On optimal upgrade level for used products under given cost structures

In spite of the growing share of the second-hand market, often customers of used products encounter the following three problems: (a) they are uncertain regarding the durability and performance of these products due to lack of information on the item’s past usage and maintenance history, (b) they are uncertain about the accurate pricing of warranties and the post-warranty repair costs, and (c) sometimes, right after the sale, used items may have high failure rate and could be harmful to their new owner. Due to these problems, the dealers are currently carrying out actions such as overhaul and upgrade of the used products before their release. Reliability improvement, which is closely related to the concept of warranty, for used products is a relatively new concept and has received very limited attention. This paper also develops a stochastic model which results in the derivation of the optimal expected upgrade level under given structures of the profit and failure rate functions. We provide a numerical study to illustrate our results.