Mathematical modelling for determining the replenishment policy for deteriorating items in an EPQ model with multiple shipments

ABSTRACT

This paper extends an economic production quantity (EPQ) model for deteriorating items when the delivery policy is based on multiple shipments. A continuous inventory policy for satisfying demand has been considered in the classic EPQ model. While in an integrated production–inventory–delivery system, the multi-shipment approach is actually used instead of the continuous issuing policy. On the other hand, the EPQ model has not been developed for deteriorating items with multiple shipments. This paper considers the time-varying deterioration rate and finds optimal replenishment lot size which minimises the long-run average cost function after proving its convexity. Finally, mathematical modelling and analysis are employed for a laboratory kit production system. Then, impact factors which can modify total cost are recognised and optimal replenishment lot size, as well as optimal quantity of each shipment, is found in different situations.

KEYWORDS:

• Mathematical modelling
• replenishment lot size
• inventory
• multiple shipments
• deteriorating items

Additional information

Notes on contributors

Solaleh Sadat Kalantari

Solaleh Sadat Kalantari received the B.Sc. degree in industrial engineering from the K.N.Toosi University of Technology, and the M.Sc. degree in industrial engineering from the University of Tehran. Currently, she is a senior PhD student in Industrial Engineering. Her research interests include Pricing and Revenue Optimization, Game theory, Inventory Control, and Supply Chain Management.

Ata Allah Taleizadeh

Ata Allah Taleizadeh received the B.Sc. degree in industrial engineering from the Islamic Azad University of Qazvin, and the M.Sc. and PhD degrees from the Iran University of Science and Technology, both in industrial engineering. He is currently an Associate Professor of Industrial Engineering, at University of Tehran. He serves as an Editor/Associated Editor/Editorial Board Member for a number of international journals and has published extensively in reputable and leading journals such as European Journal of Operational Research, OMEGA; International Journal of Management Sciences, IEEE Transactions On Systems, Man, and Cybernetics: Systems, International Journal of Production Economics, Annals of Operation Researches, Service Sciences, Transportation Research: Part E, etc. His research area includes Pricing and Revenue Optimization, Inventory Control, and Supply Chain Management.