Advance booking discount in the presence of spot market

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.