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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
Primal Bounds (infeas ≤ 1e-08)
400833.10850000 p1 ( gdx sol )
(infeas: 6e-15)
398071.20320000 p2 ( gdx sol )
(infeas: 1e-10)
397992.29510000 p3 ( gdx sol )
(infeas: 3e-12)
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)
341832.55740000 (SCIP)
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
Infeasibility of initial point 1
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
*         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: 2019-07-12 Git hash: 46a7b4f1
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