The PHP file that's called as $ajax_url in the star-rating.js file

star-rating.php

<?php
function my_function_name() {
  $postid = $_POST['postid'];
  $rating = $_POST['rating'];

  update_post_meta( $postid, 'delivery_rating', $rating );
  wp_die();
}

add_action( 'wp_ajax_my_function_name', 'my_function_name' );
add_action( 'wp_ajax_nopriv_my_function_name', 'my_function_name' );