Custom searchfield autocomplete

I have tried to fire an autocomplete on a customized search field but to no avail. I have used some codes from help sites but I really do not know what I am doing wrong. Nothing happens when I type a letter on to the search field. it is supposed to autocomplete with results from database table. This is my function defined in the functions.php

function department_action_callback(){

$mydb = new wpdb('XXXXX','XXXXX','XXXXX','localhost');

$facility_name=$_GET['facility_name'];

$facilities=$mydb->get_results("SELECT facility_name from facility where facility_name like '%".$facility_name."'");

$data = "";

        echo '<ul>';

        foreach($facilities as $dis)

        {

          echo '<li>'.$dis->facility_name.'</li>';

        }

        echo '</ul>'  ;  

        die();

}

add_action('wp_ajax_department_action','department_action_callback' );

add_action('wp_ajax_nopriv_department_action','department_action_callback' );

This is the custom template file where I have defined the JQUery

jQuery(document).ready(function($) { jQuery('#facility_name').keyup(function() { cid=jQuery(this).attr('val'); var ajaxurl=""; var data ={ action: "department_action", facility_name:facility_id }; $.post(ajaxurl, data, function (response){ $('#key').html(response); }); }); });

<div id="content" class="site-content" role="main">


    <?php while ( have_posts() ) : the_post(); ?>


        <?php get_template_part( 'content', 'page' ); ?>

// search field defined here

        <?php if ( comments_open() || '0' != get_comments_number() ) : ?>


        <?php endif; ?>


    <?php endwhile; // end of the loop. ?>


</div><!-- #content .site-content -->