Optimal pre-order strategy with delay in payments

Advance selling with pre-orders has become a common practice in many industries. To encourage more consumers to purchasing in advance, retailers now try new forms of advance selling to allow consumers to complete their pre-orders after solving valuation uncertainty. Motivated by this emerging industry practice, this paper focuses on delay in payments from a retailer to consumers during the advance selling period and considers several pre-order strategies for the retailer, namely, free pre-order (FP), deposit pre-order (DP), and deposit expansion pre-order. Under the price commitment mechanism, we first derive not only the thresholds for pre-order strategies with stochastic demand and uncertain product valuation but also the retailer's optimal price, quantity, and advance selling strategy, which are contingent on the relative size of the marginal cost and the lower bound of consumer valuation. Then, we find that the retailer should sell in advance even when the expected valuation is sufficiently low, or the marginal cost is relatively high. Besides, we reveal that the retailer is more likely to order a smaller quantity under the FP and DP strategies. Finally, we extend the model to a fixed pricing mechanism to further elucidate the retailer's optimal decisions. By comparing these two pricing mechanisms, we find that, under certain conditions, the optimal pre-announced pricing strategy converges to the fixed pricing strategy.