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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 py
Primal Bounds (infeas ≤ 1e-08)ⓘ	173983.33000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	173983.32980000 (ANTIGONE) 173983.32980000 (BARON) 173983.32280000 (COUENNE) 173983.33000000 (LINDO) 173983.33000000 (SCIP) 173983.32700000 (SHOT)
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
Minimal coefficientⓘ	2.2401e-04
Maximal coefficientⓘ	1.0000e+07
Infeasibility of initial pointⓘ	0.0004232
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$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;
m.tolproj=0.0;
$if gamsversion 242 option intvarup = 0;

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

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