TSQL Index odd and even sequence steps - sql

Question

I have a gritty industrial control problem i'm trying to solve with T-SQL.
The goal is to calculate an index position for each of two pallet loading robots, positioned in one of two ranges; 2 to 78 (robot 1) and 4 to 80 (robot 2).
Each robot indexes in steps of 4 so complete coverage of 80 spots on the pallet is achieved. The robots work side by side with a minimum spacing of 2 spots while they move along the pallet.
Two sized boxes can be placed on the pallet, one twice as long as the other. If two small boxes are placed side by side taking up 1 spot each, a single larger box can be placed on top, taking up 2 spots until a maximum height is reached. Thus the spot number for a small box is always odd and for a large box is always even and the robot index number is always even. e.g. (see diagram) from index position 14 spots 13 and 15 are loaded, and from index 20 spots 19 and 21 can be loaded.
Robot Index Positions
I need a conversion formula that calculates the Index number for a given Spot and Robot.
The calculated Index column should look like the following:
Spot Robot Index
1 1 2
2 1 2
3 1 2
- - -
13 1 14
14 1 14
15 1 14
16 2 16
17 2 16
18 1 18
19 2 20
- - -
- - -
77 1 78
78 1 78
79 2 80
80 2 80
One way would be to do an update to the Index column with every possible combination of Spot and Robot using a simple CASE WHEN selection or maybe do lookups on a reference table holding every possible combination. What I would like to explore (if any math wizards are inclined!) is a math formula that calculate the Index value.
So far I've come up with the following by converting formula developed for use in Excel. The Robot 2 section is incomplete. The 95 to 99 values are for error checking.
UPDATE MovesTable SET [Index] =
CASE
WHEN Robot = 1 THEN
CASE
WHEN Spot%4 = 0 THEN '99'
WHEN Spot = 1 or Spot = 2 or Spot = 3 THEN '02'
WHEN Spot = 5 or Spot = 6 or Spot = 7 THEN '06'
WHEN Spot = 9 or Spot = 10 or Spot = 11 THEN '10'
WHEN Spot%10 = 4 THEN CONCAT(Spot/10,'4')
WHEN Spot < 57 AND (((Spot/10)%2 = 1 AND (Spot%10)%2 = 1) AND (Spot%10 = 3 OR Spot%10 = 5)) THEN CONCAT(Spot/10,'4')
WHEN Spot%10 = 8 THEN CONCAT(Spot/10,'8')
WHEN Spot < 57 AND (((Spot/10)%2 = 1 AND (Spot%10)%2 = 1) AND (Spot%10 = 7 OR Spot%10 = 9)) THEN CONCAT(Spot/10,'8')
WHEN Spot%10 = 2 THEN CONCAT(Spot/10,'2')
WHEN Spot < 57 AND (((Spot/10)%2 = 1 AND (Spot%10)%2 = 0) AND (Spot%10 = 1 OR Spot%10 = 3)) THEN CONCAT(Spot/10,'2')
WHEN Spot%10 = 6 THEN CONCAT(Spot/10,'6')
WHEN Spot < 57 AND (((Spot/10)%2 = 0 AND (Spot%10)%2 = 1) AND (Spot%10 = 5 OR Spot%10 = 7)) THEN CONCAT(Spot/10,'6')
WHEN Spot%10 = 0 THEN CONCAT(Spot/10,'')
WHEN Spot = 49 THEN '50'
WHEN Spot < 57 AND (((Spot/10)%2 = 0 AND (Spot%10)%2 = 1) AND Spot%10 = 9) THEN '30'
WHEN Spot < 57 AND (((Spot/10)%2 = 1 AND (Spot%10)%2 = 1) AND Spot%10 = 1) THEN CONCAT(Spot/10,'0')
WHEN Spot > 56 AND (((Spot/10)%2 = 1 AND (Spot%10)%2 = 1) AND (Spot%10 = 7 OR Spot%10 = 9)) THEN CONCAT(Spot/10,'8')
WHEN Spot > 56 AND (((Spot/10)%2 = 0 AND (Spot%10)%2 = 1) AND (Spot%10 = 1 OR Spot%10 = 3)) THEN CONCAT(Spot/10,'2')
WHEN Spot > 56 AND (((Spot/10)%2 = 0 AND (Spot%10)%2 = 1) AND (Spot%10 = 5 OR Spot%10 = 7)) THEN CONCAT(Spot/10,'6')
ELSE '98'
END
ELSE
CASE
WHEN Robot = 2 THEN
CASE
WHEN (Spot%2 = 0 AND Spot%4 <> 0) OR (Spot = 1 OR Spot = 2) THEN '97'
WHEN Spot = 4 then '04'
WHEN Spot = 8 then '08'
WHEN Spot%4 = 0 THEN Spot
WHEN Spot = 2 OR Spot = 5 THEN '05'
WHEN Spot = 7 OR Spot = 9 THEN '08'
WHEN Spot = 19 THEN '20'
WHEN Spot = 39 THEN '40'
WHEN Spot = 59 THEN '60'
ELSE '96'
END
ELSE '95'
END
END

Answer 1

I tried to solve this mathematically, rather than by analyzing cases, etc. It matches all of your sample results:
declare #t table (Spot int, Robot int, [Index] int)
insert into #t(Spot,Robot,[Index]) values
(1 ,1 , 2 ),
(2 ,1 , 2 ),
(3 ,1 , 2 ),
(13 ,1 ,14 ),
(14 ,1 ,14 ),
(15 ,1 ,14 ),
(16 ,2 ,16 ),
(17 ,2 ,16 ),
(18 ,1 ,18 ),
(19 ,2 ,20 ),
(77 ,1 ,78 ),
(78 ,1 ,78 ),
(79 ,2 ,80 ),
(80 ,2 ,80 )
select *,
CONVERT(int,
ROUND((Spot +
CASE WHEN Robot = 1 THEN 2 ELSE 0 END
)/4.0,0)* 4 -
CASE WHEN Robot = 1 THEN 2 ELSE 0 END
) as Index2
from #t
The logic is "round to the nearest multiple of four" but we use a couple of expressions to offset Robot 1's results by 2.
Results:
Spot Robot Index Index2
----------- ----------- ----------- -----------
1 1 2 2
2 1 2 2
3 1 2 2
13 1 14 14
14 1 14 14
15 1 14 14
16 2 16 16
17 2 16 16
18 1 18 18
19 2 20 20
77 1 78 78
78 1 78 78
79 2 80 80
80 2 80 80