The reference effects on a retailer's dynamic pricing and inventory strategies with strategic consumers

We consider a retailer that sells the same or different versions of the product season after season. At the beginning of each season (stage 1), the retailer places an order and sells the product at the full price. As the sales unfold, the retailer has an opportunity to mark down the price (stage 2), which creates an incentive for strategic consumers to delay their purchases for price discount. However, consumers do not know the markdown price exactly when they time their purchases; instead, they learn from the retailer's past prices and form their estimate of the markdown price, called the reference price, to decide if they purchase at the full price or wait for the markdown in the current selling season. We characterize the properties of the optimal ordering and markdown decisions and show that markdowns, if adopted appropriately, do not necessarily destroy the stability of a business even in the presence of strategic consumers. Furthermore, the consumers' reference exhibits a mean reverting pattern under certain conditions; that is, the reference fluctuates around a mean value, reflecting the practice of most stable businesses. We conduct numerical studies to investigate the impact of consumer learning about the reference price and various system parameters on the retailer's optimal strategies and profitability in the presence of strategic consumers.