README

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