OPTIMAL DESIGN OF MULTIPLE BATCH UNITS WITH FEEDSTOCK/PRODUCT STORAGES

Abstract

This article derives an analytical solution for determining the optimal size 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 inventory holding cost of feedstock/product storage and the capital cost of the batch and storage units. A novel approach, which is called the PSW(Periodic Square Wave) model, is applied to represent the material flows among the batch and storage units. The PSW model presumes that the material flow between unit and storage is a periodic square shaped wave. The resulting optimal batch size has similar characteristics to the classical economic lot sizing model such as EOQ or EPQ model in the sense that the batch size is determined as the balance between setup and inventory holding cost. However, the influence of inventory holding cost of the PSW model is different from that of EOQ/EPQ model. The EOQ/ EPQ model includes only the product inventory holding 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 and is more accurate rather than EOQ/EPQ model. The optimal lot size of the PSW 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 been widely used over the last half century.