How can I write a query to carry a remaining balance of hours forward for load leveling a schedule? - common-table-expression

Question

I have a query result with a total amount of hours scheduled per week in chronological order without gaps and have a set amount of hours that can be processed each week. Any hours not processed should be carried over to one or more following weeks. The following information is available.
Week | Hours | Capacity
1 2000 160
2 100 160
3 0 140
4 150 160
5 500 160
6 1500 160
Each week it should reduce the new hours plus carried over hours by the Capacity but never go below zero. A positive value should carry into the following week(s).
Week | Hours | Capacity | LeftOver = (Hours + LAG(LeftOver) - Capacity)
1 400 160 240 (400 + 0 - 160)
2 100 160 180 (100 + 240 - 160)
3 0 140 40 ( 0 + 180 - 140)
4 20 160 0 ( 20 + 40 - 160) (no negative, change to zero)
5 500 160 340 (500 + 0 - 160)
6 0 160 180 ( 0 + 340 - 160)
I'm assuming this can be done with cte recursion and a running value that doesn't go below zero but I can't find any specific examples of how this would be written.

Answer 1

Well, you are not wrong, a recursive common table expression is indeed an option to construct a solution.
Construction of recursive queries can generally be done in steps. Run your query after every step and validate the result.
Define the "anchor" of your recursion: where does the recursion start?Here the start is defined by Week = 1.
Define a recursion iteration: what is the relation between iterations?Here that would be the incrementing week numbers d.Week = r.Week + 1.
Avoiding negative numbers can be resolved with a case expression.
Sample data
create table data
(
Week int,
Hours int,
Capacity int
);
insert into data (Week, Hours, Capacity) values
(1, 400, 160),
(2, 100, 160),
(3, 0, 140),
(4, 20, 160),
(5, 500, 160),
(6, 0, 160);
Solution
with rcte as
(
select d.Week,
d.Hours,
d.Capacity,
case
when d.Hours - d.Capacity > 0
then d.Hours - d.Capacity
else 0
end as LeftOver
from data d
where d.Week = 1
union all
select d.Week,
d.Hours,
d.Capacity,
case
when d.Hours + r.LeftOver - d.Capacity > 0
then d.Hours + r.LeftOver - d.Capacity
else 0
end
from rcte r
join data d
on d.Week = r.Week + 1
)
select r.Week,
r.Hours,
r.Capacity,
r.LeftOver
from rcte r
order by r.Week;
Result
Week Hours Capacity LeftOver
---- ----- -------- --------
1 400 160 240
2 100 160 180
3 0 140 40
4 20 160 0
5 500 160 340
6 0 160 180
Fiddle to see things in action.

Answer 2

I ended up writing a few CTEs then a recursive CTE and got what I needed. The capacity is a static number here but will be replaced later with one that takes holidays and vacations into account. Will also need to consider the initial 'LeftOver' value for the first week but could use this query with an earlier date period to find the most recent date with a zero LeftOver value then use that as a new start date, then filter out those earlier weeks in the final query.
DECLARE #StartDate date = (SELECT MAX(FirstDayOfWorkWeek) FROM dbo._Calendar WHERE Date <= GETDATE());
DECLARE #EndDate date = DATEADD(week, 12, #StartDate);
DECLARE #EmployeeQty int = (SELECT ISNULL(COUNT(*), 0) FROM Employee WHERE DefaultDepartment IN (4) AND Hidden = 0 AND DateTerminated IS NULL);
WITH hours AS (
/* GRAB ALL NEW HOURS SCHEDULED FOR EACH WEEK IN THE SELECTED PERIOD */
SELECT c.FirstDayOfWorkWeek as [Date]
, SUM(budget.Hours) as hours
FROM dbo.Project_Phase phase
JOIN dbo.Project_Budget_Labor budget on phase.ID = budget.Phase
JOIN dbo._Calendar c on CONVERT(date, phase.Date1) = c.[Date]
WHERE phase.CompletedOn IS NULL AND phase.Project <> 4266
AND phase.Date1 BETWEEN #StartDate AND #EndDate
AND budget.Department IN (4)
GROUP BY c.FirstDayOfWorkWeek
)
, weeks AS (
/* CREATE BLANK ROWS FOR EACH WEEK AND JOIN TO ACTUAL HOURS TO ELIMINATE GAPS */
/* ADD A ROW NUMBER FOR RECURSION IN NEXT CTE */
SELECT cal.[Date]
, ROW_NUMBER() OVER(ORDER BY cal.[Date]) as [rownum]
, ISNULL(SUM(hours.Hours), 0) as Hours
FROM (SELECT FirstDayOfWorkWeek as [Date] FROM dbo._Calendar WHERE [Date] BETWEEN #StartDate AND #EndDate GROUP BY FirstDayOfWorkWeek) as cal
LEFT JOIN hours on cal.[Date] = hours.[Date]
GROUP BY cal.[Date]
)
, spread AS (
/* GRAB FIRST WEEK AND USE RECURSION TO CREATE RUNNING TOTAL THAT DOES NOT DROP BELOW ZERO*/
SELECT TOP 1 [Date]
, rownum
, Hours
, #EmployeeQty * 40 as Capacity
, CONVERT(numeric(9,2), 0.00) as LeftOver
, Hours as running
FROM weeks
ORDER BY rownum
UNION ALL
SELECT curr.[Date]
, curr.rownum
, curr.Hours
, #EmployeeQty * 40 as Capacity
, CONVERT(numeric(9,2), CASE WHEN curr.Hours + prev.LeftOver - (#EmployeeQty * 40) < 0 THEN 0 ELSE curr.Hours + prev.LeftOver - (#EmployeeQty * 40) END) as LeftOver
, curr.Hours + prev.LeftOver as running
FROM weeks curr
JOIN spread prev on curr.rownum = (prev.rownum + 1)
)
SELECT spread.Hours as NewHours
, spread.LeftOver as PrevHours
, spread.Capacity
, spread.running as RunningTotal
, CASE WHEN running < Capacity THEN running ELSE Capacity END as HoursThisWeek
FROM spread