A queuing-inventory model for manufacturing systems with fluid-type inventory

This study considered a make-to-order manufacturing system combined with a fluid-type inventory. In this system, customers arrive at the system to place an order for a customized product. A machine manufactures products, thereby handling orders based on the first-come-first-served principle. The system has a preprocessing facility that converts the raw materials into a ready-to-use inventory. The inventory is stored in finite-capacity storage and consumed to manufacture finished products. The preprocessing facility replenishes the inventory based on the well-known (s,S)-policy with the setup time. This study proposes a new queuing-inventory model to analyze this composite system. The stationary joint probability distribution for the unmet demands and inventory level is presented in closed form. Next, a cost model is constructed, followed by numerical examples.