Optimal price and service rate for a product with non-negligible warranty repair time

Warranty service has attracted increasing attention in the literature, yet existing research often oversimplifies analytical models by neglecting the repair time. While a few works incorporate repair time, they primarily focus on warranty cost and demand forecasting, overlooking its influence on customer satisfaction and long-term profitability. This paper develops a profit optimization model that jointly considers warranty cost and costs from non-negligible repair time to determine optimal product pricing and warranty strategies. Using stochastic modeling and alternating renewal processes, we derive the expected repair demand and warranty cost while accounting for repair time. The model incorporates both the loss cost due to inefficiency and the marginal repair cost associated with improved service performance. Its robustness and applicability are validated under different failure modes and demand functions. Overall, the proposed model provides a theoretical foundation for optimizing pricing and warranty strategies, especially in industries where repair time plays a critical role in customer satisfaction.