Simplex Calculator

About

PHP library for solving linear programming problems using dual simplex algorithm.

NOTE: Basis cycling detection is not implemented.

Installation

The recommended way is to use Composer:

composer require uestla/simplex-calculator

You can also download the latest release as a ZIP file.

Conventions

Please name all your input variables as x<n> where <n> is a natural number (see example below for details).

Usage

Loading library

// using Composer
require_once __DIR__ . '/vendor/autoload.php';

// using manual download
require_once __DIR__ . '/Simplex/simplex.php';

Defining and solving simplex tasks

// define task: Maximize x1 + 2x2
$task = new Simplex\Task(new Simplex\Func(array(
    'x1' => 1,
    'x2' => 2,
)));

// add constraints

// 3x1 + 2x2 <= 24
$task->addRestriction(new Simplex\Restriction(array(
    'x1' => 3,
    'x2' => 2,

), Simplex\Restriction::TYPE_LOE, 24));

// -2x1 - 4x2 >= -32
$task->addRestriction(new Simplex\Restriction(array(
    'x1' => -2,
    'x2' => -4,

), Simplex\Restriction::TYPE_GOE, -32));

// create solver
$solver = new Simplex\Solver($task);

// get solutions
$solution = $solver->getSolution(); // array('x1' => 0, 'x2' => 8, 'x3' => 8, 'x4' => 0)
$alternativeSolutions = $solver->getAlternativeSolution(); // array(array('x1' => 4, 'x2' => 6, 'x3' => 0, 'x4' => 0))

// get optimal value
$optimum = $solver->getSolutionValue($solution); // 16

// print solutions
$printer = new Simplex\Printer;
$printer->printSolution($solver);

// or print the whole solution process
$printer->printSolver($solver);

Solutions

$solver->getSolutions() returns primary optimal solution. The value can be of 3 types:

• array - vector with optimal coefficients to each input variable
• false - optimal solution does not exist
• null - not enough steps to find solution

By default, solver stops the calculation after 16 simplex tables. You can increase the maximum steps limit with the second parameter:

$solver = new Simplex\Solver($task, 32);

$solver->getAlternativeSolutions() returns array of other optimal solutions if any have been found. It may return:

• array - array of vectors with alternative optimal solutions
• null - no alternative optimal solution found