Simplex MethoDe

[yefim rozenkrants]

Dear Sebastien.

Sorry for bothering you, but I couldn't find in documentation how correctly set the data for LP problem.

According to example in the documentation I assumed that for problem like following

 minimize c1*x1 + c2*x2 +c3*x3

 subject to

 b1r <= a11*x1 +a12*x2 + a13*x3 <= b1l

 a21*x1 +a22*x2 + a23*x3 <= b2l

 r1<=x1 , x2<=r2

the data should look like this:

c=[c1, c2, c3]

A=[[-1, 0, 0], [0, -1, 0], [0, 0, -1],

[a11, a12, a13], [-a11, -a12, -a13],

[-a21, -a22, -a23],

[1, 0, 0], [0, -1, 0]]

b=[0, 0, 0, b1r, -b1l, b2l, r1, -r2]

Please correct me if I'm wrong.

I'll appreciate your help

Yefim 

[Sébastien Loisel]

Hi,

Your matrices look weird. This looks better to me:

c=[c1, c2, c3]

A=[[a11, a12, a13], 

   [-a11, -a12, -a13],

   [a21, a22, a23],

   [-1, 0, 0], 

   [0, 1, 0]]

b=[b1l, -b1r, b2l, -r1, r2]

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Sébastien Loisel

Assistant Professor

Department of Mathematics, Heriot-Watt University

Riccarton, EH14 4AS, United Kingdom
web: http://www.ma.hw.ac.uk/~loisel/
email: S.Loisel at hw.ac.uk
phone: +44 131 451 3234
fax: +44 131 451 3249

[yefim rozenkrants]

-------------------------------------

Sebasien, thanks for your respond. But I still have problems.

It looks like that I’m missing something, because I got weird results. I've create data according your suggestion and got the solution where some variables have negative values.

Could you please point me in the right direction.

                Here the example:

Minimize:
 0.0269*c1 + 0.00001*c2 + 0.00001*c3 + 0.00001*c4 + 0.00001*c5 + 0.00001*c6 + 0.264*c7 + 0.0774*c8 + 0.0267*c9 + 0.053*c10 + 0.0006*c11

    subject to

 6.54*x1 + 0.01*x2 + 0.01*x3 + 1.76*x4 + 3.16*x5 + 1.82*x6 + 3.62*x7 + 2.39*x8 + 0.98*x9 + 0.56*x10 + 7.17*x11 <= 1600
 -0.1523*x1 - 0.0012*x2 - 0*x3 - 0.2563*x4 - 0.1802*x5 - 0.035*x6 - 0.078*x7 - 0.167*x8 - 0.1112*x9 - 0.041*x10 - 0.0085*x11 >= 40
 0.1523*x1 + 0.0012*x2 + 0*x3 + 0.2563*x4 + 0.1802*x5 + 0.035*x6 + 0.078*x7 + 0.167*x8 + 0.1112*x9 + 0.041*x10 + 0.0085*x11 <= 140
 -0.6521*x1 - 0.0002*x2 - 0*x3 - 0.0819*x4 - 0.2241*x5 - 0.049*x6 - 0.018*x7 - 0.14*x8 - 0.043*x9 - 0.02*x10 - 0.8111*x11 >= 35.56
 0.6521*x1 + 0.0002*x2 + 0*x3 + 0.0819*x4 + 0.2241*x5 + 0.049*x6 + 0.01*x7 + 0.14*x8 + 0.043*x9 + 0.02*x10 + 0.8111*x11 <= 65.78
 -0.1371*x1 + 0*x2 - 0.003*x3 - 0*x4 - 0.1057*x5 - 0.3075*x6 - 0.85*x7 - 0.116*x8 - 0.0338*x9 - 0.053*x10 - 0.0006*x11 >= 180
 0.1371*x1 + 0*x2 + 0.003*x3 + 0*x4 + 0.1057*x5 + 0.3075*x6 + 0.85*x7 + 0.116*x8 + 0.0338*x9 + 0.053*x10 + 0.0006*x11 <= 260
 0.06126*x1 + 0.00002*x2 + 0.00002*x3 + 0.03244*x4 + 0.04915*x5 + 0.00763*x6 + 0.004*x7 + 0.0879*x8 + 0.01718*x9 + 0.01242*x10 + 0.50489*x11 <= 12.44

The data and solution
=============================================================================================
c: [ 0.0269, 0.00001, 0.00001, 0.00001, 0.00001, 0.00001, 0.264, 0.0774, 0.0267, 0.053, 0.0006 ]

A: [
[ 6.54, 0.01, 0.01, 1.76, 3.16, 1.82, 3.62, 2.39, 0.98, 0.56, 7.17 ],
[ -0.1523, -0.0012, 0, -0.2563, -0.1802, -0.035, -0.078, -0.167, -0.1112, -0.041, -0.0085 ],
[ 0.1523, 0.0012, 0, 0.2563, 0.1802, 0.035, 0.078, 0.167, 0.1112, 0.041, 0.0085 ],
[ -0.6521, -0.0002, 0, -0.0819, -0.2241, -0.049, -0.018, -0.14, -0.043, -0.02, -0.8111 ],
[ 0.6521, 0.0002, 0, 0.0819, 0.2241, 0.049, 0.01, 0.14, 0.043, 0.02, 0.8111 ],
[ -0.1371, 0, -0.003, 0, -0.1057, -0.3075, -0.85, -0.116, -0.0338, -0.053, -0.0006 ],
[ 0.1371, 0, 0.003, 0, 0.1057, 0.3075, 0.85, 0.116, 0.0338, 0.053, 0.0006 ],
[ 0.06126, 0.00002, 0.00002, 0.03244, 0.04915, 0.00763, 0.004, 0.0879, 0.01718, 0.01242, 0.50489 ]
]

b: [ 1600, -40, 148, -35.56, 65.78, -180, 260, 12.44]
----------------------------------------------
 
SOLUTION x (iterations = 21 ):

x0: 4468.396450071527
x1: 6001.613696047467
x2: 3074.6191257127675
x3: 8927.839670335821
x4: 83444.57804672404
x5: 16198.26554441951
x6: -3777.4999999975894
x7: -58046.32498587716
x8: -60105.89789008526
x9: -42614.80254297848
x10: -14144.971656543916

Yefim

[Sébastien Loisel]

Hi,

Your inequalities have to be of the form Ax<b. That's the same mistake you made the first time around.

On Sat, Oct 11, 2014 at 11:24 PM, yefim rozenkrants <yefim.ro...@gmail.com> wrote:

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