A repairable $M/M/1$ retrial queue with setup times and reserved idle time is studied. The server holds a period of idle time after finishing the service, and customers who arrive at this time can receive the service immediately. Otherwise, the server will be closed down to reduce operating costs until a new customer arrives to activate the system. The server may break down during the busy and setup period. Firstly, the steady-state probability and stationary performance measures of the system are obtained by using the probability generating function method. Secondly, based on the reward-cost structure, the customer's equilibrium strategy and the socially optimal strategy that maximizes social benefits are obtained. Finally, we use the genetic algorithm to find the best combination of parameters that minimize the cost of the system. In addition, we construct a bi-objective optimal model and makes it possible to achieve an appropriate balance between the system cost and the service quality. The regression equation between the minimum cost and the waiting time is proposed, which is helpful to determine the minimum cost that meets service quality.