How to sort a multidimensional array of columns by a specific column in PHP?

Ugly - would be a lot easier if you formatted the input tables.

$arr = array(
  'Employee_ID' => array('1002', '4508', '0002', '1112'),
  'Business_Unit' => array('UER', 'ABC', 'XYZ', 'EER'),
  'LastName' => array('Smith', 'Vicente', 'Simpson', 'Thompson')
);
$employees = array();
foreach (range(0, sizeof($arr[current(array_keys($arr))]) - 1) as $k) {
  $emp = array();
  foreach ($arr as $col => $vals) {
    $emp[$col] = $arr[$col][$k];
  }
  $employees[] = $emp;
}
$sort = array();
foreach ($employees as $k => $v) {
  $sort[$k] = $v['Employee_ID'];
}
array_multisort($sort, SORT_ASC, $employees);
print_r($employees);

And to put back in the original format:

$arr_sorted = array();
foreach (array_keys($arr) as $col) {
  $arr_sorted[$col] = array();
  foreach ($employees as $emp) {
    $arr_sorted[$col][] = $emp[$col];
  }
}
print_r($arr_sorted);

Thank you for posting the extra details in your question, as they did help in understanding the intent of your question.
Now, you didn't tell us how that table should look; If you want the employees one per row, or one per column. Which is kind of crucial to know. Normally one would have one employee per line, especially if this is to be exported to CVS. However, I have a suspicion that it's the latter you want. Otherwise you've gone about this in a very overly complicated manner.

Point in case: Normal one-per-row layout:

<?php
$db = new PDO();

// Defining the fields we need here, to avoid having too long a string for the query.
$fields = "e.employee_id, e.first_name, e.lastname, u.business_unit, s.email";

// Do the sorting in the database itself. Not only is this faster, but it
// is also a lot easier to sort it exactly as you'd like.
// Note that I don't use prepared statements here, as there is no user-input.
$query = <<<outSQL
SELECT {$Fields} FROM `unit` AS u
INNER JOIN `employee` AS e ON e.employee_id = u.unit_id
INNER JOIN `employee` AS s ON s.employee_id = u.supervisor_id
ORDER BY e.`employee_id`
outSQL;

$data = $db->query($query);

// Creating a printf() template for the output, to make the code easier to maintain.
$rowTemplate = <<<outHTML
        <tr>
            <td>%1\$d</td>
            <td>%2\$s</td>
            <td>%3\$s</td>
        </tr>

outHTML;

// Generate the table template, using placeholders for where the data will be added..
$tableTemplate = <<<outHTML
<table>
    <thead>
        <tr>
            <th>ID</th>
            <th>First name</th>
            <th>Last name</th>
        </tr>
    </thead>
    <tbody>
%s
    </tbody>
</table>
outHTML;

// Regular table output, one employee per line.
$temp = '';
foreach ($data as $e) {
    // hs() is a shortcut function to htmlspecialchars (), to prevent against XSS.
    $temp .= sprintf($rowTemplate, $e['employee_id'], hs($e['first_name']), hs($e['lastname']));
}

// Add the rows to the table, so that you can echo the completed product wherever you need.
$employeeTable = sprintf($tableTemplate, $temp);

If you want to do it one per column, it becomes a bit more intricate. Though, still a bit easier than your first attempt. :)
Namely, something like this:

<?php
$db = new PDO();

// Defining the fields we need here, to avoid having too long a string for the query.
$fields = "employee_id, first_name, lastname";

// Do the sorting in the database itself. Not only is this faster, but it
// is also a lot easier to sort it exactly as you'd like.
// Note that I don't use prepared statements here, as there is no user-input.
$data = $db->query("SELECT {$Fields} FROM `employees` ORDER BY `employee_id`");

// We need to know how many columns we'll have. One per employee.
$columns = count ($data);

// Rows have a header in front of each line, and one td tag for each employee.
$rowTemplate = "\t\t<th>%s</th>\n".str_repeat("\t\t\t<td>%s</td>\n", $columns);

// Generate the table template, using placeholders for where the data will be added..
$tableTemplate = <<<outHTML
<table>
    <tbody>
%s
    </tbody>
</table>
outHTML;

// Reformat the array to give us the data per-column.
$temp = array ();
foreach ($data as $field => $e) {
    // Since we've already sorted the data in the database we don't need to do any further sorting here.
    // Also note that I'm doing the escaping here, seeing as this array will only be used for output.
    $temp['Employee ID'][] = intval($e['employee_id']);
    $temp['First name'][] = hs($e['first_name']);
    $temp['Last name'][] = hs($e['lastname']);
}

// Now we do the same as in the above example.
$rows = '';
foreach ($temp as $label => $l) {
    // We have the label as the first template variable to be added, so put it as the first element.
    array_unshift($l, $label);

    // Add the current row of items to the output, using the previously established template.
    $rows = vprintf($rowTemplate, $l);
}

// Add the rows to the table, so that you can echo the completed product wherever you need.
$employeeTable = sprintf($tableTemplate, $temp);

PS: Haven't tested the code, but it should work.

I ran into his problem and after much angst found a really nice solution in the notes on the php manual page - I now have the following function which i use whenever I need to solve this type of problem.

function fnArrayOrderby(){
//function to sort a database type array of rows by the values in one or more column
//source http://php.net/manual/en/function.array-multisort.php - user notes
//example of use -> $sorted = fnArrayOrderby($data, 'volume', SORT_DESC, 'edition', SORT_ASC);

$args = func_get_args(); //Gets an array of the function's argument list (which can vary in length)
//echo "sorting  ".$args[0]."<br>";
if (!isset($args[0])) { return;}
$data = array_shift($args); //Shift an element off the beginning of array
foreach ($args as $n => $field) {
if (is_string($field)) {
$tmp = array();
foreach ($data as $key => $row)
$tmp[$key] = $row[$field];
$args[$n] = $tmp;
}
}
$args[] = &$data;
call_user_func_array('array_multisort', $args);
return array_pop($args);
}