A two-warehouse integrated inventory model with imperfect production process under stock-dependent demand and quantity discount offer

ABSTRACT

This paper presents a single-vendor single-buyer integrated inventory model with an imperfect production process of the vendor. The demand at the buyer is dependent on the on-hand stock (both at the own and rented warehouses) and the vendor offers a quantity discount to motivate the buyer to buy more quantities. The buyer's own warehouse has a limited capacity but, if needed, he can use rented warehouse of unlimited capacity. The vendor fulfils the buyer's order quantity in multiple equal-sized shipments. The objective is to determine the vendor's shipment scheme in response to the buyer's order quantity so that the average total cost of the integrated system is minimised. For a numerical example, the optimal solution of the integrated inventory model is obtained and effects of key model-parameters on the optimal solution are examined.

KEYWORDS:

• Inventory
• vendor–buyer
• defective item
• two-warehouse
• quantity discount

Acknowledgments

The authors are grateful to the anonymous reviewers for their valuable comments and suggestions that helped in improving the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Payel Mandal

Payel Mandal is a NBHM Post Doctoral Fellow in the Department of Mathematics, Jadavpur University, Kolkata, India. She did her MSc in Mathematics from IIT Madras and did her PhD in Optimisation from IIT Kharagpur, Kharagpur, India. Her research interests include optimisation and convex analysis, multiobjective programming, optimal control theory, inventory/supply chain management. Her research papers have published in Applied Mathematics and Computation, International Journal of Mathematics and Operational Research and J. Adv. Math. Stud.

Bibhas Chandra Giri

Bibhas Chandra Giri is an Associate Professor in the Department of Mathematics, Jadavpur University, Kolkata, India. He did his MS in Mathematics and PhD in Operations Research both from Jadavpur University, Kolkata, India. His research interests include inventory/supply chain management, production planning and scheduling, reliability and maintenance, and his research papers have appeared in Naval Research Logistics, International Journal of Production Research, OMEGA, Journal of the Operational Research Society, European Journal of Operational Research, International Journal of Production Economics and other journals. He was a JSPS Research Fellow at Hiroshima University, Japan during the period 2002–2004, Humboldt Research Fellow at Mannheim University, Germany during the period 2007–2008 and a Fulbright-Nehru Senior Research Fellow at Louisiana State University, USA in 2012.