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Instance sssd18-06
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.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 397409.36130000 (ALPHAECP) 397992.28920000 (ANTIGONE) 397992.29470000 (BARON) 397992.29420000 (BONMIN) 172495.87000000 (COUENNE) 397992.26010000 (LINDO) 397992.29510000 (SCIP) 397992.26820000 (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ⓘ | MBNLP |
| #Variablesⓘ | 150 |
| #Binary Variablesⓘ | 126 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 6 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 132 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 66 |
| #Linear Constraintsⓘ | 48 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 18 |
| Operands in Gen. Nonlin. Functionsⓘ | div |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 324 |
| #Nonlinear Nonzeros in Jacobianⓘ | 18 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 6 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0129e-01 |
| Maximal coefficientⓘ | 9.2063e+04 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 67 25 0 42 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 151 25 126 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 457 439 18 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,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,x127,x128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
,x143,x144,x145,x146,x147,x148,x149,x150,objvar;
Positive Variables x127,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137
,x138,x139,x140,x141,x142,x143,x144,x145,x146,x147,x148,x149,x150;
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,b113,b114
,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126;
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,e59,e60,e61,e62,e63,e64,e65,e66,e67;
e1.. - 63.4638470839033*b1 - 406.464924344563*b2 - 281.054038749709*b3
- 357.899009619357*b4 - 283.867227208487*b5 - 346.427860883825*b6
- 174.902031629248*b7 - 327.682040608985*b8 - 195.408950113586*b9
- 411.209540848557*b10 - 341.151615907997*b11 - 306.690501464422*b12
- 217.736042166853*b13 - 590.531921051569*b14 - 469.541866006763*b15
- 371.170896461036*b16 - 301.885481955089*b17 - 482.559449428939*b18
- 266.695094430501*b19 - 661.407332369201*b20 - 469.726457930889*b21
- 365.202026294741*b22 - 207.423237700342*b23 - 464.900263444655*b24
- 416.573440009268*b25 - 427.21293769024*b26 - 421.557561337466*b27
- 131.588490152482*b28 - 195.079739824454*b29 - 327.092772346777*b30
- 284.74538638165*b31 - 91.2881292105079*b32 - 151.13720061786*b33
- 158.491236423963*b34 - 174.161578418524*b35 - 70.9637233498753*b36
- 455.733220723331*b37 - 159.976116957465*b38 - 94.4221181484321*b39
- 501.080276859661*b40 - 450.105521915833*b41 - 218.986984440606*b42
- 754.787490214755*b43 - 145.720505553027*b44 - 360.826762020128*b45
- 512.320209445762*b46 - 533.899656702829*b47 - 217.438198555652*b48
- 257.356951080936*b49 - 469.748170208231*b50 - 224.941373479115*b51
- 574.696478620214*b52 - 453.651669444504*b53 - 396.680178831932*b54
- 355.480538495142*b55 - 455.001425048605*b56 - 410.327875101372*b57
- 107.716832660101*b58 - 127.140023996384*b59 - 331.094295675558*b60
- 182.462253711509*b61 - 460.500595074032*b62 - 320.358519241588*b63
- 267.389834464462*b64 - 154.515161518257*b65 - 322.544727498533*b66
- 33.1863391968753*b67 - 615.771638171722*b68 - 401.573448620245*b69
- 502.776036957456*b70 - 369.539939879878*b71 - 490.231458199826*b72
- 180.326894384108*b73 - 351.782220377873*b74 - 230.814529409496*b75
- 424.244156625063*b76 - 357.224268091235*b77 - 334.18273348498*b78
- 501.721049311591*b79 - 663.739169113737*b80 - 452.23673398428*b81
- 920.634818812952*b82 - 798.472532832495*b83 - 676.77410056404*b84
- 407.527006741593*b85 - 510.493559429826*b86 - 468.587901001095*b87
- 140.053665522904*b88 - 171.808834000698*b89 - 381.118854530951*b90
- 179.901289120497*b91 - 881.284249355185*b92 - 649.077324059404*b93
- 661.262090699325*b94 - 520.002854424345*b95 - 730.978694813241*b96
- 678.238937211925*b97 - 398.969088179479*b98 - 483.529007052756*b99
- 249.519882483891*b100 - 342.614106364254*b101 - 292.077181816541*b102
- 170.281172626711*b103 - 225.734424617283*b104 - 168.147658999551*b105
- 104.518622131715*b106 - 46.8477886786758*b107 - 136.089840994616*b108
- 310.191094*b109 - 117.377523177255*b110 - 76.582257499663*b111
- 439.61435975*b112 - 149.716022877401*b113 - 92.6683043463223*b114
- 350.33553925*b115 - 135.660413957549*b116 - 89.5371309630422*b117
- 261.032076*b118 - 112.326275197259*b119 - 78.152225609751*b120
- 473.56432275*b121 - 158.186763322588*b122 - 96.9684211447128*b123
- 351.54659075*b124 - 129.748325387621*b125 - 83.6038830543306*b126
- 92063.4818812952*x127 - 92063.4818812952*x128 - 92063.4818812952*x129
- 92063.4818812952*x130 - 92063.4818812952*x131 - 92063.4818812952*x132
+ objvar =E= 0;
e2.. 0.669744132*b1 + 0.711284112*b7 + 0.798385084*b13 + 1.430176337*b19
+ 0.706194095*b25 + 0.501285943*b31 + 1.04003433*b37 + 1.252787639*b43
+ 1.278441868*b49 + 0.80906674*b55 + 1.021192966*b61 + 1.20737712*b67
+ 0.657698048*b73 + 1.314509471*b79 + 0.849949545*b85 + 1.327992452*b91
+ 1.118160701*b97 + 0.605008155*b103 - 2.10079896525*x133
- 4.2015979305*x134 - 6.30239689575*x135 =E= 0;
e3.. 0.669744132*b2 + 0.711284112*b8 + 0.798385084*b14 + 1.430176337*b20
+ 0.706194095*b26 + 0.501285943*b32 + 1.04003433*b38 + 1.252787639*b44
+ 1.278441868*b50 + 0.80906674*b56 + 1.021192966*b62 + 1.20737712*b68
+ 0.657698048*b74 + 1.314509471*b80 + 0.849949545*b86 + 1.327992452*b92
+ 1.118160701*b98 + 0.605008155*b104 - 2.1704413425*x136
- 4.340882685*x137 - 6.5113240275*x138 =E= 0;
e4.. 0.669744132*b3 + 0.711284112*b9 + 0.798385084*b15 + 1.430176337*b21
+ 0.706194095*b27 + 0.501285943*b33 + 1.04003433*b39 + 1.252787639*b45
+ 1.278441868*b51 + 0.80906674*b57 + 1.021192966*b63 + 1.20737712*b69
+ 0.657698048*b75 + 1.314509471*b81 + 0.849949545*b87 + 1.327992452*b93
+ 1.118160701*b99 + 0.605008155*b105 - 2.5426093695*x139
- 5.085218739*x140 - 7.6278281085*x141 =E= 0;
e5.. 0.669744132*b4 + 0.711284112*b10 + 0.798385084*b16 + 1.430176337*b22
+ 0.706194095*b28 + 0.501285943*b34 + 1.04003433*b40 + 1.252787639*b46
+ 1.278441868*b52 + 0.80906674*b58 + 1.021192966*b64 + 1.20737712*b70
+ 0.657698048*b76 + 1.314509471*b82 + 0.849949545*b88 + 1.327992452*b94
+ 1.118160701*b100 + 0.605008155*b106 - 2.59983815925*x142
- 5.1996763185*x143 - 7.79951447775*x144 =E= 0;
e6.. 0.669744132*b5 + 0.711284112*b11 + 0.798385084*b17 + 1.430176337*b23
+ 0.706194095*b29 + 0.501285943*b35 + 1.04003433*b41 + 1.252787639*b47
+ 1.278441868*b53 + 0.80906674*b59 + 1.021192966*b65 + 1.20737712*b71
+ 0.657698048*b77 + 1.314509471*b83 + 0.849949545*b89 + 1.327992452*b95
+ 1.118160701*b101 + 0.605008155*b107 - 2.20617095775*x145
- 4.4123419155*x146 - 6.61851287325*x147 =E= 0;
e7.. 0.669744132*b6 + 0.711284112*b12 + 0.798385084*b18 + 1.430176337*b24
+ 0.706194095*b30 + 0.501285943*b36 + 1.04003433*b42 + 1.252787639*b48
+ 1.278441868*b54 + 0.80906674*b60 + 1.021192966*b66 + 1.20737712*b72
+ 0.657698048*b78 + 1.314509471*b84 + 0.849949545*b90 + 1.327992452*b96
+ 1.118160701*b102 + 0.605008155*b108 - 2.20916166375*x148
- 4.4183233275*x149 - 6.62748499125*x150 =E= 0;
e8.. b1 + b2 + b3 + b4 + b5 + b6 =E= 1;
e9.. b7 + b8 + b9 + b10 + b11 + b12 =E= 1;
e10.. b13 + b14 + b15 + b16 + b17 + b18 =E= 1;
e11.. b19 + b20 + b21 + b22 + b23 + b24 =E= 1;
e12.. b25 + b26 + b27 + b28 + b29 + b30 =E= 1;
e13.. b31 + b32 + b33 + b34 + b35 + b36 =E= 1;
e14.. b37 + b38 + b39 + b40 + b41 + b42 =E= 1;
e15.. b43 + b44 + b45 + b46 + b47 + b48 =E= 1;
e16.. b49 + b50 + b51 + b52 + b53 + b54 =E= 1;
e17.. b55 + b56 + b57 + b58 + b59 + b60 =E= 1;
e18.. b61 + b62 + b63 + b64 + b65 + b66 =E= 1;
e19.. b67 + b68 + b69 + b70 + b71 + b72 =E= 1;
e20.. b73 + b74 + b75 + b76 + b77 + b78 =E= 1;
e21.. b79 + b80 + b81 + b82 + b83 + b84 =E= 1;
e22.. b85 + b86 + b87 + b88 + b89 + b90 =E= 1;
e23.. b91 + b92 + b93 + b94 + b95 + b96 =E= 1;
e24.. b97 + b98 + b99 + b100 + b101 + b102 =E= 1;
e25.. b103 + b104 + b105 + b106 + b107 + b108 =E= 1;
e26.. b109 + b110 + b111 =L= 1;
e27.. b112 + b113 + b114 =L= 1;
e28.. b115 + b116 + b117 =L= 1;
e29.. b118 + b119 + b120 =L= 1;
e30.. b121 + b122 + b123 =L= 1;
e31.. b124 + b125 + b126 =L= 1;
e32.. - b109 + x133 =L= 0;
e33.. - b110 + x134 =L= 0;
e34.. - b111 + x135 =L= 0;
e35.. - b112 + x136 =L= 0;
e36.. - b113 + x137 =L= 0;
e37.. - b114 + x138 =L= 0;
e38.. - b115 + x139 =L= 0;
e39.. - b116 + x140 =L= 0;
e40.. - b117 + x141 =L= 0;
e41.. - b118 + x142 =L= 0;
e42.. - b119 + x143 =L= 0;
e43.. - b120 + x144 =L= 0;
e44.. - b121 + x145 =L= 0;
e45.. - b122 + x146 =L= 0;
e46.. - b123 + x147 =L= 0;
e47.. - b124 + x148 =L= 0;
e48.. - b125 + x149 =L= 0;
e49.. - b126 + x150 =L= 0;
e50.. -x127/(1 + x127) + x133 =L= 0;
e51.. -x127/(1 + x127) + x134 =L= 0;
e52.. -x127/(1 + x127) + x135 =L= 0;
e53.. -x128/(1 + x128) + x136 =L= 0;
e54.. -x128/(1 + x128) + x137 =L= 0;
e55.. -x128/(1 + x128) + x138 =L= 0;
e56.. -x129/(1 + x129) + x139 =L= 0;
e57.. -x129/(1 + x129) + x140 =L= 0;
e58.. -x129/(1 + x129) + x141 =L= 0;
e59.. -x130/(1 + x130) + x142 =L= 0;
e60.. -x130/(1 + x130) + x143 =L= 0;
e61.. -x130/(1 + x130) + x144 =L= 0;
e62.. -x131/(1 + x131) + x145 =L= 0;
e63.. -x131/(1 + x131) + x146 =L= 0;
e64.. -x131/(1 + x131) + x147 =L= 0;
e65.. -x132/(1 + x132) + x148 =L= 0;
e66.. -x132/(1 + x132) + x149 =L= 0;
e67.. -x132/(1 + x132) + x150 =L= 0;
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