MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance supplychainr1_020306
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 437551.18250000 (ANTIGONE) 437551.18250000 (BARON) 437551.13000000 (COUENNE) 437551.18290000 (LINDO) 437551.18300000 (SCIP) 49310.65491000 (SHOT) |
| Referencesⓘ | Nyberg, Axel, Grossmann, I E, and Westerlund, Tapio, The optimal design of a three-echelon supply chain with inventories under uncertainty, 2012. |
| Sourceⓘ | r1-236.gms from minlp.org model 157 |
| Applicationⓘ | Supply Chain Design with Stochastic Inventory Management |
| Added to libraryⓘ | 25 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 93 |
| #Binary Variablesⓘ | 27 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 9 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | concave |
| #Nonzeros in Objectiveⓘ | 36 |
| #Nonlinear Nonzeros in Objectiveⓘ | 9 |
| #Constraintsⓘ | 114 |
| #Linear Constraintsⓘ | 114 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | sqrt |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 348 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 9 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 9 |
| #Blocks in Hessian of Lagrangianⓘ | 9 |
| 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ⓘ | 1.0000e-08 |
| Maximal coefficientⓘ | 1.5843e+05 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 115 37 6 72 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 94 67 27 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 385 376 9 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,x28,x29,x30,x31,x32,x33,x34,x35,x36
,objvar,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
,x87,x88,x89,x90,x91,x92,x93,x94;
Positive Variables x28,x29,x30,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48
,x49,x50,x51,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65
,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82
,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94;
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;
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,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115;
e1.. -(322.234552934*sqrt(1e-8 + x47) + 302.50169455058*sqrt(1e-8 + x48) +
228.02026850162*sqrt(1e-8 + x49) + 6050.05692401735*sqrt(1e-8 + x31) +
5835.32285968594*sqrt(1e-8 + x32) + 5989.86353513014*sqrt(1e-8 + x33) +
539.712349032506*sqrt(1e-8 + x34) + 16850.0288492985*sqrt(1e-8 + x35) +
8222.60184978362*sqrt(1e-8 + x36)) - 151717.47132*b7 - 158432.66708*b8
- 155503.75356*b9 - 17986.4749305945*b10 - 16608.1293312542*b11
- 12718.9428305151*b12 - 31542.1682444641*b13 - 27684.4467382033*b14
- 21088.788254886*b15 - 32968.2805196111*b16 - 15382.4826683217*b17
- 13024.4125650671*b18 - 32589.6848153206*b19 - 20134.3014301096*b20
- 32223.2266900764*b21 - 17748.5846986448*b22 - 17549.9907064495*b23
- 36772.5625416759*b24 - 31609.4271891265*b25 - 9416.32984942185*b26
- 21045.6190121083*b27 + objvar - 98.8943913335*x38 - 1266.710322673*x39
- 576.31843179225*x40 - 505.9367490175*x41 - 2181.163873483*x42
- 544.0949228475*x43 =E= 0;
e2.. b1 + b4 - b7 =E= 0;
e3.. b2 + b5 - b8 =E= 0;
e4.. b3 + b6 - b9 =E= 0;
e5.. - b7 + b10 =L= 0;
e6.. - b7 + b11 =L= 0;
e7.. - b7 + b12 =L= 0;
e8.. - b7 + b13 =L= 0;
e9.. - b7 + b14 =L= 0;
e10.. - b7 + b15 =L= 0;
e11.. - b8 + b16 =L= 0;
e12.. - b8 + b17 =L= 0;
e13.. - b8 + b18 =L= 0;
e14.. - b8 + b19 =L= 0;
e15.. - b8 + b20 =L= 0;
e16.. - b8 + b21 =L= 0;
e17.. - b9 + b22 =L= 0;
e18.. - b9 + b23 =L= 0;
e19.. - b9 + b24 =L= 0;
e20.. - b9 + b25 =L= 0;
e21.. - b9 + b26 =L= 0;
e22.. - b9 + b27 =L= 0;
e23.. b10 + b16 + b22 =E= 1;
e24.. b11 + b17 + b23 =E= 1;
e25.. b12 + b18 + b24 =E= 1;
e26.. b13 + b19 + b25 =E= 1;
e27.. b14 + b20 + b26 =E= 1;
e28.. b15 + b21 + b27 =E= 1;
e29.. - b10 - 2*b16 - b22 + x31 - x50 - x56 - x62 =G= 0;
e30.. - 2*b11 - 2*b17 - 2*b23 + x32 - x51 - x57 - x63 =G= 0;
e31.. - b12 - b18 - 3*b24 + x33 - x52 - x58 - x64 =G= 0;
e32.. - b13 - b19 - b25 + x34 - x53 - x59 - x65 =G= 0;
e33.. - 3*b14 - 2*b20 - b26 + x35 - x54 - x60 - x66 =G= 0;
e34.. - 2*b15 - 3*b21 - 2*b27 + x36 - x55 - x61 - x67 =G= 0;
e35.. - 123.093836325*b10 - 115.89821235*b11 - 77.3643639*b12
- 134.42704815*b13 - 80.45752485*b14 - 88.174578675*b15 + x38 + x41
+ x44 =E= 0;
e36.. - 123.093836325*b16 - 115.89821235*b17 - 77.3643639*b18
- 134.42704815*b19 - 80.45752485*b20 - 88.174578675*b21 + x39 + x42
+ x45 =E= 0;
e37.. - 123.093836325*b22 - 115.89821235*b23 - 77.3643639*b24
- 134.42704815*b25 - 80.45752485*b26 - 88.174578675*b27 + x40 + x43
+ x46 =E= 0;
e38.. - 619.41556425*b1 + x38 =L= 0;
e39.. - 619.41556425*b2 + x39 =L= 0;
e40.. - 619.41556425*b3 + x40 =L= 0;
e41.. - 619.41556425*b4 + x41 =L= 0;
e42.. - 619.41556425*b5 + x42 =L= 0;
e43.. - 619.41556425*b6 + x43 =L= 0;
e44.. 619.41556425*b7 + x44 =L= 619.41556425;
e45.. 619.41556425*b8 + x45 =L= 619.41556425;
e46.. 619.41556425*b9 + x46 =L= 619.41556425;
e47.. - x28 + x50 + x68 =E= 0;
e48.. - x28 + x51 + x69 =E= 0;
e49.. - x28 + x52 + x70 =E= 0;
e50.. - x28 + x53 + x71 =E= 0;
e51.. - x28 + x54 + x72 =E= 0;
e52.. - x28 + x55 + x73 =E= 0;
e53.. - x29 + x56 + x74 =E= 0;
e54.. - x29 + x57 + x75 =E= 0;
e55.. - x29 + x58 + x76 =E= 0;
e56.. - x29 + x59 + x77 =E= 0;
e57.. - x29 + x60 + x78 =E= 0;
e58.. - x29 + x61 + x79 =E= 0;
e59.. - x30 + x62 + x80 =E= 0;
e60.. - x30 + x63 + x81 =E= 0;
e61.. - x30 + x64 + x82 =E= 0;
e62.. - x30 + x65 + x83 =E= 0;
e63.. - x30 + x66 + x84 =E= 0;
e64.. - x30 + x67 + x85 =E= 0;
e65.. - 10*b10 + x50 =L= 0;
e66.. - 10*b11 + x51 =L= 0;
e67.. - 10*b12 + x52 =L= 0;
e68.. - 10*b13 + x53 =L= 0;
e69.. - 10*b14 + x54 =L= 0;
e70.. - 10*b15 + x55 =L= 0;
e71.. - 12*b16 + x56 =L= 0;
e72.. - 12*b17 + x57 =L= 0;
e73.. - 12*b18 + x58 =L= 0;
e74.. - 12*b19 + x59 =L= 0;
e75.. - 12*b20 + x60 =L= 0;
e76.. - 12*b21 + x61 =L= 0;
e77.. - 11*b22 + x62 =L= 0;
e78.. - 11*b23 + x63 =L= 0;
e79.. - 11*b24 + x64 =L= 0;
e80.. - 11*b25 + x65 =L= 0;
e81.. - 11*b26 + x66 =L= 0;
e82.. - 11*b27 + x67 =L= 0;
e83.. 10*b10 + x68 =L= 10;
e84.. 10*b11 + x69 =L= 10;
e85.. 10*b12 + x70 =L= 10;
e86.. 10*b13 + x71 =L= 10;
e87.. 10*b14 + x72 =L= 10;
e88.. 10*b15 + x73 =L= 10;
e89.. 12*b16 + x74 =L= 12;
e90.. 12*b17 + x75 =L= 12;
e91.. 12*b18 + x76 =L= 12;
e92.. 12*b19 + x77 =L= 12;
e93.. 12*b20 + x78 =L= 12;
e94.. 12*b21 + x79 =L= 12;
e95.. 11*b22 + x80 =L= 11;
e96.. 11*b23 + x81 =L= 11;
e97.. 11*b24 + x82 =L= 11;
e98.. 11*b25 + x83 =L= 11;
e99.. 11*b26 + x84 =L= 11;
e100.. 11*b27 + x85 =L= 11;
e101.. - 690.72410962302*b10 - 1407.02886656603*b11 - 79.3201437228845*b12
- 2.91401731263049*b13 - 855.94622404089*b14 - 964.816732551601*b15
+ x86 + x89 + x92 =E= 0;
e102.. - 690.72410962302*b16 - 1407.02886656603*b17 - 79.3201437228845*b18
- 2.91401731263049*b19 - 855.94622404089*b20 - 964.816732551601*b21
+ x87 + x90 + x93 =E= 0;
e103.. - 690.72410962302*b22 - 1407.02886656603*b23 - 79.3201437228845*b24
- 2.91401731263049*b25 - 855.94622404089*b26 - 964.816732551601*b27
+ x88 + x91 + x94 =E= 0;
e104.. - 4000.75009381706*b1 + x86 =L= 0;
e105.. - 4000.75009381706*b2 + x87 =L= 0;
e106.. - 4000.75009381706*b3 + x88 =L= 0;
e107.. - 4000.75009381706*b4 + x89 =L= 0;
e108.. - 4000.75009381706*b5 + x90 =L= 0;
e109.. - 4000.75009381706*b6 + x91 =L= 0;
e110.. 4000.75009381706*b7 + x92 =L= 4000.75009381706;
e111.. 4000.75009381706*b8 + x93 =L= 4000.75009381706;
e112.. 4000.75009381706*b9 + x94 =L= 4000.75009381706;
e113.. x47 + 690.72410962302*x50 + 1407.02886656603*x51
+ 79.3201437228845*x52 + 2.91401731263049*x53 + 855.94622404089*x54
+ 964.816732551601*x55 - 3*x86 - 10*x89 =E= 0;
e114.. x48 + 690.72410962302*x56 + 1407.02886656603*x57
+ 79.3201437228845*x58 + 2.91401731263049*x59 + 855.94622404089*x60
+ 964.816732551601*x61 - 6*x87 - 12*x90 =E= 0;
e115.. x49 + 690.72410962302*x62 + 1407.02886656603*x63
+ 79.3201437228845*x64 + 2.91401731263049*x65 + 855.94622404089*x66
+ 964.816732551601*x67 - 9*x88 - 11*x91 =E= 0;
* set non-default bounds
x28.up = 10;
x29.up = 12;
x30.up = 11;
x31.lo = 1; x31.up = 14;
x32.lo = 2; x32.up = 14;
x33.lo = 1; x33.up = 14;
x34.lo = 1; x34.up = 13;
x35.lo = 1; x35.up = 14;
x36.lo = 2; x36.up = 15;
x47.up = 40007.5009381706;
x48.up = 48009.0011258047;
x49.up = 44008.2510319877;
x50.up = 10;
x51.up = 10;
x52.up = 10;
x53.up = 10;
x54.up = 10;
x55.up = 10;
x56.up = 12;
x57.up = 12;
x58.up = 12;
x59.up = 12;
x60.up = 12;
x61.up = 12;
x62.up = 11;
x63.up = 11;
x64.up = 11;
x65.up = 11;
x66.up = 11;
x67.up = 11;
x68.up = 10;
x69.up = 10;
x70.up = 10;
x71.up = 10;
x72.up = 10;
x73.up = 10;
x74.up = 12;
x75.up = 12;
x76.up = 12;
x77.up = 12;
x78.up = 12;
x79.up = 12;
x80.up = 11;
x81.up = 11;
x82.up = 11;
x83.up = 11;
x84.up = 11;
x85.up = 11;
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: 2024-08-26 Git hash: 6cc1607f