Advance booking discount in the presence of spot market

Abstract

We consider a risk-neutral firm that can procure raw material via long-term contract as well as in spot market, using the material as a one-to-one input to produce a seasonal product and selling it in the customer market. The firm can use the advance booking discount (ABD) program to entice customers to place their orders prior to the selling season. The ABD program provides an opportunity for the firm to update its understanding of the regular demand and spot price. We separately analyse two cases: (NI) no information updating and (IU) information updating cases. In each case, we derive the optimal discount pricing strategy and corresponding expected profit of the firm. By comparing them, we investigate the value of information updating obtained from the pre-committed order. Among others, our study finds that if the product has a relatively high profit margin, or a low profit margin where the raw material spot price is more sensitive to the trading volume, it is optimal for the firm to implement the discount strategy. The optimal discount coefficient in the IU case is never lower than in the NI case. We further find that the optimal discount coefficient in the NI case decreases in spot market volatility; however, it increases in spot market volatility if and only if the firm’s market share is larger than half of the total market demand in the IU case.

Keywords:

• advance booking discount
• spot market
• forward contract
• discount

Acknowledgements

The authors wish to thank three anonymous reviewers who gave valuable suggestions that have helped to improve the quality of the manuscript.

Notes

1 Customers are heterogenous, and in reality not all customers buy through discount. For example, some customers would like to pay at the time of consumption; some customers may not even know when the discount is offered.

Additional information

Funding

This study is supported by the National Natural Science Foundation, China [grant number 71071114], [grant number 70971076], [grant number 71101081] and [grant number 71471101]; Shanghai Leading Academic Discipline Project [grant number B310]; The program of Humanities and Social Sciences of Education Ministry [grant number 11YJC630216] and The Program of Natural Sciences of Guangdong Province [grant number S2012010010794]. This research is also supported by the Natural Sciences and Engineering Research Council of Canada [grant number 312572]. The authors thank the anonymous reviewers and the senior editor for their constructive comments and suggestions.