I already finish a shopping cart function, but when I create a INSERT function for check out page, I got error

this is code of customer function page which give $_SESSION values to customer id

Code:
<?php

/*
	Check if a session user id exist or not. If not set redirect
	to login page. If the user session id exist and there's found
	$_GET['logout'] in the query string logout the user
*/
function checkUser()
{
	// if the session id is not set, redirect to login page
	if (!isset($_SESSION['valid_user'])) {
		header('Location: ' . WEB_ROOT . 'customer/login.php');
		exit;
	}
	
	// the user want to logout
	if (isset($_GET['logout'])) {
		doLogout();
	}
}

/*
	
*/
function doLogin()
{
	// if we found an error save the error message in this variable
	$errorMessage = '';
	
	$userName = $_POST['txtUserName'];
	$password = $_POST['txtPassword'];
	$_SESSION['valid_user'] = $userName;
	$_SESSION['valid_password'] = $password;
	
	// first, make sure the username & password are not empty
	if ($userName == '') {
		$errorMessage = 'You must enter your username';
	} else if ($password == '') {
		$errorMessage = 'You must enter the password';
	} else {
		// check the database and see if the username and password combo do match
		$sql = "SELECT *
				FROM tbl_customer
				WHERE customer_name = '$userName'
				AND customer_password =  md5('$password')";
		$result = dbQuery($sql);
	
		if (dbNumRows($result) == 1) {
			$row = dbFetchAssoc($result);
			$_SESSION['valid_user'] = $row['customer_id'];
			$_SESSION['valid_name'] = $row['customer_name'];
			// log the time when the user last login
			$sql = "UPDATE tbl_customer
			        SET customer_last_login = NOW() 
					WHERE customer_id = '{$row['customer_id']}'";
			dbQuery($sql);

			// now that the user is verified we move on to the next page
            // if the user had been in the admin pages before we move to
			// the last page visited
			if (isset($_SESSION['login_return_url'])) {
				header('Location: ' . $_SESSION['login_return_url']);
				exit;
			} else {
				header('Location: index.php');
				exit;
			}
		} else {
			$errorMessage = 'Wrong username or password';
		}		
			
	}
	
	return $errorMessage;
}

/*
	Logout a user
*/
function doLogout()
{
	if (isset($_SESSION['valid_user'])) {
		session_unset($_SESSION['valid_user']);
		session_destroy();
	}
		
	header('Location: login.php');
	exit;
}
?>
đây là code cũa trang checkout_function.php

Code:
<?php
require_once 'config.php';
//using session of logined customer
require_once ('customer/library/functions.php');
$customer_id = $_SESSION['valid_user'];
/*********************************************************
*                 CHECKOUT FUNCTIONS 
*********************************************************/
function saveOrder()
{
	$orderId       = 0;
	$shippingCost  = 5;
	$requiredField = array('hidShippingFirstName', 'hidShippingLastName', 'hidShippingAddress1', 'hidShippingCity', 'hidShippingPostalCode',
						   'hidPaymentFirstName', 'hidPaymentLastName', 'hidPaymentAddress1', 'hidPaymentCity', 'hidPaymentPostalCode');
						   
	if (checkRequiredPost($requiredField)) {
	    extract($_POST);
		
		// make sure the first character in the 
		// customer and city name are properly upper cased
		$hidShippingFirstName = ucwords($hidShippingFirstName);
		$hidShippingLastName  = ucwords($hidShippingLastName);
		$hidPaymentFirstName  = ucwords($hidPaymentFirstName);
		$hidPaymentLastName   = ucwords($hidPaymentLastName);
		$hidShippingCity      = ucwords($hidShippingCity);
		$hidPaymentCity       = ucwords($hidPaymentCity);
				
		$cartContent = getCartContent();
		$numItem     = count($cartContent);
		
		// save order & get order id
		$sql = "INSERT INTO tbl_order(od_date, od_last_update, od_shipping_first_name, od_shipping_last_name, od_shipping_address1, 
		                              od_shipping_address2, od_shipping_phone, od_shipping_state, od_shipping_city, od_shipping_postal_code, od_shipping_cost,
                                      od_payment_first_name, od_payment_last_name, od_payment_address1, od_payment_address2, 
									  od_payment_phone, od_payment_state, od_payment_city, od_payment_postal_code, customer_id)
                VALUES (NOW(), NOW(), '$hidShippingFirstName', '$hidShippingLastName', '$hidShippingAddress1', 
				        '$hidShippingAddress2', '$hidShippingPhone', '$hidShippingState', '$hidShippingCity', '$hidShippingPostalCode', '$shippingCost',
						'$hidPaymentFirstName', '$hidPaymentLastName', '$hidPaymentAddress1', 
						'$hidPaymentAddress2', '$hidPaymentPhone', '$hidPaymentState', '$hidPaymentCity', '$hidPaymentPostalCode','$customer_id')";
		$result = dbQuery($sql);
		
		// get the order id
		$orderId = dbInsertId();
		
		if ($orderId) {
			// save order items
			for ($i = 0; $i < $numItem; $i++) {
				$sql = "INSERT INTO tbl_order_item(od_id, pd_id, od_qty)
						VALUES ($orderId, {$cartContent[$i]['pd_id']}, {$cartContent[$i]['ct_qty']})";
				$result = dbQuery($sql);					
			}
		
			
			// update product stock
			for ($i = 0; $i < $numItem; $i++) {
				$sql = "UPDATE tbl_product 
				        SET pd_qty = pd_qty - {$cartContent[$i]['ct_qty']}
						WHERE pd_id = {$cartContent[$i]['pd_id']}";
				$result = dbQuery($sql);					
			}
			
			
			// then remove the ordered items from cart
			for ($i = 0; $i < $numItem; $i++) {
				$sql = "DELETE FROM tbl_cart
				        WHERE ct_id = {$cartContent[$i]['ct_id']}";
				$result = dbQuery($sql);					
			}							
		}					
	}
	
	return $orderId;
}

/*
	Get order total amount ( total purchase + shipping cost )
*/
function getOrderAmount($orderId)
{
	$orderAmount = 0;
	
	$sql = "SELECT SUM(pd_price * od_qty)
	        FROM tbl_order_item oi, tbl_product p 
		    WHERE oi.pd_id = p.pd_id and oi.od_id = $orderId
			
			UNION
			
			SELECT od_shipping_cost 
			FROM tbl_order
			WHERE od_id = $orderId";
	$result = dbQuery($sql);

	if (dbNumRows($result) == 2) {
		$row = dbFetchRow($result);
		$totalPurchase = $row[0];
		
		$row = dbFetchRow($result);
		$shippingCost = $row[0];
		
		$orderAmount = $totalPurchase + $shippingCost;
	}	
	
	return $orderAmount;	
}

?>
My idea is, after user logined , there is session variable for valid user, then continue to process shopping cart.
there are 3 steps:
1 - input all shipping and payment infor
2- review all infor



3- INSERT all the infor into database table order with the user id

In 3rd step, I got error when customer id is insert into table order:

Notice: Undefined variable: customer_id in /home/content/v/h/p/vhp0003/html/library/checkout-functions.php on line 38

Warning: Cannot modify header information - headers already sent by (output started at /home/content/v/h/p/vhp0003/html/library/checkout-functions.php:38) in /home/content/v/h/p/vhp0003/html/checkout.php on line 33


so in the checkout code, I have:
$customer_id = $_SESSION['valid_user'];
and INSERT INTO table order:

$sql = "INSERT INTO tbl_order(od_date, od_last_update, od_shipping_first_name, od_shipping_last_name, od_shipping_address1,
od_shipping_address2, od_shipping_phone, od_shipping_state, od_shipping_city, od_shipping_postal_code, od_shipping_cost,
od_payment_first_name, od_payment_last_name, od_payment_address1, od_payment_address2,
od_payment_phone, od_payment_state, od_payment_city, od_payment_postal_code, customer_id)
VALUES (NOW(), NOW(), '$hidShippingFirstName', '$hidShippingLastName', '$hidShippingAddress1',
'$hidShippingAddress2', '$hidShippingPhone', '$hidShippingState', '$hidShippingCity', '$hidShippingPostalCode', '$shippingCost',
'$hidPaymentFirstName', '$hidPaymentLastName', '$hidPaymentAddress1',
'$hidPaymentAddress2', '$hidPaymentPhone', '$hidPaymentState', '$hidPaymentCity', '$hidPaymentPostalCode','$customer_id')";
How can I insert the valid_user session into database order ? If I remove $customer_id, the INSERT function will work nicely.