SQL Server 2014

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IF OBJECT_ID('tempdb.dbo.#Temp', 'U') IS NOT NULL
    DROP TABLE #Temp;

CREATE TABLE #Temp
(
    ID VARCHAR(6), ProcessDate DATETIME, Quantity INT
);

INSERT INTO #Temp
(
    ID, ProcessDate, Quantity
)
VALUES
('001931', '2016-06-30', 24),  ('001931', '2016-07-29', 22)
, ('001931', '2016-08-31', 23), ('001931', '2016-09-30', 21)
, ('001931', '2016-10-31', 21), ('001931', '2016-11-30', 19)
, ('001931', '2016-12-30', 18), ('001931', '2017-01-31', 30)
, ('000691', '2016-06-30', 24), ('000691', '2016-07-29', 22);

SELECT ID, ProcessDate, Quantity FROM #Temp ORDER BY ID, ProcessDate;

-- use subquery with MAX(ProcessDate) for each ID
SELECT     a.ID
         , a.ProcessDate
         , a.Quantity
FROM       (
               SELECT   ID
                      , MAX(ProcessDate) AS MaxProcessDate
               FROM     #Temp
               GROUP BY ID
           )     AS x
INNER JOIN #Temp AS a ON x.ID = a.ID
                         AND x.MaxProcessDate = a.ProcessDate
ORDER BY   a.ID;

-- user OVER clause with ROW_NUMBER function to get the first row for each ID
SELECT   x.ID
       , x.ProcessDate
       , x.Quantity
FROM     (
             SELECT ID
                  , ProcessDate
                  , Quantity
                  , ROW_NUMBER() OVER (PARTITION BY ID ORDER BY ProcessDate DESC) 
                  AS IDRowNumber
             FROM   #Temp
         ) AS x
WHERE    x.IDRowNumber = 1
ORDER BY x.ID;

ID	ProcessDate	Quantity
000691	2016-06-30 00:00:00.000	24
000691	2016-07-29 00:00:00.000	22
001931	2016-06-30 00:00:00.000	24
001931	2016-07-29 00:00:00.000	22
001931	2016-08-31 00:00:00.000	23
001931	2016-09-30 00:00:00.000	21
001931	2016-10-31 00:00:00.000	21
001931	2016-11-30 00:00:00.000	19
001931	2016-12-30 00:00:00.000	18
001931	2017-01-31 00:00:00.000	30

ID	ProcessDate	Quantity
000691	2016-07-29 00:00:00.000	22
001931	2017-01-31 00:00:00.000	30

ID	ProcessDate	Quantity
000691	2016-07-29 00:00:00.000	22
001931	2017-01-31 00:00:00.000	30