# Copyright J.S. Roy ([email protected]), 2003-2005
# Copyright Stuart A. Mitchell ([email protected])
# See the LICENSE file for copyright information.

PuLP is an LP modeler written in python. PuLP can generate MPS or LP files
and call GLPK[1], COIN CLP/CBC[2], CPLEX[3], and GUROBI[4] to solve linear
problems.

See the examples directory for examples.

PuLP requires Python >= 2.5.

The examples require at least a solver in your PATH or a shared library file.

Documentation is found on https://www.coin-or.org/PuLP/.
A comprehensive wiki can be found at https://www.coin-or.org/PuLP/

Use LpVariable() to create new variables. To create a variable 0 <= x <= 3
>>> x = LpVariable("x", 0, 3)

To create a variable 0 <= y <= 1
>>> y = LpVariable("y", 0, 1)

Use LpProblem() to create new problems. Create "myProblem"
>>> prob = LpProblem("myProblem", LpMinimize)

Combine variables to create expressions and constraints and add them to the
problem. 
>>> prob += x + y <= 2

If you add an expression (not a constraint), it will
become the objective.
>>> prob += -4*x + y

Choose a solver and solve the problem. ex:
>>> status = prob.solve(GLPK(msg = 0))

Display the status of the solution
>>> LpStatus[status]
'Optimal'

You can get the value of the variables using value(). ex:
>>> value(x)
2.0

Exported Classes:
    - LpProblem -- Container class for a Linear programming problem
    - LpVariable -- Variables that are added to constraints in the LP
    - LpConstraint -- A constraint of the general form 
      a1x1+a2x2 ...anxn (<=, =, >=) b 
    - LpConstraintVar -- Used to construct a column of the model in column-wise 
      modelling

Exported Functions:
    - value() -- Finds the value of a variable or expression
    - lpSum() -- given a list of the form [a1*x1, a2x2, ..., anxn] will construct 
      a linear expression to be used as a constraint or variable
    - lpDot() --given two lists of the form [a1, a2, ..., an] and 
      [ x1, x2, ..., xn] will construct a linear epression to be used 
      as a constraint or variable

Comments, bug reports, patches and suggestions are welcome.
[email protected]

References:
[1] http://www.gnu.org/software/glpk/glpk.html
[2] http://www.coin-or.org/
[3] http://www.cplex.com/
[4] http://www.gurobi.com/