Simplex

A python package that solve linear programming problems using the simplex method.
Features:

• The Problem is input into the program by a file containing python expression.
  
• Solves both min and max problems(duh!).
  
• Uses the big M method to find a basic feasible solution when there are none available in the original program.
  
• Handles adding slack variables to convert the problem into standard form.
  
• Uses the lexicographic rule to prevent ending up in a loop due to degenerate extreme points.
  
• outputs in html.
  

Run Help to get a list of available commandline options.

./test.py --help                                                                                                                                                                             [INSERT] 32mS 0↵ L3
usage: test.py [-h] [--equs EQUS] [--csv CSV] [--delim DELIM] [--slack SLACK] [--aux AUX] [--iter ITER] [--min] [--verbose] [--debug] [--out] [--numba]

options:
  -h, --help            show this help message and exit
  --equs EQUS, -e EQUS  the path to the file containing the equations
  --csv CSV, -c CSV     the path to the CSV file containing the problem
  --delim DELIM, -l DELIM
                        the separator for the csv file
  --slack SLACK, -s SLACK
                        slack variable base name, names are cretedby adding a number to the string
  --aux AUX, -a AUX     aux variable base name, names are cretedby adding a number to the string
  --iter ITER, -i ITER  maximum number of iterations
  --min, -m             determines whether its a minimization problem.if not, its a maximization problem
  --verbose, -v         whether to print output verbosely
  --debug, -d           whether to print debug info
  --out, -o             path to the output file
  --numba, -n           whether to print debug info]q

Example usage:

dsimplex -e ./tests/equ6.py -a xa -v -s z -m

The Equation File

dsimplex currently accepts two input formats:

Python Expressions

Each equation in the equations file should a valid python expression. There are a couple notes though:

• For conditions that end in equality you must use == instead of = to make it a legal python expression.
• Nothing will be evaluated so writing something like 4/5*x1 is illegal. Use .8*x1 instead.
• You can use comments inside the equations file. They are the same format as the python comments.
• The cost equation is one without a binary comparison operator, e.g. <=,<,>=,>.
• The order of the equations in the equations file is not important. You can put them in in any order you want. As an example:
  

# cyclic test
-0.75 * x4 + 20 * x5 - 0.5 * x6 + 6 * x7
x1 + 0.25 * x4 - 8 * x5 - x6 + 9 * x7 == 0
x2 + 0.5 * x4 - 12 * x5 - 0.5 * x6 + 3 * x7 == 0
x3 + x6 == 1
x1 >= 0
x2 >= 0
x3 >= 0
x4 >= 0
x5 >= 0
x6 >= 0
x7 >= 0

CSV

• The order of the equations is not important. It is also not important where the cost function is in the csv file as long as it is there.
• The variables with zero coefficients should be left empty.

x1,x2,x3,x4,x5,x6,x7,cond,rhs
,,,-0.75,20,-0.5,6,,
1,,,0.25,-8,-1,9,=,0
,1,,0.5,-12,-0.5,3,=,0
,,1,,,1,,=,1
1,,,,,,,>=,0
,1,,,,,,>=,0
,,1,,,,,>=,0
,,,1,,,,>=,0
,,,,1,,,>=,0
,,,,,1,,>=,0
,,,,,,1,>=,0

x1,x2,x3,x4,x5,x6,x7,cond,rhs
,,,-0.75,20,-0.5,6,,
1,,,0.25,-8,-1,9,=,0
,1,,0.5,-12,-0.5,3,=,0
,,1,,,1,,=,1
1,,,,,,,>=,0
,1,,,,,,>=,0
,,1,,,,,>=,0
,,,1,,,,>=,0
,,,,1,,,>=,0
,,,,,1,,>=,0
,,,,,,1,>=,0
null,,,,,,,,
,,,-0.75,20,-0.5,6,,
1,,,0.25,-8,-1,9,=,0
,1,,0.5,-12,-0.5,3,=,0
,,1,,,1,,=,1
1,,,,,,,>=,0
,1,,,,,,>=,0
,,1,,,,,>=,0
,,,1,,,,>=,0
,,,,1,,,>=,0
,,,,,1,,>=,0
,,,,,,1,>=,0
null,,,,,,,,
,,,-0.75,20,-0.5,6,,
1,,,0.25,-8,-1,9,=,0
,1,,0.5,-12,-0.5,3,=,0
,,1,,,1,,=,1
1,,,,,,,>=,0
,1,,,,,,>=,0
,,1,,,,,>=,0
,,,1,,,,>=,0
,,,,1,,,>=,0
,,,,,1,,>=,0
,,,,,,1,>=,0
null,,,,,,,,
,,,-0.75,20,-0.5,6,,
1,,,0.25,-8,-1,9,=,0
,1,,0.5,-12,-0.5,3,=,0
,,1,,,1,,=,1
1,,,,,,,>=,0
,1,,,,,,>=,0
,,1,,,,,>=,0
,,,1,,,,>=,0
,,,,1,,,>=,0
,,,,,1,,>=,0
,,,,,,1,>=,0

x1,x2,x3,condition,rhs
1,1,-4,,
1,1,2,<=,9
1,1,-1,<=,2
-1,1,1,<=,4
1,,,>=,0
,1,,>=,0
,,1,>=,0
x1,x2,cond,rhs
1,-2,,
1,1,>=,2
-1,1,>=,1
,1,<=,3
1,,>=,0
,1,>=,0
x1,x2,x3,x4,x5,x6,x7,cond,rhs
,,,-0.75,20,-0.5,6,,
1,,,0.25,-8,-1,9,=,0
,1,,0.5,-12,-0.5,3,=,0
,,1,,,1,,=,1
1,,,,,,,>=,0
,1,,,,,,>=,0
,,1,,,,,>=,0
,,,1,,,,>=,0
,,,,1,,,>=,0
,,,,,1,,>=,0
,,,,,,1,>=,0

How to Get

You can get it from pypi:

pip3 install dsimplex

Or you can clone this repo and run it like that:

git clone https://github.com/terminaldweller/simplex && cd simplex && poetry install