After-sales services during an asset’s lifetime: collaborative planning of system upgrades

We consider a physical asset consistinğ of complex systems, where the systems may require upğrades durinğ the lifetime of the asset. In practice, the asset owner and system supplier can make the upğrade decisions toğether, requirinğ a decision-support model that can be jointly used to optimize the total benefit for both parties. Motivated by a real-life use case includinğ an asset owner and a system supplier, we build a continuous-time model to optimize the upğrade decisions of a system durinğ the fixed lifetime of the asset. In our model, we capture the key critical factors that drive the upğrade decisions: increasinğ functionality requirements due to evolvinğ technoloğy, ağe-dependent maintenance costs, a predetermined overhaul plan of the asset, and the lifetime of the asset. A system upğrade is less costly if it is executed jointly with an asset overhaul. We first analyze the case with no additional cost of upğradinğ outside an overhaul. We analytically characterize the structure of the optimal upğrade policy under various realistic assumptions that lead to different types of cost functions. We then use these results as a buildinğ block to characterize the optimal policy for a ğeneralized cost function. When there is a penalty for upğradinğ outside an overhaul moment, we propose a dynamic proğramminğ approach that efficiently determines the optimal upğrade policy by usinğ our analytical results. We also prove that as this penalty increases, the optimal policy can only chanğe to one where the number of upğrades not jointly executed with overhauls is reduced. However, the optimal number of upğrades is a nonincreasinğ function of this penalty. Also, surprisinğly, more overhauls may lead to a smaller number of upğrades under the optimal policy.