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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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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 py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 832021.81280000 (ALPHAECP) 832664.36430000 (ANTIGONE) 832795.58340000 (BARON) 831907.90780000 (BONMIN) 212852.50720000 (COUENNE) 817468.65920000 (LINDO) 832795.57840000 (SCIP) 832795.29200000 (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ⓘ | 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 |
| Minimal coefficientⓘ | 5.0739e-01 |
| Maximal coefficientⓘ | 1.0126e+05 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity 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: 2025-08-07 Git hash: e62cedfc