A serial inventory system with lead-time-dependent backordering: A reduced-state approximation

Abstract

We study a serial inventory system where the external customers may have a maximum time that they would be willing to wait for delivery in cases of stock-out and the demand would be lost if the remaining delivery lead time of the next available item is longer. This lead-time-dependent backordering behavior subsumes the models of partial backordering regardless of the wait that a customer would experience. In the inventory literature, this behavior has only been analyzed in single-location settings. We study this behavior in a multi-stage setting. We consider continuous review $(S-1,S)$ policies at all stages facing external Poisson demands. Using the method of supplementary variables, we define the stochastic process representing the inventory system and obtain the expressions for the operating characteristics of the inventory system. Based on the solution structures for the special cases, we propose an approximate solution which rests on replacing the state-dependent purchasing decision of the customer with an averaged-out purchase probability computed using only the age of the oldest item. An extensive numerical study indicates that the proposed approximation performs very well. Our numerical study provides additional insights about the sensitivity and allocation of stock levels across stages.

Keywords:

• Inventory theory and control
• multi-echelon inventory
• lead-time-dependent backordering
• method of supplementary variables

Acknowledgments

We thank I.Kiric for his contribution at the early stages of this work.

Notes on contributors

Emre Berk graduated with a B.S. and an M.S. in mechanical engineering from, respectively, Bogazici University, Turkey and Washington State University, USA as a Fulbright scholar. After receiving his M.B.A. from the same institution, he received his Ph.D. from University of Washington. He is currently an associate professor in operations management at the Faculty of Business Administration, Bilkent University. He has also been a visiting scholar at Marshall School of Business, USC and Texas A&M University, USA. His current research projects focus on revenue and supply chain management and sustainability. He has published articles in journals such as Management Science, Operations Research, European Journal of Operational Research, International Journal of Production Economics, IIE Transactions and Annals of Operations Research.

Ayhan Özgür Toy graduated with a B.S. in operations analysis/management from Turkish Naval Academy, an M.S. in operations research from US Naval Postgraduate School. He received his Ph.D. from Bilkent University. He served as a faculty member in Turkish Naval Academy and İstanbul Bilgi University. He is currently an associate professor in Industrial Engineering Department, Yaşar University. He has published articles in journals such as European Journal of Operational Research, International Journal of Production Economics, IIE Transactions, Naval Research Logistics and Applied Soft Computing.

Additional information

Funding

This research has been partially funded by TUBITAK (The Scientific and Technological Research Council of Turkey).