How can you automate the monthly opening of MM periods (transaction MMPV - program RMMMPERI) with 
SM36?

RMMMPERI accepts a period/year or a date.

If you enter a date the period is derived by it.

1. create a variant and check the attribute 'selection variable' for the parameter date. Then click the button 'Selection variables' and set the current date. Every time this variant is used the parameter DATE is filled with the current date.

2. create a job for RMMMPERI with the variant created in the preceding step. Set it as periodic.
If you're not using a fiscal year variant simply schedule it as monthly (to be executed the first day of the month).
If you are using a fiscal year variant you'd have to define a calendar with only the first day of each period defined as working 
day and use it in the periodicity restrictions.

Another possibility:
Write a very simple ABAP which run daily to check if the period has changed and submit RMMMPERI.

MM Related:

• Re-Open The Previous Period
• Allow/Disallowed Backposting of Inventory Posting
• Movement Error - Posting Only Possible Between

SAP Material Management Books
SAP MM Books - Certification, Interview Questions and Configuration

SAP Materials Management Tips
SAP MM Configuration Tips and Materials Management Discussion Forum

Best regards,
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