Application of optimal control theory to product pricing and warranty of free replacement under the influence of basic lifetime distributions

This study investigates optimal policies for determining price and warranty length when free replacement of defective items is the business policy and the demand is dependent on price, warranty, and cumulative sales. We apply optimal control theory to a profit-maximization model that takes into consideration the expected warranty cost per item. The maximization of market values is based on a pre-determined life cycle and spans across both expansion and saturation phases of the market. We further investigate the optimal policies for a number of basic lifetime distributions, when the demand function is under the setting of separable and logistic growth. We found that as the growth of a product enters different phases of the market, optimal decision policies are characterized by simultaneously increasing or reducing both price and warranty length.