I think this will work (please note how I supplied some test data):

DECLARE @inventory_history table(itm_code INT, tran_type VARCHAR(15), itm_qty INT, doc_date datetime)

DECLARE @date DATETIME

SET @date = '3/31/2009'

INSERT INTO @inventory_history (

itm_code,

tran_type,

itm_qty,

doc_date

)

SELECT

1,

'Received',

100,

'3/28/09'

UNION ALL

SELECT

1,

'Allocated',

25,

'3/30/09'

UNION ALL

SELECT

1,

'Received',

50,

'4/2/09'

UNION ALL

SELECT

1,

'Allocated',

80,

'4/05/09'

SELECT

itm_code,

SUM(CASE WHEN tran_type = 'Received' THEN itm_qty ELSE itm_qty * -1 END) AS quantity

FROM

@inventory_history

WHERE

doc_date <= @date

GROUP BY

itm_code

This assumes that all transactions are stored in positive numbers so I need to reverse the sign on all other transactions other than receipts. You should be able to figure out the rest.