Determination of price and warranty length for a Gamma lifetime distributed product

In this paper, a decision model is presented for manufacturing firms to determine the optimal price and warranty length to maximize profits based on the pre-determined life cycle. We consider the free renewal warranty policy under which failed items are renewed free of charge until a specified total operating time has been achieved. The expected number of renewals based on the warranty length is derived for a gamma lifetime distributed product and the total cost of production and providing warranty is evaluated. A solution approach using the maximum principle is described, and is applied to two specific types of markets. The first type of market considers the case of static sales rate function with a positive discount rate, and the second type of market considers the case of separable sales rate function with a zero discount rate. A sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal solution. Some conclusions are drawn based on the sensitivity analysis.