Warehouse location and two-echelon inventory management with concave operating cost

Abstract

In this paper, we study a location–inventory network design problem which jointly optimises the warehouse location, the warehouse–retailer assignments, the warehouse–retailer echelon inventory replenishment and the safety stock-level decisions over an infinite planning horizon. The consideration of the facility operating cost, the safety stock cost and the two-echelon inventory cost results in an MIP model with several nonlinear terms. Due to the complex trade-offs among the various costs and multiple nonlinear terms in the model, traditional solution approaches no longer work for this problem. We outline a polymatroid cutting-plane approach based on the submodular property of the cost terms to address this problem. Computational results demonstrate that the cutting-plane method based on polymatroid inequalities can efficiently solve randomly generated instances with moderate sizes.

Keywords:

• supply chain network design
• facility location
• multi-echelon inventory management
• polymatroid cutting plane

Acknowledgements

We would like to thank the Editor and the referees for constructive comments that led to this improved version.

Additional information

Funding

This research is supported by National Natural Science Foundation of China [grant number 70801014], [grant number 71171047], [grant number 71222103], [grant number 71201080]. Natural Science Foundation of Jiangsu Province [grant number BK2011541]. Qing Lan Project of Jiangsu Province, Social Science Foundation of Jiangsu Province [grant number 14GLC001]. MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant number 11YJCZH188], and China Postdoctoral Science Foundation [grant number 2012M511256], [grant number 2013T60526].