Pune Institute

From my sources and information, if you want a good quality education at a lower cost I would suggest you to go for ADMI. If you go to the ground reality of MITSOM, MITSOB, Balaji and Indira their fee is high. Infrastructure is good in these colleges but, 100% placement is not guaranteed in any of these colleges except for Indira with some costs.
The faculty is excellent in ADMI gives good attention to almost all students to clear doubts or other educational additional student wants to go for. If you are getting PUMBA nothing like that.
But when it comes to final campus placements, ADMI is competing with these colleges and getting the same job.
But as your hometown is Pune, expenses in Mumbai will add up an extra cost of around Rs. 2-3 lakhs for 2 years.
If you manage to get campus hostel for accommodation it will be definitely less than Rs. 2 lakhs for 2 years. (Assuming general expenses)

Yes, you can definitely join.
Indian Institute of Materials Management (IIMM) with its Headquarters at Navi Mumbai, is the National Apex body representing a wide spectrum of professionals engaged in various facets of Material Management, responsible for planning, sourcing, Logistics & Supply Chain Management. Through its wide network of 44 branches and 16 chapters having over 8000 members drawn form public and private sectors, (IIMM is dedicated to the promotion of the profession of Materials Management) and with its multifarious activities, including EDP, seminars, workshops, in-house training programs and consultancy assignment & Advance Materials Management Programs & Research Programs. To have more effective global interaction, Institute is a chartered member of International Federation of Purchasing and Supply Management (IFPSM), Atlanta (USA) Incorporated in Switzerland, which has its members in over 44 countries.