Optimal pricing and inventory policies with reference price effect and loss-Averse customers

Research on customer behavior and marketing has shown that reference prices significantly influence the customers' purchase behaviors and retailers' policies. In this paper, we consider a retailer selling a single product to loss-averse customers over a finite planning horizon, and we address the reference price effect on the retailer's optimal pricing and inventory policies. The customers' demand is determined from their purchasing utility through a Multinomial Logit (MNL) model, and the utility is contingent on the reference price and the current sales price. A generalized model is presented to jointly characterize the optimal pricing and inventory policies to maximize the retailer's total expected profit. First, we derive the optimal myopic policy for the retailer in a single-period and reveal the sensitivity of the optimal myopic policy to the reference price. Next, we perform an equivalent transformation on the model such that the single-period revenue is jointly concave, which is critical to characterize the optimal policy in the multi-period case. Dynamic programming is then used to analyze the optimal policy for the retailer. Interestingly, we find that a reference price-dependent base-stock-list-price policy is proved to be optimal in each period.