Multi-period optimization with loss-averse customer behavior: Joint pricing and inventory decisions with stochastic demand

To maximize a firm's profit over a finite planning horizon, we develop a dynamic optimization model by considering loss aversion when making pricing and inventory decisions. We estimate customer demand through a choice model, which incorporates reference price, utility function and customer loss aversion. Our model forms the core of the expert system for decision support. Through a sequence of Bellman equations, we find that the firm's profit is a concave function of price and inventory, and we solve the model optimally. The profit is positively correlated with the reference price, and the price and inventory decisions are non-monotonic functions of loss aversion intensity. Our results shed new light on pricing and inventory management with customer behavior in a multi-period system. Through various theorem developments, we are able to identify the optimal inventory level and the corresponding price. Numerical examples are provided to illustrate and validate the model and to derive managerial insights. To show the potential significance, we demonstrate how a dynamic programming model yields good results with customer loss aversion under realistic customer behavior assumptions. Our system can improve the efficiency of decision making and provide better customer service.