Determining the optimal warranty price based on the producer's and customers' risk preferences

We propose a warranty model for the free-replacement, fixed-period warranty policy that determines the optimal warranty price for a given warranty period. We assume a constant failure rate for the product, constant repair costs throughout the warranty period, and a producer's and customers' risk aversion for future repair costs. Using the exponential utility function and the gamma failure rate distribution, we derive the decision model that maximizes the producer's certainty profit equivalent. Furthermore, the sensitivity of the optimal warranty price is analyzed with a numerical example with respect to such factors as (1) the producer's and customers' risk preferences, (2) their perceptions about the product failure rate, (3) the customers' loyalty to the original producer in repairing failed products, and (4) the customers' repair price.