Workload distribution in Oracle SQL - sql

Question

I try to make a Workload distribution in SQL but it's seems hard.
My data are :
work-station | workload
------------------------
Station1 | 500
Station2 | 450
Station3 | 50
Station4 | 600
Station5 | 2
Station6 | 350
And :
Real Worker Number : 5
My needs are the following :
I required the exact match between real worker number than theoretical worker number (distribution)
I don't want to put someone in a station if it's not required (example : station5)
I don't want to know if my workers will be able to finish the complete workload
I want the best theoretical placement of my workers to have the best productivity
Is it possible to make this WorkLoad Distribution in a sql Request ?
Possible result :
work-station | workload | theoretical worker distribution
------------------------
Station1 | 500 | 1
Station2 | 450 | 1
Station3 | 50 | 0
Station4 | 600 | 2
Station5 | 2 | 0
Station6 | 350 | 1

Answer 1

Here is a very simplistic way to do it by prorating the workers by the percentage of total work assigned to each station.
The complexity comes from making sure that an integer number of workers is assigned and that the total number of assigned workers equals the number of workers that are available. Here is the query that does that:
with params as ( SELECT 5 total_workers FROM DUAL),
info ( station, workload) AS (
SELECT 'Station1', 500 FROM DUAL UNION ALL
SELECT 'Station2', 450 FROM DUAL UNION ALL
SELECT 'Station3', 50 FROM DUAL UNION ALL
SELECT 'Station4', 600 FROM DUAL UNION ALL
SELECT 'Station5', 2 FROM DUAL UNION ALL
SELECT 'Station6', 350 FROM DUAL ),
targets as (
select station,
workload,
-- What % of total work is assigned to station?
workload/sum(workload) over ( partition by null) pct_work,
-- How many workers (target_workers) would we assign if we could assign fractional workers?
total_workers * (workload/sum(workload) over ( partition by null)) target_workers,
-- Take the integer part of target_workers
floor(total_workers * (workload/sum(workload) over ( partition by null))) target_workers_floor,
-- Take the fractional part of target workers
mod(total_workers * (workload/sum(workload) over ( partition by null)),1) target_workers_frac
from params, info )
select t.station,
t.workload,
-- Start with the integer part of target workers
target_workers_floor +
-- Order the stations by the fractional part of target workers and assign 1 additional worker to each station until
-- the total number of workers assigned = the number of workers we have available.
case when row_number() over ( partition by null order by target_workers_frac desc )
<= total_workers - sum(target_workers_floor) over ( partition by null) THEN 1 ELSE 0 END target_workers
from params, targets t
order by station;
+----------+----------+----------------+--+
| STATION | WORKLOAD | TARGET_WORKERS | |
+----------+----------+----------------+--+
| Station1 | 500 | 1 | |
+----------+----------+----------------+--+
| Station2 | 450 | 1 | |
+----------+----------+----------------+--+
| Station3 | 50 | 0 | |
+----------+----------+----------------+--+
| Station4 | 600 | 2 | |
+----------+----------+----------------+--+
| Station5 | 2 | 0 | |
+----------+----------+----------------+--+
| Station6 | 350 | 1 | |
+----------+----------+----------------+--+

Answer 2

Below query should work:
First I divide workers to the stations that has more workload than mean work load.
Then I divide the rest of the workers to the stations in the same order of their remaining workloads.
http://sqlfiddle.com/#!4/55491/12
5 represent the number of workers.
SELECT
workload,
station,
SUM (worker_count)
FROM
(
SELECT workload, station, floor( workload / ( SELECT SUM (workload) / 5 FROM work_station ) ) worker_count -- divide workers to the stations have more workload then mean
FROM
work_station works
UNION ALL
SELECT t_table.*, 1
FROM ( SELECT workload, station
FROM work_station
ORDER BY
( workload - floor( workload / ( SELECT SUM (workload) / 5 FROM work_station ) ) * ( SELECT SUM (workload) / 5 FROM work_station )
) DESC
) t_table
WHERE
rownum < ( 5 - ( SELECT SUM ( floor( workload / ( SELECT SUM (workload) / 5 FROM work_station ) ) ) FROM work_station ) + 1
) -- count of the rest of the workers
) table_sum
GROUP BY
workload,
station
ORDER BY
station