I believe this would have been discussed earlier on this forum and also lots of customers have asked for this requirement as part of SAP IBP implementation in their Landscape where key figure data be it Unconstrained Forecast from IBP DP or Safety Stock from IBP IO has to be published back to APO Time-series key figure or to an SNP Forecast Key figure.
I know there are a couple of methods ( or more may be ) to achieve so which include a web service call or an RFC call from CI DS.
We used RFC Call for one of our customers using 'BAPI_PBSRVAPS_CHANGEKEYFIGVAL2' with the use of a wrapper program around this FM.
But we ran into problems such as 'No Partial Commit in case one of the Product Location returns an error.'
For another customer, we are using a web service call that puts data into a cube via PSA. Then from the cube, we are using //TSCUBE to publish data.
If the data volume is huge and the frequency of publishing is once a week, what would be the best method to extract and publish data from IBP To the SAP APO system.
A lot of pre-made integration templates are available in CPI-DS which are covering lot of scenarios based on the best practices.
Here you can see all the IBP related templates:
SAP Help Portal - Master Data Templates
I hope you find the one you need.