In modern supply chain networks, multiple buyers often generate high and uncertain demand, making fixed production policies insufficient for achieving cost efficiency and maintaining product quality. This paper develops a single-vendor multi-buyer supply chain model that incorporates variable production rates, imperfect product quality, service-level constraints, and distribution-free lead-time demand. The unit production cost is assumed to depend on the production rate, and three alternative quality functions are proposed to characterize the relationship between production rate and process quality. The objective is to determine the optimal production and inventory policy that minimizes the total supply chain cost under a single-setup multiple-delivery framework. Closed-form analytical results and an efficient solution algorithm are developed to obtain the optimal decisions. Numerical examples and sensitivity analyses are presented to validate the model and investigate the effects of key parameters. The findings reveal that production-rate flexibility plays a critical role in reducing total supply chain cost while mitigating quality deterioration, providing valuable managerial insights for coordinated supply chain operations.