Dynamic pricing strategies for new products with extended warranty contracts

Abstract

An extended warranty provides consumers the opportunity to rectify product failures at little or no cost after the expiry of the base warranty. Empirical evidence has shown that the selling of extended warranty contract (EWC) has become a profitable business in many manufacturing and retail industries. This thesis investigates the dynamic pricing problem for a new product with the option of purchasing an extended warranty contract (EWC). The research simultaneously determines the pricing strategies for both the product and the associated EWC, and the production rate to maximize the manufacturer’s long-term total profit. The results show that the provision of EWC will significantly affect the optimal pricing strategy for the new product, and may also affect its optimal production plan. The research establishes three mathematical models for making optimal pricing decisions under different operational settings. The first model considers a centralized selling system in which the manufacturer sells the product and offers the associated EWC to the consumer directly. The second model extends the first one by incorporating the production and inventory decisions in the analysis. The third model considers a decentralized system in which the manufacturer sells the new product to consumers through an independent retailer. The EWC can be offered either by the manufacturer or by the retailer. It is shown that each scenario leads to a differential Stackelberg game in which the manufacturer and the retailer are players. For the first model, the Pontryagin maximum principle is used to derive the necessary condition for the optimal pricing strategies for both the new product and the associated EWC. Some properties for pricing the new product optimally are then studied. Apart from analysing the characteristics of the optimal pricing strategy under general demand conditions, closed-form solutions for the problem are also derived for some specific demand functions. In cases where closed-form solutions cannot be found, a gradient algorithm is applied to solve the problem numerically. In the second model, the production rate becomes a decision variable because the unit production cost depends on the chosen production rate. Results of the analysis show that the optimal selling price for the EWC remains the same as that in the first model, while the optimal selling price for the new product are affected by the production rate. The results also show that the gradient algorithm fails to converge, thus is no longer suitable for the second model due to the complexity caused by the boundary conditions. A more robust control vector parameterization method is then developed to compute the numerical solution. Analysing the third model theoretically indicates that some necessary conditions related to the optimal wholesale price and the optimal retail price must be satisfied for the existence of an open-loop Stackelberg equilibrium. Some important managerial insights are derived on the basis of the properties characterizing the optimal solution. The control vector parameterization method is then further developed to solve the differential game problem. Numerical experiments are then carried out to demonstrate which distribution channel results in the largest profit.