globalpolicy/index.html Secret

## index.html
<!DOCTYPE html>
<html>

<head>
	<title>Simplex solver</title>
	<script src="https://code.jquery.com/jquery-3.4.1.slim.min.js"
		integrity="sha256-pasqAKBDmFT4eHoN2ndd6lN370kFiGUFyTiUHWhU7k8=" crossorigin="anonymous"></script>
	<style>
		input[type=number] {
			width: 80px;
			margin: 5px;
		}

		input[type=button] {
			margin: 5px
		}
	</style>
</head>

<body>
	<script type="text/javascript" src="simplex.js"></script>

	<div>
		<label for="num_vars">Number of decision variables:</label>
		<input type="number" id="num_vars">
	</div>
	<div>
		<label for="num_constraints">Number of constraints:</label>
		<input type="number" id="num_constraints">
	</div>
	<div>
		<input type="button" id="btn_next" value="Next" onclick="onNextClicked()">
	</div>
	<div id="maximize_func_div">

	</div>
	<div id="constraints_div">

	</div>
	<div id="optimize_btn_div">

	</div>
	<div id="result_div">

	</div>
	<script>
		function onNextClicked() {
			var num_constraints = parseInt(Number(document.getElementById("num_constraints").value));
			var num_vars = parseInt(Number(document.getElementById("num_vars").value));

			if (num_constraints < 1 && num_vars < 2) {
				return;
			}

			$("div#maximize_func_div").empty();
			$("div#maximize_func_div").append("Maximize: Z=");

			for (var i = 0; i < num_vars; i++) {
				textboxText = "x" + (i + 1) + ((i == (num_vars - 1)) ? "" : "+");
				textboxId = "x" + (i);
				$("div#maximize_func_div").append("<input type='number' id='" + textboxId + "'>" +
					textboxText);
			}


			$("div#constraints_div").empty();
			$("div#constraints_div").append("Constraints:<br>");

			for (var j = 0; j < num_constraints; j++) {
				for (var i = 0; i < num_vars; i++) {
					textboxText = "x" + (i + 1) + ((i == (num_vars - 1)) ? "" : "+");
					textboxId = "c" + (j) + (i);
					$("div#constraints_div").append("<input type='number' id='" + textboxId + "'>" +
						textboxText);
				}
				$("div#constraints_div").append("<=<input type='number' id='c" + j + (i) + "'>");
				$("div#constraints_div").append("<br>")
			}

			for (var i = 0; i < num_vars; i++) {
				$("div#constraints_div").append("x" + (i + 1) + ((i == num_vars - 1) ? " " : ", "));
			}
			$("div#constraints_div").append(">=0");


			$("div#optimize_btn_div").empty();
			$("div#optimize_btn_div").append(
				"<input type='button' id='btn_optimize' value='Optimize' onclick='onOptimizeClicked()'>");
		}

		function onOptimizeClicked() {
			var num_constraints = parseInt(Number(document.getElementById("num_constraints").value));
			var num_vars = parseInt(Number(document.getElementById("num_vars").value));

			var matrix = [];
			for (var i = 0; i < num_constraints; i++) {
				var row = [];
				row.push(0);
				for (var j = 0; j < num_vars; j++) {
					var c_ij = parseInt(Number(document.getElementById("c" + (i) + (j)).value));
					row.push(c_ij);
				}
				for (var k = 0; k < num_constraints; k++) {
					if (i == k) {
						row.push(1);
					} else {
						row.push(0);
					}
				}
				var c_ij_plus1 = parseInt(Number(document.getElementById("c" + (i) + (j)).value));
				row.push(c_ij_plus1);
				matrix.push(row);
			}
			var z_row = [];
			z_row.push(1);
			for (var i = 0; i < num_vars; i++) {
				var x_i = parseInt(Number(document.getElementById("x" + i).value));
				z_row.push(-x_i);
			}
			for (var i = num_vars; i < matrix[0].length; i++) {
				z_row.push(0);
			}
			matrix.push(z_row);

			var result = solveSimplex(matrix);
			$("div#result_div").empty();
			if (!result['error']) {
				$("div#result_div").append("Optimum solution:<br>");
				var basicvars = result['vars'];
				var optimizedVars = {};
				for (var i = 0; i < basicvars.length; i++) {
					if (basicvars[i].includes("x")) {
						optimizedVars[basicvars[i]] = matrix[i][matrix[0].length - 1];
					}
				}
				var sortedOptimizedVars = {};
				for (var i = 0; i < num_vars; i++) {
					if (!optimizedVars.hasOwnProperty("x" + (i + 1))) {
						sortedOptimizedVars["x" + (i + 1)] = 0;
					} else {
						sortedOptimizedVars["x" + (i + 1)] = optimizedVars["x" + (i + 1)];
					}
				}
				for (var key of Object.keys(sortedOptimizedVars)) {
					$("div#result_div").append(key + " : " + sortedOptimizedVars[key] + "<br>")
				}
				$("div#result_div").append("Z : " + matrix[num_constraints + 1 - 1][matrix[0].length - 1]);
			} else {
				$("div#result_div").append(result['message']);
			}
		}
	</script>
</body>

</html>

## simplex.js
function solveSimplex(matrix) {


	//By s0ft
	//29th May, 2019 - 12:40AM
	//Part of M.Sc. Water Resource Engineering - System Mathematics/Operations Research assignment

	//the simplex table format is based on Hamdy A. Taha's book on Operations Research - Tenth Edition
	//with one difference in that the z-row is kept as the last row of the table

	/*
	HA Taha - Page 106 - Reddy Mikks problem:
	Maximize:
	z = 5x1 + 4x2
	subject to:
	6x1 + 4x2 <= 24
	x1 + 2x2 <= 6
	-x1 + x2 <=1
	x2 <= 2
	Answer for verification: x1=3,x2=1.5,z=21 for maximum

	Matrix formulation:
	matrix=[[0,6,4,1,0,0,0,24],
			[0,1,2,0,1,0,0,6],
			[0,-1,1,0,0,1,0,1],
			[0,0,1,0,0,0,1,2],
			[1,-5,-4,0,0,0,0,0]];
	*/

	numColumns = matrix[0].length;
	numRows = matrix.length;
	basicVarsNum = numRows - 1;

	//populate basic variable strings
	basicVars = [];
	for (var i = 0; i < numRows - 1; i++) {
		basicVars.push('s' + (i + 1));
	}

	//populate column header strings
	columnHeaderVars = [];
	columnHeaderVars.push('z');
	for (var i = 1; i <= numColumns - 2 - (numRows - 1); i++) {
		columnHeaderVars.push('x' + i);
	}
	columnHeaderVars.push(...basicVars);

	//get pivot column index
	pivotColumnIndex = getPivotColumnIndex(matrix);


	while (pivotColumnIndex != null) {


		//populate ratios column
		ratios = getRatios(matrix, numColumns, pivotColumnIndex)

		//get pivot row index
		pivotRowIndex = getPivotRowIndex(ratios);
		if (pivotRowIndex == null) {
			return {
				error: true,
				message: "Problem is unbounded."
			};
		}

		//replace the 'leaving' basic variable with 'entering' variable
		basicVars[pivotRowIndex] = columnHeaderVars[pivotColumnIndex];

		//update pivot row
		pivotElement = matrix[pivotRowIndex][pivotColumnIndex];
		for (var i = 0; i < numColumns; i++) {
			matrix[pivotRowIndex][i] /= pivotElement;
		}

		//update non-pivot rows
		for (var i = 0; i < numRows; i++) {
			oldrow = matrix[i].slice(); //copy by value for intra-row operations in the for-loop below
			for (var j = 0; j < numColumns; j++) {
				if (i != pivotRowIndex) {
					matrix[i][j] = oldrow[j] - oldrow[pivotColumnIndex] * matrix[pivotRowIndex][j];
				}
			}
		}

		//get pivot column index
		pivotColumnIndex = getPivotColumnIndex(matrix);

	}

	return {
		error: false,
		vars: basicVars
	};
}


function getPivotColumnIndex(matrix) {
	//check z-row for most negative element (and thus find pivot column index)
	numRows = matrix.length;
	zrow = matrix[numRows - 1];
	mostNegativeElement = 0
	pivotColumnIndex = null
	for (var i = 0; i < zrow.length; i++) {
		if (zrow[i] < mostNegativeElement) {
			mostNegativeElement = zrow[i];
			pivotColumnIndex = i;
		}
	}
	return pivotColumnIndex;
}

function getRatios(matrix, numColumns, pivotColumnIndex) {
	//calculate ratios
	ratios = [];
	for (var i = 0; i < matrix.length - 1; i++) { //matrix.length-1 because we don't want ratio for z-row(last row)
		row = matrix[i];
		rowSolution = row[numColumns - 1];
		if (row[pivotColumnIndex] == 0) {
			ratios.push(-1); //prevents division by zero and renders it ignorable
		} else {
			ratios.push(rowSolution / row[pivotColumnIndex])
		}
	}
	return ratios;
}

function getPivotRowIndex(ratios) {
	//check ratios column for smallest positive element (and thus find pivot row index)
	smallestPositiveElement = Infinity;
	pivotRowIndex = null;
	for (var i = 0; i < ratios.length; i++) {
		if (ratios[i] > 0) { //check if only positive
			if (ratios[i] < smallestPositiveElement) {
				smallestPositiveElement = ratios[i];
				pivotRowIndex = i;
			}
		}
	}
	return pivotRowIndex;
}
	<!DOCTYPE html>
	<html>

	<head>
	<title>Simplex solver</title>
	<script src="https://code.jquery.com/jquery-3.4.1.slim.min.js"
	integrity="sha256-pasqAKBDmFT4eHoN2ndd6lN370kFiGUFyTiUHWhU7k8=" crossorigin="anonymous"></script>
	<style>
	input[type=number] {
	width: 80px;
	margin: 5px;
	}

	input[type=button] {
	margin: 5px
	}
	</style>
	</head>

	<body>
	<script type="text/javascript" src="simplex.js"></script>

	<div>
	<label for="num_vars">Number of decision variables:</label>
	<input type="number" id="num_vars">
	</div>
	<div>
	<label for="num_constraints">Number of constraints:</label>
	<input type="number" id="num_constraints">
	</div>
	<div>
	<input type="button" id="btn_next" value="Next" onclick="onNextClicked()">
	</div>
	<div id="maximize_func_div">

	</div>
	<div id="constraints_div">

	</div>
	<div id="optimize_btn_div">

	</div>
	<div id="result_div">

	</div>
	<script>
	function onNextClicked() {
	var num_constraints = parseInt(Number(document.getElementById("num_constraints").value));
	var num_vars = parseInt(Number(document.getElementById("num_vars").value));

	if (num_constraints < 1 && num_vars < 2) {
	return;
	}

	$("div#maximize_func_div").empty();
	$("div#maximize_func_div").append("Maximize: Z=");

	for (var i = 0; i < num_vars; i++) {
	textboxText = "x" + (i + 1) + ((i == (num_vars - 1)) ? "" : "+");
	textboxId = "x" + (i);
	$("div#maximize_func_div").append("<input type='number' id='" + textboxId + "'>" +
	textboxText);
	}


	$("div#constraints_div").empty();
	$("div#constraints_div").append("Constraints:<br>");

	for (var j = 0; j < num_constraints; j++) {
	for (var i = 0; i < num_vars; i++) {
	textboxText = "x" + (i + 1) + ((i == (num_vars - 1)) ? "" : "+");
	textboxId = "c" + (j) + (i);
	$("div#constraints_div").append("<input type='number' id='" + textboxId + "'>" +
	textboxText);
	}
	$("div#constraints_div").append("<=<input type='number' id='c" + j + (i) + "'>");
	$("div#constraints_div").append("<br>")
	}

	for (var i = 0; i < num_vars; i++) {
	$("div#constraints_div").append("x" + (i + 1) + ((i == num_vars - 1) ? " " : ", "));
	}
	$("div#constraints_div").append(">=0");


	$("div#optimize_btn_div").empty();
	$("div#optimize_btn_div").append(
	"<input type='button' id='btn_optimize' value='Optimize' onclick='onOptimizeClicked()'>");
	}

	function onOptimizeClicked() {
	var num_constraints = parseInt(Number(document.getElementById("num_constraints").value));
	var num_vars = parseInt(Number(document.getElementById("num_vars").value));

	var matrix = [];
	for (var i = 0; i < num_constraints; i++) {
	var row = [];
	row.push(0);
	for (var j = 0; j < num_vars; j++) {
	var c_ij = parseInt(Number(document.getElementById("c" + (i) + (j)).value));
	row.push(c_ij);
	}
	for (var k = 0; k < num_constraints; k++) {
	if (i == k) {
	row.push(1);
	} else {
	row.push(0);
	}
	}
	var c_ij_plus1 = parseInt(Number(document.getElementById("c" + (i) + (j)).value));
	row.push(c_ij_plus1);
	matrix.push(row);
	}
	var z_row = [];
	z_row.push(1);
	for (var i = 0; i < num_vars; i++) {
	var x_i = parseInt(Number(document.getElementById("x" + i).value));
	z_row.push(-x_i);
	}
	for (var i = num_vars; i < matrix[0].length; i++) {
	z_row.push(0);
	}
	matrix.push(z_row);

	var result = solveSimplex(matrix);
	$("div#result_div").empty();
	if (!result['error']) {
	$("div#result_div").append("Optimum solution:<br>");
	var basicvars = result['vars'];
	var optimizedVars = {};
	for (var i = 0; i < basicvars.length; i++) {
	if (basicvars[i].includes("x")) {
	optimizedVars[basicvars[i]] = matrix[i][matrix[0].length - 1];
	}
	}
	var sortedOptimizedVars = {};
	for (var i = 0; i < num_vars; i++) {
	if (!optimizedVars.hasOwnProperty("x" + (i + 1))) {
	sortedOptimizedVars["x" + (i + 1)] = 0;
	} else {
	sortedOptimizedVars["x" + (i + 1)] = optimizedVars["x" + (i + 1)];
	}
	}
	for (var key of Object.keys(sortedOptimizedVars)) {
	$("div#result_div").append(key + " : " + sortedOptimizedVars[key] + "<br>")
	}
	$("div#result_div").append("Z : " + matrix[num_constraints + 1 - 1][matrix[0].length - 1]);
	} else {
	$("div#result_div").append(result['message']);
	}
	}
	</script>
	</body>

	</html>
	function solveSimplex(matrix) {


	//By s0ft
	//29th May, 2019 - 12:40AM
	//Part of M.Sc. Water Resource Engineering - System Mathematics/Operations Research assignment

	//the simplex table format is based on Hamdy A. Taha's book on Operations Research - Tenth Edition
	//with one difference in that the z-row is kept as the last row of the table

	/*
	HA Taha - Page 106 - Reddy Mikks problem:
	Maximize:
	z = 5x1 + 4x2
	subject to:
	6x1 + 4x2 <= 24
	x1 + 2x2 <= 6
	-x1 + x2 <=1
	x2 <= 2
	Answer for verification: x1=3,x2=1.5,z=21 for maximum

	Matrix formulation:
	matrix=[[0,6,4,1,0,0,0,24],
	[0,1,2,0,1,0,0,6],
	[0,-1,1,0,0,1,0,1],
	[0,0,1,0,0,0,1,2],
	[1,-5,-4,0,0,0,0,0]];
	*/

	numColumns = matrix[0].length;
	numRows = matrix.length;
	basicVarsNum = numRows - 1;

	//populate basic variable strings
	basicVars = [];
	for (var i = 0; i < numRows - 1; i++) {
	basicVars.push('s' + (i + 1));
	}

	//populate column header strings
	columnHeaderVars = [];
	columnHeaderVars.push('z');
	for (var i = 1; i <= numColumns - 2 - (numRows - 1); i++) {
	columnHeaderVars.push('x' + i);
	}
	columnHeaderVars.push(...basicVars);

	//get pivot column index
	pivotColumnIndex = getPivotColumnIndex(matrix);


	while (pivotColumnIndex != null) {


	//populate ratios column
	ratios = getRatios(matrix, numColumns, pivotColumnIndex)

	//get pivot row index
	pivotRowIndex = getPivotRowIndex(ratios);
	if (pivotRowIndex == null) {
	return {
	error: true,
	message: "Problem is unbounded."
	};
	}

	//replace the 'leaving' basic variable with 'entering' variable
	basicVars[pivotRowIndex] = columnHeaderVars[pivotColumnIndex];

	//update pivot row
	pivotElement = matrix[pivotRowIndex][pivotColumnIndex];
	for (var i = 0; i < numColumns; i++) {
	matrix[pivotRowIndex][i] /= pivotElement;
	}

	//update non-pivot rows
	for (var i = 0; i < numRows; i++) {
	oldrow = matrix[i].slice(); //copy by value for intra-row operations in the for-loop below
	for (var j = 0; j < numColumns; j++) {
	if (i != pivotRowIndex) {
	matrix[i][j] = oldrow[j] - oldrow[pivotColumnIndex] * matrix[pivotRowIndex][j];
	}
	}
	}

	//get pivot column index
	pivotColumnIndex = getPivotColumnIndex(matrix);

	}

	return {
	error: false,
	vars: basicVars
	};
	}



	function getPivotColumnIndex(matrix) {
	//check z-row for most negative element (and thus find pivot column index)
	numRows = matrix.length;
	zrow = matrix[numRows - 1];
	mostNegativeElement = 0
	pivotColumnIndex = null
	for (var i = 0; i < zrow.length; i++) {
	if (zrow[i] < mostNegativeElement) {
	mostNegativeElement = zrow[i];
	pivotColumnIndex = i;
	}
	}
	return pivotColumnIndex;
	}

	function getRatios(matrix, numColumns, pivotColumnIndex) {
	//calculate ratios
	ratios = [];
	for (var i = 0; i < matrix.length - 1; i++) { //matrix.length-1 because we don't want ratio for z-row(last row)
	row = matrix[i];
	rowSolution = row[numColumns - 1];
	if (row[pivotColumnIndex] == 0) {
	ratios.push(-1); //prevents division by zero and renders it ignorable
	} else {
	ratios.push(rowSolution / row[pivotColumnIndex])
	}
	}
	return ratios;
	}

	function getPivotRowIndex(ratios) {
	//check ratios column for smallest positive element (and thus find pivot row index)
	smallestPositiveElement = Infinity;
	pivotRowIndex = null;
	for (var i = 0; i < ratios.length; i++) {
	if (ratios[i] > 0) { //check if only positive
	if (ratios[i] < smallestPositiveElement) {
	smallestPositiveElement = ratios[i];
	pivotRowIndex = i;
	}
	}
	}
	return pivotRowIndex;
	}