A new EPQ model: integrating lower pricing, rework and reject situations

Abstract

The economic production quantity (EPQ) is a well-known and commonly used inventory control technique. It has been used for well over 50 years to optimize lot sizes in transportation/production. The standard results are easy to apply but are based on a number of assumptions. A common assumption in the EPQ model is that all units produced are of perfect quality, this will underestimate the actual required quantity. Many researchers have studied the effects after relaxing this assumption on the EPQ model. The previous studies had considered that imperfect quality and defective items are either to be reworked instantaneously and kept in stock or rejected at a cost. The objective of this paper is to provide a framework to integrate lower pricing, rework and reject situations into a single EPQ model. A 100% inspection is performed in order to identify the amount of good quality items, imperfect quality items and defective items in each lot. This model assumes that items of imperfect quality, not necessarily defective, could be used in another production situation or sold to a particular purchaser at a lower price. The electronic and clothing industries give good examples for such situations. A mathematical model is developed and a numerical example is presented to illustrate the solution procedures. It is found that the time factor of when to sell the imperfect items is critical, as this decision will affect the inventory cost and the batch quantities.

Keywords:

• lower pricing
• imperfect quality items
• defective items
• lot size
• EPQ

Acknowledgement

The authors would like to thank the anonymous referees for their helpful suggestions and comments, which have improved the contents and style of this article.

WENG MENG CHAN is a PhD candidate in the Department of Mechanical Engineering at Monash University, Caulfield Campus. His research interests include quality engineering and management, statistical process control and production and inventory systems.

RAAFAT IBRAHIM is an Associate Professor and has a distinguished and internationally recognized track record and more than 20 years experience in research in production management, operation research, quality improvement, concurrent engineering and supply chain management. He has more than 170 refereed international journal and conference publications in the areas of failure analysis, quality improvement, supply chain management, and operation research. He has carried out several major investigations of failures due to cracks and flaws in pressure vessels. He has supervised postgraduate research students in the areas of quality improvement, supply chain management and operation research.

PAUL B. LOCHERT, MSc (Monash) BSc, Dip Ed (Adelaide) currently holds the positions of Chair, NORCA Consulting Pty Ltd, Principal, PBL Statistical Consultancy and Honorary Research Associate, Department of Mechanical Engineering Monash University; formerly he was an Associate Professor in the Department of Mathematics at Monash University. He has over 35 years of teaching experience in the areas of applied statistics and operations research with a focus on applications in business, computing, engineering and social science. Research interests include modelling business systems particularly in the area of supply chain management and statistical modelling of business and environmental systems.