Joint Dynamic Optimization of Price and Two-Dimensional Warranty Policy

This paper studies the joint optimization of price and two-dimensional (2-D) warranty policy with limits of both warranty length and usage. For this purpose, in this paper, we first propose a new sales function to characterize the joint influence of price, warranty length, and usage limit on the sales rate while considering the influence of the heterogeneous customer usage rate. Then, we model the joint dynamic optimization of price and 2-D warranty policy as a nonlinear optimal control problem, and solve it via a numerical approach based on Pontryagin's maximum principle. We show that the proposed dynamic 2-D warranty policy can help achieve higher profits than the existing one-dimensional policies and static 2-D policy.