Optimal design of multiple batch units with feedstock/product storages

This article derives an analytical solution for determining the optimal siz e of the multiple batch unit plant with storage units. The total cost to be minimized consists of the setup cost of the batch processing units, the in ventory holding cost of feedstock/product storage and the capital cost of t he batch and storage units. A novel approach, which is called the PSW(Perio dic Square Wave) model, is applied to represent the material Rows among the batch and storage units. The PSW model presumes that the material Row betw een unit and storage is a periodic square shaped wave. The resulting optima l batch size has similar characteristics to the classical economic lot sizi ng model such as EOQ or EPQ model in the sense that the batch size is deter mined as the balance between setup and inventory holding cost. However, the influence of inventory holding cost of the PSW model is different from tha t of EOQ/EPQ model. The EOQ/EPQ model includes only the product inventory h olding cost while the PSW model includes all inventory holding costs around the batch unit. The PSW model is suitable for analyzing interlinked batch-storage system an d is more accurate rather than EOQ/EPQ model. The optimal lot size of the P SW model is much smaller than that of EOQ/EPQ model as shown at an example. This is quite a remarkable result considering that the EOQ/EPQ model has b een widely used over the last half century.