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db<>fiddle
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create table mytable (
TicketNumber int,
[AssignedLocator] INT,
[PartNo] INT
);

insert into mytable values
(10, 1, 1),
(11, 2, 2),
(12, 3, 3);


DECLARE @TicketNumber INT;
SET @TicketNumber = 100000;

WITH CTE AS (
SELECT *, @TicketNumber + ROW_NUMBER() OVER (ORDER BY [AssignedLocator], [PartNo]) AS RowNum
FROM mytable
)
UPDATE CTE
SET [TicketNumber] = CTE.RowNum
6 rows affected
SELECT *
FROM mytable
TicketNumber AssignedLocator PartNo
100001 1 1
100002 2 2
100003 3 3