Update only rows which match another table in sql with SP

you desctibed everything in your question but did not write what error you get?

you have attached only the SP without any tables script sp no one can execute the SP and no one can find out what's the error in it.

However, looking at your script, it seems you are getting more than one record in the in following subqueires which gives you error. You have to use top 1 or some condition so that you get only 1 record from subquery:

SET @begin_date_time = (select begin_date_time from shipment_assignment)
SET @end_date_time = (select end_date_time from shipment_assignment where end_date_time <> NULL)