Joint Bundle Design and Pricing for Extended Warranty Providers Servicing Multi-Tier Products
Yajing Chen, Yanrong Li, Xiao-Lin Wang, Zhi-Sheng Ye
TL;DR
This work tackles the joint design and pricing of extended warranty contracts for multi-tier products from a third-party provider, where each contract covers a differentiated bundle of subsystems. The problem, denoted as JDPEW, is NP-hard due to the combinatorial growth of subsystem bundles, and is solved via two approaches: a globally optimal MISOCP reformulation (JDPEW-MISOCP) suitable for small-scale instances, and an Iterative Two-Step (ITS) method that alternates EW design and pricing to scale to larger problem sizes. Numerical experiments on an automobile EW setting show that the joint design/pricing framework consistently outperforms benchmarks, with profits increasing in the number of subsystems and higher failure probabilities, while ITS achieves near-optimal profit at a fraction of the computational cost. The results provide practical guidance for third-party EW providers to tailor differentiated bundles and prices across customer groups, reduce advertising costs, and respond to risk and market heterogeneity, with managerial insights highlighting the importance of high-value customers and the impact of promotion costs. Future work could integrate personalized usage data and subsystem interactions to further refine demand and pricing signals.
Abstract
Extended warranties (EWs) constitute a significant source of revenue for capital-intensive products. Such products comprise multiple subsystems, enabling flexible EW design. For example, providers can bundle tailored sets of subsystems within different EW contracts, facilitating the creation of a service menu with differentiated warranty options. From the perspective of a third-party EW provider servicing multi-tier products, we develop a novel model to jointly optimize bundle design and pricing for EW options in order to maximize the expected total profit. Specifically, the problem involves determining which contracts-each containing a differentiated bundle of subsystems-to recommend for the multi-tier products and identifying the appropriate price for each contract. As the complexity of the joint optimization problem increases exponentially with the number of subsystems, we devise two solution approaches. The first approach leverages a mixed-integer second-order cone programming reformulation, which guarantees optimality but is applicable only for a small number of subsystems. The second approach utilizes an iterative two-step process, offering enhanced computational efficiency for scenarios involving a large number of subsystems. Numerical experiments validate the effectiveness of our model, particularly in scenarios characterized by high failure probabilities and a large number of subsystems.