
b56.l = 0.2;
b57.l = 0.2;
b58.l = 0.2;
b59.l = 0.2;
b60.l = 0.2;
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;
b73.l = 0.333333333333333;
b74.l = 0.333333333333333;
b75.l = 0.333333333333333;
x76.l = 1.18464727499703;
x77.l = 2.21055142184158;
x78.l = 1.19998063005095;
x79.l = 1.11549458684761;
x80.l = 1.13890807654545;
x81.l = 0.18075340102651;
x82.l = 0.18075340102651;
x83.l = 0.18075340102651;
x84.l = 0.229509008619004;
x85.l = 0.229509008619004;
x86.l = 0.229509008619004;
x87.l = 0.181816847787907;
x88.l = 0.181816847787907;
x89.l = 0.181816847787907;
x90.l = 0.175765767145396;
x91.l = 0.175765767145396;
x92.l = 0.175765767145396;
x93.l = 0.177490575531558;
x94.l = 0.177490575531558;
x95.l = 0.177490575531558;
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