The value of modeling with reference effects in stochastic inventory and pricing problems

• We analyze a periodic-review inventory system under reference effects.
• The random demand is dependent on the price and the reference price.
• We show that high dependence on a good history increases the profit.
• The firm that ignores the dynamic structure suffers from the revenue.
• The firm loses profit if it cannot recognize the existence of reference effects.

We analyze a periodic review inventory system in which the random demand is contingent on the current price and the reference price. The reference price captures the price history and acts as a benchmark against which the current price is compared. The randomness is due to additive and multiplicative random terms. The objective is to maximize the discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We study three key issues using numerical computation and simulation. First, we study the effects of reference price mechanism on the total expected profit. It is shown that high dependence on a good history increases the profit. Second, we investigate the value of dynamic programming and show that the firm that ignores the dynamic structure suffers from the revenue. Third, we analyze the value of estimating the correct demand model with reference effects. We observe that this value is significant when the inventory related costs are low.