An Economic Production Quantity Model with Work-In-Process Inventories

Several extensions of the classical Economic Production Quantity (EPQ) have been proposed in the past, but only few of them considered Work-In-Process (WIP) inventories. When considering manufacturing and/or process systems, these inventories may represent a significant, as well as strategic, inventory cost. In particular, processing raw materials to obtain finished products requires significant investments of resources and processing times, thus giving evidence to the critical issues linked to the WIP growth. Therefore, when calculating the optimal production batch size in cases, e.g., of long processing times, it may be worthily to consider the holding costs due to the WIP piling, along with raw materials purchasing and the inventory of finished products. Starting from a literature analysis and some industrial cases of reference, the present contribution proposes a new EPQ model, encompassing the Work-In-Process inventory, in a complete systematisation of the company inventories, defined as EPQ-WIP model. Depending on different industrial applications (e.g. milk processing, rubber manufacturing, etc.) different variants of the EPQ-WIP model will be analytically investigated and compared, initially starting from the classical EPQ hypotheses and, then, progressively introducing new features and removing hypotheses, so as to consider different productive situations. Finally, a numerical analysis will show the impact of the proposed model, when compared to the basic EPQ approach, thus leading to managerial and applicative considerations. In fact, the savings related to the adoption of the EPQ-WIP model, allowing a better detail of the system cost components, will be compared to the results determined by the classical EPQ approach.