Someone else’s utility model patent authorizes us to produce, but his patent is not perfect. Can we apply for a patent if we improve on his patent?

Yes. If your patent is a change to the original patent, it is a brand-new solution that can be implemented independently and does not need to be authorized by his patent; if it is an optimization based on the original patent and the protection scope of the original patent cannot be avoided during implementation, then you can even You have this new patent, but you still need to obtain authorization from the original patent when you want to implement it.