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Instance supplychainr1_020306

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
437551.18300000 p1 ( gdx sol )
(infeas: 5e-13)
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 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
*        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: 2022-04-26 Git hash: de668763
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