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We consider a physical asset consisting of complex systems, where the systemsmay require upgrades during the lifetime of the asset. In practice, the assetowner and system supplier can make the upgrade decisions together, requiring adecision support model that can be jointly used to optimize the total benefitfor both parties. Motivated by a real-life use case including an asset ownerand a system supplier, we build a continuous-time model to optimize the upgradedecisions of a system during the fixed lifetime of the asset. In our model, wecapture the key critical factors that drive the upgrade decisions: increasingfunctionality requirements due to evolving technology, age-dependentmaintenance costs, a predetermined overhaul plan of the asset, and the lifetimeof the asset. A system upgrade is less costly if it is executed jointly with anasset overhaul. We first analyze the case with no additional cost of upgradingoutside an overhaul. We analytically characterize the structure of the optimalupgrade policy under various realistic assumptions that lead to different typesof cost functions. We then use these results as a building block tocharacterize the optimal policy for a generalized cost function. When there isa penalty for upgrading outside an overhaul moment, we propose a dynamicprogramming approach that efficiently determines the optimal upgrade policy byusing our analytical results. We also prove that as this penalty increases, theoptimal policy can only change to one where the number of upgrades not jointlyexecuted with overhauls is reduced. However, the optimal number of upgrades isa non-increasing function of this penalty. Also surprisingly, more overhaulsmay lead to a smaller number of upgrades under the optimal policy.

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