Is it permissible for an employee who works in a company and is responsible for contractors to establish another company with a partner and bid on projects for his company without the employer's knowledge?

Since the questioner is responsible for the contractors, he is an agent for his company in dealing with them. It is not permissible for him to be one of the contractors himself unless his principal (the company owner) is aware; because he will be accused of favoring himself, especially since he will be privy to the other contractors' prices.