The multi-part identifier could not be bound error for duplicates

In my code below, I am getting an error:

> The multi-part identifier "i.Inventoryid" could not be bound.

CREATE TRIGGER trg_UpdateOrderMultiple
ON tbl_InventoryPolicy
AFTER INSERT, UPDATE
AS
BEGIN
    DECLARE @OldOrderMultiple INT
    DECLARE @NewOrderMultiple INT
    DECLARE @Timestamp DATETIME

    SELECT @OldOrderMultiple = d.ordermultiple
    FROM deleted d
    INNER JOIN inserted i ON i.Inventoryid = d.Inventoryid

    SELECT @NewOrderMultiple = i.ordermultiple
    FROM inserted i

    SET @Timestamp = GETDATE()
    IF NOT EXISTS (
            SELECT 1
            FROM tbl_InventoryPolicyChanges
            WHERE Inventoryid = i.Inventoryid
            AND OldOrderMultiple = @OldOrderMultiple
            AND NewOrderMultiple = @NewOrderMultiple
        )
        BEGIN
            INSERT INTO tbl_InventoryPolicyChanges 
                        (InventoryID, OldOrderMultiple, NewOrderMultiple, Timestamp)
            SELECT i.InventoryID, @OldOrderMultiple, 
                    @NewOrderMultiple, @Timestamp
            FROM inserted i
        END
END

I want to avoid inserting duplicate entries into the tbl_InventoryPolicyChanges.

You're making the classic mistake many people make when it comes to triggers, and that is to suddenly change from regular SQL set-based operations into some sort of procedural logic. Don't do it, continue to use set-based operations as you would for any other query. I think the following converts your existing logic into set-based logic, but you'll need to validate it yourself.

1. Use joins with the Inserted and Deleted pseudo tables when required

2. Add a where clause to filter out unwanted changes

INSERT INTO tbl_InventoryPolicyChanges (InventoryID, OldOrderMultiple, NewOrderMultiple, [Timestamp])
SELECT i.InventoryID, d.ordermultiple, i.ordermultiple, GETDATE()
FROM Inserted i
INNER JOIN Deleted d on d.InventoryId = i.InventoryId
WHERE NOT EXISTS (
    SELECT 1
    FROM tbl_InventoryPolicyChanges
    WHERE Inventoryid = i.Inventoryid
    AND NewOrderMultiple = i.ordermultiple
    AND OldOrderMultiple = d.ordermultiple
);

Note: Your trigger is also an insert trigger, but your logic doesn't handle insert because you assume Deleted will have rows in it. If it should also handle inserts then the logic needs to be modified to handle no rows in the Deleted pseudo table.

I think the following also handles the INSERT case, note the LEFT JOIN and the null compare:

INSERT INTO tbl_InventoryPolicyChanges (InventoryID, OldOrderMultiple, NewOrderMultiple, [Timestamp])
SELECT i.InventoryID, d.ordermultiple, i.ordermultiple, GETDATE()
FROM Inserted i
LEFT JOIN Deleted d on d.InventoryId = i.InventoryId
WHERE NOT EXISTS (
    SELECT 1
    FROM tbl_InventoryPolicyChanges c
    WHERE c.Inventoryid = i.Inventoryid
    AND c.NewOrderMultiple = i.ordermultiple
    AND (c.OldOrderMultiple = d.ordermultiple OR (d.ordermultiple IS NULL AND c.OldOrderMultiple IS NULL))
);