How can we develop reliable ERP open source systems for the management of our institutions?

use existing programs that may helps OpenERP but i think its not free you need 33 USD per user/month or check this http://ofbiz.apache.org/ , its totally free

I think that depends on the need of the institutions because there are different major factors that should be taken into consideration .
1) costing method such as FIFO, weight method 2) the cycle of PO and SO 3) the item types like items, serial, batch 4) some institutions use dissassembly and assembly for the inventory module 5) the financial integration with other modules the above points are a small sample of the major factors because the industry of each institutions plays a major role to define "what i really need" for example, in medicine industry they need to use batches for the items because they have expiry dates but in furniture fields they use serials and they don't care about the expiry dates

Try these ERP Odoo or Openbravo or webERP

You can depend on any existing open source ERP and adapt it and customize it for your needs rather than starting from scratch, there is a wide variety of open source ERPs: OpenERP Openbravo Apache OFBiz and many others.