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Instance: jit1

This just-in-time flowshop problem involves P products and S stages. Each stage contains identical equipment performing the same type of operation on different products. The objective is to minimize the total equipment related cost.
Formats ams gms mod nl osil
Primal Bounds
173983.33000000 p1 ( gdx sol ) (infeas: 0)
Dual Bounds
173983.28980000 (ANTIGONE)
173983.32980000 (BARON)
173983.32280000 (COUENNE)
173983.33000000 (LINDO)
173983.33000000 (SCIP)
References Gutierrez, R A and Sahinidis, N V, A branch-and-bound approach for machine selection in just-in-time manufacturing systems, International Journal of Production Research, 34:3, 1996, 797-818.
Gunasekaran, A, Goyal, S K, Martikainen, T, and Yli-Olli, P, Equipment Selection Problems in just-in-time Manufacturing Systems, Journal of the Operational Research Society, 44, 1993, 345-353.
Source case1 in GAMS Model Library model jit
Application Design of Just-in-Time Flowshops
Added to library 28 Feb 2014
Problem type MINLP
#Variables 25
#Binary Variables 0
#Integer Variables 4
#Nonlinear Variables 12
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature convex
#Nonzeros in Objective 25
#Nonlinear Nonzeros in Objective 12
#Constraints 32
#Linear Constraints 32
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 86
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 12
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 12
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 0.0004232
Sparsity Jacobian
Sparsity Lag. Hessian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         33       13       18        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         26       22        0        4        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        112      100       12        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,objvar;

Integer Variables  i1,i2,i3,i4;

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;


e1.. -(7.5/x5 + 5.625/x6 + 11.25/x7 + 7.5/x8 + 8.57142857142857/x9 + 
     7.14285714285714/x10 + 2.85714285714286/x11 + 5.71428571428571/x12 + 
     8.88888888888889/x13 + 8.88888888888889/x14 + 8.88888888888889/x15 + 
     4.44444444444444/x16) - 5000*i1 - 5500*i2 - 4000*i3 - 6000*i4
      - 6000000*x17 - 9000000*x18 - 6000000*x19 - 9000000*x20 - 8000000*x21
      - 8000000*x22 - 8000000*x23 - 10000000*x24 - 8000000*x25 + objvar =E= 0;

e2..  - 0.000252525252525253*i1 + x5 =E= 0;

e3..  - 0.000508388408744281*i2 + x6 =E= 0;

e4..  - 0.000635162601626016*i3 + x7 =E= 0;

e5..  - 0.000636456211812627*i4 + x8 =E= 0;

e6..  - 0.000861450107681263*i1 + x9 =E= 0;

e7..  - 0.000438212094653812*i2 + x10 =E= 0;

e8..  - 0.000433776749566223*i3 + x11 =E= 0;

e9..  - 0.000289184499710815*i4 + x12 =E= 0;

e10..  - 0.000224466891133558*i1 + x13 =E= 0;

e11..  - 0.00033892560582952*i2 + x14 =E= 0;

e12..  - 0.000224014336917563*i3 + x15 =E= 0;

e13..  - 0.000337381916329285*i4 + x16 =E= 0;

e14..    5000*i1 + 5500*i2 + 4000*i3 + 6000*i4 =L= 6000000;

e15..    60*i1 + 50*i2 + 80*i3 + 40*i4 =L= 3000;

e16..  - x5 + x6 + x17 =G= 0;

e17..  - x6 + x7 + x18 =G= 0;

e18..  - x7 + x8 + x19 =G= 0;

e19..  - x9 + x10 + x20 =G= 0;

e20..  - x10 + x11 + x21 =G= 0;

e21..  - x11 + x12 + x22 =G= 0;

e22..  - x13 + x14 + x23 =G= 0;

e23..  - x14 + x15 + x24 =G= 0;

e24..  - x15 + x16 + x25 =G= 0;

e25..    x5 - x6 + x17 =G= 0;

e26..    x6 - x7 + x18 =G= 0;

e27..    x7 - x8 + x19 =G= 0;

e28..    x9 - x10 + x20 =G= 0;

e29..    x10 - x11 + x21 =G= 0;

e30..    x11 - x12 + x22 =G= 0;

e31..    x13 - x14 + x23 =G= 0;

e32..    x14 - x15 + x24 =G= 0;

e33..    x15 - x16 + x25 =G= 0;

* set non-default bounds
i1.lo = 1;
i2.lo = 1;
i3.lo = 1;
i4.lo = 1;
x5.lo = 0.000252525252525253;
x6.lo = 0.000508388408744281;
x7.lo = 0.000635162601626016;
x8.lo = 0.000636456211812627;
x9.lo = 0.000861450107681263;
x10.lo = 0.000438212094653812;
x11.lo = 0.000433776749566223;
x12.lo = 0.000289184499710815;
x13.lo = 0.000224466891133558;
x14.lo = 0.00033892560582952;
x15.lo = 0.000224014336917563;
x16.lo = 0.000337381916329285;

Model m / all /;

m.limrow=0; m.limcol=0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2018-01-13
Git hash: e280d95a