How to Form Minimum Groups which should not exceed a max value

Mehdi answer and the Best Fit Algorithm[^] is an excellent starting point.

But the algorithm will not always give the optimal answer as you can see from the example used.
So after having run the algorithm iterate through the bins once more and see if you can empty them into the other bins. Used the same principle of placing the value in the most filled bin.

In case of the algorithm example you can empty group 3, leaving you with one less bin to use.

This works but not sure about the performance ?...

Create procedure Test as
DECLARE @ID int,
        @Salary money,
        @RunningTotal money,
		@GroupCount int
		
SET @RunningTotal = 0
SET @GroupCount=1

DECLARE rt_cursor CURSOR
FOR SELECT ID, Salary FROM employee
order by ID

select ID, SPACE(50) Grouped into #temp from employee
OPEN rt_cursor

FETCH NEXT FROM rt_cursor INTO @ID,@Salary

WHILE @@FETCH_STATUS = 0
 BEGIN
 if (@RunningTotal +@Salary > 5000)
	Begin
		SET @GroupCount=@GroupCount+1
		SET @RunningTotal = @Salary
	End
 else
	Begin
		SET @RunningTotal = @RunningTotal + @Salary
	End
	update #temp
	set Grouped='Group ' + STR(@GroupCount)
	where ID=@ID
	
	
	
  FETCH NEXT FROM rt_cursor INTO @ID,@Salary
 END

CLOSE rt_cursor
DEALLOCATE rt_cursor
select * from #temp