Production and distribution are fundamental operational functions in supply chains. The main challenge is to design algorithms that optimize operational performance by jointly scheduling production and delivery of customer orders. In this paper we study a model of scheduling customer orders on multiple identical machines and their distribution to customers afterwards. The goal is to minimize the total time from release to distribution plus total distribution cost to the customers. We design the first poly-logarithmic competitive algorithm for the problem, improving upon previous algorithms with linear competitive ratios. Our model generalizes two fundamental problems: scheduling of jobs on multiple identical machines (where the goal function is to minimize the total flow time) as well as the TCP Acknowledgment problem.