Different Possible combinations possible

I am not sure if this is the answer that you want as you have mentioned a lot of requirements (SUMs AVERAGEs and so on) but you should be able to work from this:

USE [adventureworks]
go
IF OBJECT_ID('test1') > 0 
    DROP TABLE [dbo].[test1]
CREATE TABLE test1
    (
      Batch CHAR(6) ,
      Qty INT ,
      Rate INT
    )
go

INSERT  INTO test1
VALUES
        ( 'D-0001', 120, 13 ),
        ( 'D-0001', 105, 15 ),
        ( 'D-0001', 109, 13 ),
        ( 'D-0001', 100, 16 ),
        ( 'D-0001', 110, 15 ),
        ( 'D-0002', 120, 12 ),
        ( 'D-0002', 122, 12 ),
        ( 'D-0002', 125, 16 ),
        ( 'D-0003', 118, 14 ),
        ( 'D-0003', 115, 10 ),
        ( 'D-0014', 123, 13 ),
        ( 'D-0014', 116, 14 ),
        ( 'D-0014', 135, 16 ),
        ( 'D-0014', 121, 14 ),
        ( 'D-0015', 112, 15 )

SELECT
    [dbo].[test1].[Batch] ,
    avg([dbo].[test1].[Qty]) AS [Avg Qty],
    avg([dbo].[test1].[Rate]) AS [Avg Rate]
FROM
    test1 
GROUP BY
    [dbo].[test1].[Batch]

GO

    DROP TABLE [dbo].[test1]93

Now if you want to test the values of the average columns and filter if they are between certain values then you may do this with a simple WHERE avg([dbo].[test1].[Qty]) AS [Avg Qty] BETWEEN 100 and 200 of you may need to return all the results into a CTE and then filter from that, depending on your table/data sizes and how your system performs.

Please note that I have used a different set of data from you as your sample gave no chance of returning AVERAGE values

This is my solution to the problem.

create table #tmp (Batch varchar(50), qty int, rate int)

insert #tmp select 'D-0001'   , 120  ,    13
insert #tmp select 'D-0002'   , 105  ,    15
insert #tmp select 'D-0003'   , 109  ,    13
insert #tmp select 'D-0004'   , 100  ,    16
insert #tmp select 'D-0005'   , 110  ,    15
insert #tmp select 'D-0006'   , 120  ,    12
insert #tmp select 'D-0007'   , 122  ,    12
insert #tmp select 'D-0008'   , 125  ,    16
insert #tmp select 'D-0009'   , 118  ,    14
insert #tmp select 'D-0010'   , 115  ,    10
insert #tmp select 'D-0011'   , 123  ,    13
insert #tmp select 'D-0012'   , 116  ,    14
insert #tmp select 'D-0013'   , 135  ,    16
insert #tmp select 'D-0014'   , 121  ,    14
insert #tmp select 'D-0015'   , 112   ,   15

select *,
      (a.Qty + b.Qty + c.Qty + d.Qty + e.Qty)/5.0 as QtyAvg,
      (a.Rate + b.Rate + c.Rate + d.Rate + e.Rate)/5.0 as RateAvg
    join #tmp b on b.Batch not in (a.Batch)
    join #tmp c on c.Batch not in (a.Batch, b.Batch)
    join #tmp d on d.Batch not in (a.Batch, b.Batch, c.Batch)
    join #tmp e on e.Batch not in (a.Batch, b.Batch, c.Batch, d.Batch)
    where (a.Qty + b.Qty + c.Qty + d.Qty + e.Qty)/5.0 between 110 and 115
    and (a.Rate + b.Rate + c.Rate + d.Rate + e.Rate)/5.0 between 10 and 15

Running this query produces 140,760 results. Note that this produced permutations, so rows representing the same combination will appear several times e.g. combination (D-0001, D-0002, D-0003, D-0004, D-0006) and combination (D-0001, D-0002, D-0003, D-0006, D-0004).

I've amended the query above to produce combinations instead of permutations.

select *, 
  (a.Qty + b.Qty + c.Qty + d.Qty + e.Qty)/5.0 as QtyAvg,
  (a.Rate + b.Rate + c.Rate + d.Rate + e.Rate)/5.0 as RateAvg
from #tmp a
join #tmp b on a.batch < b.batch
join #tmp c on b.batch < c.batch
join #tmp d on c.batch < d.batch
join #tmp e on d.batch < e.batch
where (a.Qty + b.Qty + c.Qty + d.Qty + e.Qty)/5.0 between 110 and 115
and (a.Rate + b.Rate + c.Rate + d.Rate + e.Rate)/5.0 between 10 and 15

This yields 1173 results and executes a lot faster than the previous one! The next step is to make the code generic to take an arbitray number of batch numbers...

Ok, Here is my first attempt - it works very happily for groups of 10 or less, after that it starts to take a bit of time...

SET NOCOUNT ON
GO

DROP TABLE #tmp
GO

CREATE TABLE #tmp (Batch VARCHAR(50), qty INT, rate INT)

INSERT #tmp SELECT 'D-0001'   , 120  ,    13
INSERT #tmp SELECT 'D-0002'   , 105  ,    15
INSERT #tmp SELECT 'D-0003'   , 109  ,    13
INSERT #tmp SELECT 'D-0004'   , 100  ,    16
INSERT #tmp SELECT 'D-0005'   , 110  ,    15
INSERT #tmp SELECT 'D-0006'   , 120  ,    12
INSERT #tmp SELECT 'D-0007'   , 122  ,    12
INSERT #tmp SELECT 'D-0008'   , 125  ,    16
INSERT #tmp SELECT 'D-0009'   , 118  ,    14
INSERT #tmp SELECT 'D-0010'   , 115  ,    10
INSERT #tmp SELECT 'D-0011'   , 123  ,    13
INSERT #tmp SELECT 'D-0012'   , 116  ,    14
INSERT #tmp SELECT 'D-0013'   , 135  ,    16
INSERT #tmp SELECT 'D-0014'   , 121  ,    14
INSERT #tmp SELECT 'D-0015'   , 112   ,   15
INSERT #tmp SELECT 'D-0101'   , 120  ,    13
INSERT #tmp SELECT 'D-0102'   , 105  ,    15
INSERT #tmp SELECT 'D-0103'   , 109  ,    13
INSERT #tmp SELECT 'D-0104'   , 100  ,    16
INSERT #tmp SELECT 'D-0105'   , 110  ,    15
INSERT #tmp SELECT 'D-0106'   , 120  ,    12
INSERT #tmp SELECT 'D-0107'   , 122  ,    12
INSERT #tmp SELECT 'D-0108'   , 125  ,    16
INSERT #tmp SELECT 'D-0109'   , 118  ,    14
INSERT #tmp SELECT 'D-0110'   , 115  ,    10
INSERT #tmp SELECT 'D-0111'   , 123  ,    13
INSERT #tmp SELECT 'D-0112'   , 116  ,    14
INSERT #tmp SELECT 'D-0113'   , 135  ,    16
INSERT #tmp SELECT 'D-0114'   , 121  ,    14
INSERT #tmp SELECT 'D-0115'   , 112   ,   15

DECLARE @GroupSize INT 
SET @GroupSize = 5

;WITH groups AS
(
SELECT 
     Batch
    ,qty
    ,rate
    ,1 AS LEVEL
    ,CAST(Batch AS VARCHAR(280)) AS chain
FROM #tmp 
UNION ALL
SELECT 
     t.Batch
    ,g.qty+t.qty
    ,g.rate+t.rate
    ,g.level+1
    ,CONVERT(VARCHAR(280),g.chain +','+t.Batch )
FROM #tmp t
JOIN groups g
ON CHARINDEX(t.Batch,g.chain)=0
AND t.Batch>g.Batch 
--== uncomment these four lines to get a huge speed boost but you may miss some valid groups
--and t.qty >= (110 * (g.level+1) - g.qty)
--and t.qty <= (115 * (g.level+1) - g.qty)
--and t.rate >= (10 * (g.level+1) - g.rate)
--and t.rate <= (15 * (g.level+1) - g.rate)
WHERE g.level<@GroupSize 
)
SELECT 
      DENSE_RANK() OVER(ORDER BY g.chain) AS [GROUP]
    , t.Batch
    , t.qty 
    , t.rate 
    , AVG(t.qty) OVER (PARTITION BY chain) as AverageQty
    , AVG(t.rate) OVER (PARTITION BY chain) as AverageRate
FROM (
    --== remove the top 1 and the "Order by NEWID()" if you want ALL groups that fit.
    SELECT TOP 1 
         g.chain
    from groups g 
    WHERE LEVEL=@GroupSize 
    AND g.qty BETWEEN (@GroupSize*110) AND (@GroupSize *115)
    AND g.rate BETWEEN (@GroupSize*10) AND (@GroupSize *15)
    --== remove the following line to just get the first set of @Groupsize batches that fit
    --== leave it in to get a "random" group of @Groupsize batches that fit
    order by NEWID()
) g
JOIN #tmp t
ON CHARINDEX(t.Batch ,g.chain)>0
ORDER BY g.chain,t.Batch 

Sample output :

9393