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Instance: sssd18-08

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)
839483.81040000 p1 ( gdx sol )
(infeas: 9e-15)
832802.29020000 p2 ( gdx sol )
(infeas: 4e-16)
832795.58520000 p3 ( gdx sol )
(infeas: 2e-12)
Other points (infeas > 1e-08)  
Dual Bounds
832021.81280000 (ALPHAECP)
832227.32060000 (ANTIGONE)
832795.58340000 (BARON)
831907.90780000 (BONMIN)
212852.50720000 (COUENNE)
388859.09720000 (LINDO)
646070.53000000 (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 200
#Binary Variables 168
#Integer Variables 0
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 176
#Nonlinear Nonzeros in Objective 0
#Constraints 82
#Linear Constraints 58
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 24
Operands in Gen. Nonlin. Functions div
Constraints curvature convex
#Nonzeros in Jacobian 432
#Nonlinear Nonzeros in Jacobian 24
#Nonzeros in (Upper-Left) Hessian of Lagrangian 8
#Nonzeros in Diagonal of Hessian of Lagrangian 8
#Blocks in Hessian of Lagrangian 8
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
*         83       27        0       56        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        201       33      168        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        609      585       24        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,b127,b128,b129
          ,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
          ,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
          ,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
          ,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180,x181
          ,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192,x193,x194
          ,x195,x196,x197,x198,x199,x200,objvar;

Positive Variables  x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179
          ,x180,x181,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192
          ,x193,x194,x195,x196,x197,x198,x199,x200;

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,b127
          ,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
          ,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153
          ,b154,b155,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166
          ,b167,b168;

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,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83;


e1..  - 552.281145549261*b1 - 426.236209278853*b2 - 411.027424117795*b3
      - 466.68869062928*b4 - 288.317250921223*b5 - 590.182468227663*b6
      - 381.017859269849*b7 - 572.544284039417*b8 - 433.107424736324*b9
      - 429.289469802582*b10 - 722.101048978265*b11 - 30.0952649131444*b12
      - 408.663734727663*b13 - 327.144961122973*b14 - 408.872583504261*b15
      - 371.229606779419*b16 - 743.231830330272*b17 - 424.123388295749*b18
      - 1012.59483684509*b19 - 325.068016443889*b20 - 489.829200609382*b21
      - 616.392367634356*b22 - 717.376121177217*b23 - 671.497074168691*b24
      - 333.243033401626*b25 - 469.212452608196*b26 - 55.3101521264496*b27
      - 439.078549562248*b28 - 397.954628500691*b29 - 404.754476708584*b30
      - 260.583114103962*b31 - 374.661728741154*b32 - 705.865114334154*b33
      - 409.260796409624*b34 - 941.121512213036*b35 - 352.661317024937*b36
      - 478.410844041197*b37 - 592.864375784787*b38 - 688.804587834202*b39
      - 642.137051102147*b40 - 675.37494220409*b41 - 537.327976828555*b42
      - 326.270384675669*b43 - 667.587791945904*b44 - 430.879246065957*b45
      - 741.317344127774*b46 - 525.377882163679*b47 - 713.734501618144*b48
      - 449.47820772841*b49 - 590.656036300788*b50 - 825.357606588055*b51
      - 234.546168311308*b52 - 591.462084387522*b53 - 311.109367719916*b54
      - 500.934150264854*b55 - 370.791485521561*b56 - 344.058371833736*b57
      - 204.379731785556*b58 - 212.615335031657*b59 - 304.078143674645*b60
      - 160.084737093308*b61 - 363.67946743236*b62 - 273.136822990176*b63
      - 355.563806296337*b64 - 194.046191003143*b65 - 99.0010715125356*b66
      - 250.598725578763*b67 - 67.6669605181366*b68 - 88.2421148072165*b69
      - 169.700774043074*b70 - 163.618413602519*b71 - 179.622443088529*b72
      - 503.06832772418*b73 - 179.201297229611*b74 - 414.285319927326*b75
      - 359.134843842496*b76 - 90.9738416529607*b77 - 505.334430249411*b78
      - 394.341605011239*b79 - 504.182673743417*b80 - 232.742365145843*b81
      - 707.696470886055*b82 - 710.448776297179*b83 - 250.562514769084*b84
      - 650.238440560302*b85 - 77.1170572675807*b86 - 312.633669961727*b87
      - 142.269450675157*b88 - 153.022776132362*b89 - 551.147919857098*b90
      - 287.831002149329*b91 - 336.782937608947*b92 - 463.701548212201*b93
      - 241.611196591671*b94 - 24.1639213931607*b95 - 200.643830319498*b96
      - 376.097990316451*b97 - 154.600594109087*b98 - 278.64599329384*b99
      - 295.429713043008*b100 - 113.945955775425*b101 - 383.962346931602*b102
      - 302.65105541664*b103 - 380.813914126253*b104 - 773.198288152452*b105
      - 265.047476834782*b106 - 632.465317742327*b107 - 586.791111855992*b108
      - 260.082638813274*b109 - 769.354688759475*b110 - 657.006566335408*b111
      - 771.861427768791*b112 - 540.885172741987*b113 - 560.594490776333*b114
      - 890.488880299848*b115 - 259.942482707707*b116 - 580.756336311101*b117
      - 404.516739709834*b118 - 574.739678540771*b119 - 463.535898137432*b120
      - 245.785748722981*b121 - 872.250506358296*b122 - 704.377804059606*b123
      - 481.541576364034*b124 - 814.563195802202*b125 - 217.645632620131*b126
      - 397.523527704031*b127 - 215.278878363054*b128 - 660.689322162664*b129
      - 766.389526160548*b130 - 160.247965176608*b131 - 779.837433303884*b132
      - 633.958305188238*b133 - 773.22857535608*b134 - 502.341772532799*b135
      - 725.863386674913*b136 - 443.26403170523*b137 - 135.166265997905*b138
      - 513.770662349363*b139 - 239.391320299212*b140 - 194.33615146318*b141
      - 395.043386622235*b142 - 407.638910845368*b143 - 416.170540899117*b144
      - 268.22715225*b145 - 101.841745437534*b146 - 66.5583916008528*b147
      - 327.416664*b148 - 113.0930596242*b149 - 70.496630802465*b150
      - 318.91031775*b151 - 106.016440623009*b152 - 64.8321038352068*b153
      - 354.20971275*b154 - 116.787224755912*b155 - 71.1258209679967*b156
      - 409.67052*b157 - 127.189145909207*b158 - 75.1660702970269*b159
      - 440.1576845*b160 - 133.588180245023*b161 - 78.0570051826685*b162
      - 422.36333725*b163 - 136.77241788249*b164 - 82.5503807534421*b165
      - 437.47924675*b166 - 131.974510024443*b167 - 76.8812256404764*b168
      - 101259.483684509*x169 - 101259.483684509*x170 - 101259.483684509*x171
      - 101259.483684509*x172 - 101259.483684509*x173 - 101259.483684509*x174
      - 101259.483684509*x175 - 101259.483684509*x176 + objvar =E= 0;

e2..    1.465020132*b1 + 1.359734944*b9 + 1.421554108*b17 + 0.749119501*b25
      + 1.211666119*b33 + 1.222030951*b41 + 1.224720338*b49 + 0.583392775*b57
      + 0.507387528*b65 + 1.007181208*b73 + 1.448218778*b81 + 1.128698856*b89
      + 0.64088422*b97 + 1.073533103*b105 + 1.242005841*b113 + 1.242671696*b121
      + 1.400550697*b129 + 0.704652931*b137 - 1.8351027624375*x177
      - 3.670205524875*x178 - 5.5053082873125*x179 =E= 0;

e3..    1.465020132*b2 + 1.359734944*b10 + 1.421554108*b18 + 0.749119501*b26
      + 1.211666119*b34 + 1.222030951*b42 + 1.224720338*b50 + 0.583392775*b58
      + 0.507387528*b66 + 1.007181208*b74 + 1.448218778*b82 + 1.128698856*b90
      + 0.64088422*b98 + 1.073533103*b106 + 1.242005841*b114 + 1.242671696*b122
      + 1.400550697*b130 + 0.704652931*b138 - 1.686527528625*x180
      - 3.37305505725*x181 - 5.059582585875*x182 =E= 0;

e4..    1.465020132*b3 + 1.359734944*b11 + 1.421554108*b19 + 0.749119501*b27
      + 1.211666119*b35 + 1.222030951*b43 + 1.224720338*b51 + 0.583392775*b59
      + 0.507387528*b67 + 1.007181208*b75 + 1.448218778*b83 + 1.128698856*b91
      + 0.64088422*b99 + 1.073533103*b107 + 1.242005841*b115 + 1.242671696*b123
      + 1.400550697*b131 + 0.704652931*b139 - 1.464431797125*x183
      - 2.92886359425*x184 - 4.393295391375*x185 =E= 0;

e5..    1.465020132*b4 + 1.359734944*b12 + 1.421554108*b20 + 0.749119501*b28
      + 1.211666119*b36 + 1.222030951*b44 + 1.224720338*b52 + 0.583392775*b60
      + 0.507387528*b68 + 1.007181208*b76 + 1.448218778*b84 + 1.128698856*b92
      + 0.64088422*b100 + 1.073533103*b108 + 1.242005841*b116
      + 1.242671696*b124 + 1.400550697*b132 + 0.704652931*b140
      - 1.5869074876875*x186 - 3.173814975375*x187 - 4.7607224630625*x188 =E= 0
     ;

e6..    1.465020132*b5 + 1.359734944*b13 + 1.421554108*b21 + 0.749119501*b29
      + 1.211666119*b37 + 1.222030951*b45 + 1.224720338*b53 + 0.583392775*b61
      + 0.507387528*b69 + 1.007181208*b77 + 1.448218778*b85 + 1.128698856*b93
      + 0.64088422*b101 + 1.073533103*b109 + 1.242005841*b117
      + 1.242671696*b125 + 1.400550697*b133 + 0.704652931*b141
      - 1.5323799785625*x189 - 3.064759957125*x190 - 4.5971399356875*x191 =E= 0
     ;

e7..    1.465020132*b6 + 1.359734944*b14 + 1.421554108*b22 + 0.749119501*b30
      + 1.211666119*b38 + 1.222030951*b46 + 1.224720338*b54 + 0.583392775*b62
      + 0.507387528*b70 + 1.007181208*b78 + 1.448218778*b86 + 1.128698856*b94
      + 0.64088422*b102 + 1.073533103*b110 + 1.242005841*b118
      + 1.242671696*b126 + 1.400550697*b134 + 0.704652931*b142
      - 1.5380589155625*x192 - 3.076117831125*x193 - 4.6141767466875*x194 =E= 0
     ;

e8..    1.465020132*b7 + 1.359734944*b15 + 1.421554108*b23 + 0.749119501*b31
      + 1.211666119*b39 + 1.222030951*b47 + 1.224720338*b55 + 0.583392775*b63
      + 0.507387528*b71 + 1.007181208*b79 + 1.448218778*b87 + 1.128698856*b95
      + 0.64088422*b103 + 1.073533103*b111 + 1.242005841*b119
      + 1.242671696*b127 + 1.400550697*b135 + 0.704652931*b143
      - 1.792707516*x195 - 3.585415032*x196 - 5.378122548*x197 =E= 0;

e9..    1.465020132*b8 + 1.359734944*b16 + 1.421554108*b24 + 0.749119501*b32
      + 1.211666119*b40 + 1.222030951*b48 + 1.224720338*b56 + 0.583392775*b64
      + 0.507387528*b72 + 1.007181208*b80 + 1.448218778*b88 + 1.128698856*b96
      + 0.64088422*b104 + 1.073533103*b112 + 1.242005841*b120
      + 1.242671696*b128 + 1.400550697*b136 + 0.704652931*b144
      - 1.5012071746875*x198 - 3.002414349375*x199 - 4.5036215240625*x200 =E= 0
     ;

e10..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 =E= 1;

e11..    b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 =E= 1;

e12..    b17 + b18 + b19 + b20 + b21 + b22 + b23 + b24 =E= 1;

e13..    b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 =E= 1;

e14..    b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e15..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 =E= 1;

e16..    b49 + b50 + b51 + b52 + b53 + b54 + b55 + b56 =E= 1;

e17..    b57 + b58 + b59 + b60 + b61 + b62 + b63 + b64 =E= 1;

e18..    b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72 =E= 1;

e19..    b73 + b74 + b75 + b76 + b77 + b78 + b79 + b80 =E= 1;

e20..    b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88 =E= 1;

e21..    b89 + b90 + b91 + b92 + b93 + b94 + b95 + b96 =E= 1;

e22..    b97 + b98 + b99 + b100 + b101 + b102 + b103 + b104 =E= 1;

e23..    b105 + b106 + b107 + b108 + b109 + b110 + b111 + b112 =E= 1;

e24..    b113 + b114 + b115 + b116 + b117 + b118 + b119 + b120 =E= 1;

e25..    b121 + b122 + b123 + b124 + b125 + b126 + b127 + b128 =E= 1;

e26..    b129 + b130 + b131 + b132 + b133 + b134 + b135 + b136 =E= 1;

e27..    b137 + b138 + b139 + b140 + b141 + b142 + b143 + b144 =E= 1;

e28..    b145 + b146 + b147 =L= 1;

e29..    b148 + b149 + b150 =L= 1;

e30..    b151 + b152 + b153 =L= 1;

e31..    b154 + b155 + b156 =L= 1;

e32..    b157 + b158 + b159 =L= 1;

e33..    b160 + b161 + b162 =L= 1;

e34..    b163 + b164 + b165 =L= 1;

e35..    b166 + b167 + b168 =L= 1;

e36..  - b145 + x177 =L= 0;

e37..  - b146 + x178 =L= 0;

e38..  - b147 + x179 =L= 0;

e39..  - b148 + x180 =L= 0;

e40..  - b149 + x181 =L= 0;

e41..  - b150 + x182 =L= 0;

e42..  - b151 + x183 =L= 0;

e43..  - b152 + x184 =L= 0;

e44..  - b153 + x185 =L= 0;

e45..  - b154 + x186 =L= 0;

e46..  - b155 + x187 =L= 0;

e47..  - b156 + x188 =L= 0;

e48..  - b157 + x189 =L= 0;

e49..  - b158 + x190 =L= 0;

e50..  - b159 + x191 =L= 0;

e51..  - b160 + x192 =L= 0;

e52..  - b161 + x193 =L= 0;

e53..  - b162 + x194 =L= 0;

e54..  - b163 + x195 =L= 0;

e55..  - b164 + x196 =L= 0;

e56..  - b165 + x197 =L= 0;

e57..  - b166 + x198 =L= 0;

e58..  - b167 + x199 =L= 0;

e59..  - b168 + x200 =L= 0;

e60.. -x169/(1 + x169) + x177 =L= 0;

e61.. -x169/(1 + x169) + x178 =L= 0;

e62.. -x169/(1 + x169) + x179 =L= 0;

e63.. -x170/(1 + x170) + x180 =L= 0;

e64.. -x170/(1 + x170) + x181 =L= 0;

e65.. -x170/(1 + x170) + x182 =L= 0;

e66.. -x171/(1 + x171) + x183 =L= 0;

e67.. -x171/(1 + x171) + x184 =L= 0;

e68.. -x171/(1 + x171) + x185 =L= 0;

e69.. -x172/(1 + x172) + x186 =L= 0;

e70.. -x172/(1 + x172) + x187 =L= 0;

e71.. -x172/(1 + x172) + x188 =L= 0;

e72.. -x173/(1 + x173) + x189 =L= 0;

e73.. -x173/(1 + x173) + x190 =L= 0;

e74.. -x173/(1 + x173) + x191 =L= 0;

e75.. -x174/(1 + x174) + x192 =L= 0;

e76.. -x174/(1 + x174) + x193 =L= 0;

e77.. -x174/(1 + x174) + x194 =L= 0;

e78.. -x175/(1 + x175) + x195 =L= 0;

e79.. -x175/(1 + x175) + x196 =L= 0;

e80.. -x175/(1 + x175) + x197 =L= 0;

e81.. -x176/(1 + x176) + x198 =L= 0;

e82.. -x176/(1 + x176) + x199 =L= 0;

e83.. -x176/(1 + x176) + x200 =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: 2019-06-04 Git hash: 78444eaa
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