Setting fulfillment-time guarantees for accepting customer orders in a periodic-review base-stock inventory system

Abstract

Retailers are increasingly promising a maximum fulfillment time window for fulfilling customer orders. Motivated by such guarantees, we consider an infinite-horizon periodic-review base-stock inventory system that imposes an endogenously determined fulfillment-time limit for accepted orders. The inventory position is reviewed every fixed T periods and an order is placed to bring the system inventory up to R, the target base stock. The replenishment lead time is a constant of L periods. In each period, the realized consumer demand is accepted only if it can be filled within a guaranteed time limit of $\tau$ periods. By incorporating a fulfillment-time limit, the model allows both backorders and lost sales. The objective is to find the strategy that minimizes the long-term average cost per unit time by selecting the base stock and guaranteed-delivery time limit. The behavior of the optimal R with respect to the guaranteed service time $\tau$ is investigated, and subsequently, the best value of $\tau$ is identified. Interestingly, when $\tau$ is greater than or equal to L, the best value of $\tau$ is independent of the holding cost and the base stock R. Regularity conditions are developed that assure the cost function is unimodal in R, guaranteeing the optimal base-stock solution can be found easily for a broad family of demand distributions. The solution procedure is extended to the case when the mean customer demand depends on the fulfillment time window promised by the retailer. We find greater customer sensitivity to the fulfillment time leads to a decrease in the optimal fulfillment time guarantee.

Keywords:

• Inventory
• periodic review
• (R
• T) policy
• service time guarantees
• fulfillment time window
• customer impatience
• lost sales
• partial backorders

Acknowledgments

The authors are grateful to the department editor, the associate editor, and anonymous reviewers for their helpful comments and constructive suggestions which significantly improved this study.

Additional information

Funding

The fisrt author is supported by the National Natural Science Foundation of China (No. 71772063).

Notes on contributors

Yanyi Xu

Yanyi Xu is a professor in the School of Business at East China University of Science and Technology. He received his PhD in 2006 in operations management from Purdue University.  His research interests include supply chain risk management and inventory management. 

Doğan A. Serel

Doğan A. Serel is a faculty member at Institute of Management Technology Dubai, UAE. His research interests lie in supply chain management, inventory and pricing models, and quality management. He holds a PhD in management from Purdue University.

Arnab Bisi

Arnab Bisi is an associate professor of practice in operations management and business analytics at the Johns Hopkins University Carey Business School. His teaching and research interests include operations management, business analytics, supply chain management, data analytics, asset pricing, optimization models, and business statistics. Dr. Bisi received a PhD in statistics and mathematics from Hong Kong University of Science and Technology, and an MStat degree from the Indian Statistical Institute. 

Maqbool Dada

Maqbool Dada is a professor of operations management and business analytics in the Carey Business School of Johns Hopkins University. His research interests include stochastic inventory theory, pricing models and healthcare operations.