LPSOLVE package

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Optimization with LPSOLVE (lpsolve)

Routines for the LPSOLVE library.

Optimization with LPSOLVE

LPSOLVE package (ported by Peter Notebaert), and ilpsolve() routine. The full documentation is available on

http://lpsolve.sourceforge.net/5.5/Euler.htm

load with "load lpsolve"

The package is also used by ilpsolve() in the simplex package.

Documentation for ilpsolve()

function lpsolve (f, a, b, e, vlb = [], vub = [], ..
    xint = [], scalemode = 0, keep = 0)

  Solves mixed integer linear programming problems.
  
  SYNOPSIS: {obj, x, duals, stat} = lpsolve(f,a,b,e,vlb,vub,xint,scalemode,keep)
  
  solves the MILP problem
  
  max v = f'*x
  a*x <> b
  vlb <= x <= vub
  x(int) are integer
  
  ARGUMENTS: The first four arguments are required:
  
  f: n vector of coefficients for a linear objective function.
  a: m by n matrix representing linear constraints.
  b: m vector of right sides for the inequality constraints.
  e: m vector that determines the sense of the inequalities:
  e(i) = -1  ==> Less Than
  e(i) =  0  ==> Equals
  e(i) =  1  ==> Greater Than
  vlb: n vector of lower bounds. If empty or omitted,
  then the lower bounds are set to zero.
  vub: n vector of upper bounds. May be omitted or empty.
  xint: vector of integer variables. May be omitted or empty.
  scalemode: scale flag. Off when 0 or omitted.
  keep: Flag for keeping the lp problem after it's been solved.
  If omitted, the lp will be deleted when solved.
  
  OUTPUT: A nonempty output is returned if a solution is found:
  
  x: Optimal value of the decision variables.
  obj: Optimal value of the objective function.
  duals: solution of the dual problem.
  
  >A=random(50,5)+1; b=ones(50,1)*1000; // random problem
  >c=ones(1,5);
  >load lpsolve;
  >lpsolve(c,A,b,-1)
  95.1407198075
  80.6576473906
  222.637610333
  171.292331463
  0

function lpmaker (f, a, b, e, vlb = [], vub = [], xint = [], ..
    scalemode = 0, setminim = 0)

  Makes mixed integer linear programming problems.
  
  SYNOPSIS: lp_handle = lpmaker(f,a,b,e,vlb,vub,xint,scalemode,setminim)
  make the MILP problem
  max v = f'*x
  a*x <> b
  vlb <= x <= vub
  x(int) are integer
  
  ARGUMENTS: The first four arguments are required:
  f: n vector of coefficients for a linear objective function.
  a: m by n matrix representing linear constraints.
  b: m vector of right sides for the inequality constraints.
  e: m vector that determines the sense of the inequalities:
  e(i) < 0  ==> Less Than
  e(i) = 0  ==> Equals
  e(i) > 0  ==> Greater Than
  vlb: n vector of non-negative lower bounds. If empty or omitted,
  then the lower bounds are set to zero.
  vub: n vector of upper bounds. May be omitted or empty.
  xint: vector of integer variables. May be omitted or empty.
  scalemode: Autoscale flag. Off when 0 or omitted.
  setminim: Set maximum lp when this flag equals 0 or omitted.
  
  OUTPUT: lp_handle is an integer handle to the lp created.

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