Damaged and destroyed industrial centres are handled quite differently.
1. Damaged industrial centre.
(a) Both the Japanese and Allied player can repair a damaged industrial centre.
(b) To initiate the repair the base needs to have a bond of 10k supplies stockpiled plus 1k supplies expended per single damaged industrial centre to be repaired daily.
(c) Each industrial facility at the base can only have a single centre repaired daily.
Hence if you have a base with 8 Resource centres damaged and 13 Light Industry centres damaged you need 12k supplies present for 8 days, and 11k supplies present for a further 5 days afterwards to fully repair both industrial facilities. The total supply expenditure cost would be 21k.
2. Destroyed industrial centre.
(a) Only the Japanese player can build additional industrial centres. The Allied player never can.
(b) As per s.13.3.2 of the manual, the only industrial facilities which can be built are:
- aircraft
- engine
- vehicle
- armament
- heavy industry
- shipyards (naval, merchant, repair)
NB: This part of the manual is a carry over from classical WITP which IIRC did not have Light Industry hence why it it is omitted.
(c) The cost of the expansion, paid per additional industrial centre, is:
- 10 manpower
- 10 heavy industry
- 100 supply
As the OP appears to be from an Allied perspective, the short answer is no. However manpower centres is not a consideration for an Allied player. Destroyed on map Allied aircraft factories and heavy industry is a problem for the Allied player however as he can never build new centres.
Alfred