Joint pricing and inventory control with reference price effects and price thresholds: A deep reinforcement learning approach

Abstract

The literature has recognized that the consumers’ purchase behaviour and retailers’ policies are significantly influenced by reference price effects, but has yet to provide flexible operational decisions on the threshold-based reference price. In this study, we consider an infinite-horizon joint pricing and inventory control problem in which the customers’ psychological behaviour is modelled as reference price effects and price thresholds. Specifically, there is a region of price insensitivity allowing for threshold effects around the reference price, which is formulated as a three-regime piecewise function with the consideration of gain, loss, and indifference. A resolution approach based on proximal policy optimization is proposed to address the combinatorial complexity of continuous domains in action-state spaces. Tested on eight different market environments, we demonstrate how the deep reinforcement learning (DRL) approaches the ground-truth algorithm and outperforms three other algorithms. Moreover, near-optimal strategies and convergence results are obtained with regard to initial states and price thresholds of the system. The results show that the order-up-to level is increasing in price thresholds and the sales price is decreasing in them, while the retailer’s profits suffer from the increase in thresholds. Besides, the sales price is increasing in the reference price. In the steady state of the environment, the average profits are higher than those in which the retailer ignores reference price effects with thresholds. Our study provides evidence that black-box DRL algorithms can effectively solve joint pricing and inventory control problems with psychologic and behavioural concerns.