Joint Dynamic Optimization Of Price And Two-dimensional Warranty Policy

With the rapid development of technology and improvement of living standards,various durables,such as different types of automobiles,have become accessible and affordable for individuals.In addition to price,customers' decisions are also significantly influenced by the durables' reliability,which is generally perceived by customers indirectly through warranty policy,especially for new products.Warranty can well signal the reliability and quality of a product,and has been recognized as an important marketing variable in addition to price.Manufacturers usually apply two-dimensional warranty policy(i.e.,warranty with both warranty length limit and usage limit)on expensive durables such as automobiles.Compared with inexpensive products,the optimization on marketing decisions of expensive products may bring a lot more benefits to manufacturers.Moreover,there is usually diffusion effect in the sales of durables,so that the application of dynamic decision is effective.Thus,it is of great interest to jointly optimize both warranty policy and price to maximize the profit.Note that both warranty length limit and usage limit influence the sales rate and warranty cost.Providing higher warranty length limit and usage limit can promote sales,but will also cause higher warranty cost.Furthermore,the usage rate of products has been known to be highly heterogeneous among customers.The usage rate distribution among customers also influences the sales rate and warranty cost.The attractiveness of the given warranty length limit and usage limit is different to customers with different usage rate.For products under different usage rate,the growth of hazard rate is also different,which leads to different warranty cost.In order to perform joint dynamic optimization of price and two-dimensional warranty,we firstly propose a new sales function to characterize the joint influence of price,warranty length and usage limit on the sales rate,utilizing Bass model and Glickman-Berger model,while also considering the influence of diffusion effect and heterogeneous customer usage rate.In addition,we also take the influences of heterogeneous customer usage rate on product failures into account through considering the usage degradation.We then describe the joint dynamic optimization of price and two-dimensional warranty policy as a nonlinear optimal control problem.To deal with its analytically computational complexity,the proposed problem is solved by numerical approach while employing the Pontryagin's maximum principle.Moreover,we implement sensitivity analysis on the proposed strategy and compare it with four alternative strategies.