Quality improvement and pricing with reference quality effect

This article studies a problem of joint pricing and dynamic product quality investment with consumers' reference quality effect under the existence of quality inflation. Optimal control models are constructed to maximize the total profit with a limited quality investment capacity, where the demand is sensitive to historical product quality level. The optimal quality investment strategies for finite and infinite planning horizon are given respectively by solving these optimal control models on the basis of Pontryagin's maximum principle, which enables the exact trajectory of the optimal quality investment with the reference quality effect over time to be depicted. In addition, an effective algorithm is designed to generate the optimal joint pricing and dynamic quality investment policy for the system. The main difference between the strategy of finite planning horizon and that of infinite planning horizon is that the latter is a constant. Our study indicates that it is never optimal for firm to increase quality investment all the way throughout the planning horizon. The level of quality investment is higher when taking into account the impact of reference quality. Moreover, numerical example is given to illustrate the validness of the theoretical results. Also, sensitivity analysis is carried out to show how system parameters affect the optimal policies, and some managerial suggestions are presented.