Optimal option purchase decision of a loss-averse retailer under emergent replenishment

Abstract

This paper studies the optimal option purchase of a loss-averse retailer under emergent replenishment. It is assumed that all or part of the excess demands in a stock-out situation can be replenished, and the loss-averse retailer's optimal option purchase quantity is investigated. It is found that the loss-averse retailer should not purchase options and only needs to replenish the inventory under certain conditions. When maximizing the expected utility without shortage cost, the loss-averse retailer's optimal option purchase quantity is decreasing in the loss aversion coefficient. To maximise the expected utility with shortage cost, a larger shortage cost implies a bigger option purchase quantity. If the shortage cost exists, there will be a loss on the expected profit and utility for the loss-averse retailer who selects an optimal option purchase quantity without shortage cost. Given the optimal option purchase quantity, it is proven that the loss-averse retailer's expected profit is decreasing in the loss aversion coefficient. Therefore the retailer should choose a proper loss aversion preference to balance between the two objectives of profit maximization and loss aversion preference. As a result of these findings, some management insights are recommended to the loss-averse retailer in selecting the option purchase quantity.

Keywords:

• purchasing
• option contract
• replenishment
• loss-averse
• shortage cost

Acknowledgments

The authors would like to thank the associate editor and three anonymous referees for their valuable suggestions and comments, which help us to improve this paper greatly.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Felix T. S. Chan   http://orcid.org/0000-0001-7374-2396

Notes

1 http://www.fcbco.com/blog/bid/156174/The-True-Cost-of-a-Back-Order

2 The proof can be found in the Appendix.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China with grant 71871026, the Humanities and Social Sciences Foundation of Ministry of Education of China with grant 18YJC630214, the Natural Science Foundation of Shandong Province with grant ZR2017MG002 and the Research Committee of The Hong Kong Polytechnic University.