An appropriate scheduling system is needed in manufacturing activities to minimize production time and costs. Flow shop is one type of production flow that widely used in manufacturing. Based on the demand criteria, it has been known as a scheduling problem called closed shop. This scheduling emphasizes the make-to-stock (MTS) which produces a stock. We take the closed shop scheduling case studies from an existing literature and optimize scheduling using max-plus automata optimum. We compare the result with regular scheduling and the previous result in the literature. We show that the result of max-plus automata optimum scheduling are optimum compared than the existing regular scheduling and the existing previous result of the literature.