After-Sales Services During an Asset’s Lifetime: Collaborative Planning of System Upgrades

Fiona Sloothaak, Alp Akçay, Geert-Jan van Houtum (Corresponding author), Matthieu van der Heijden

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We consider a physical asset consisting of complex systems, where the systems may require upgrades during the lifetime of the asset. In practice, the asset owner and system supplier can make the upgrade decisions together, requiring a decision-support model that can be jointly used to optimize the total benefit for both parties. Motivated by a real-life use case including an asset owner and a system supplier, we build a continuous-time model to optimize the upgrade decisions of a system during the fixed lifetime of the asset. In our model, we capture the key critical factors that drive the upgrade decisions: increasing functionality requirements due to evolving technology, age-dependent maintenance costs, a predetermined overhaul plan of the asset, and the lifetime of the asset. A system upgrade is less costly if it is executed jointly with an asset overhaul. We first analyze the case with no additional cost of upgrading outside an overhaul. We analytically characterize the structure of the optimal upgrade policy under various realistic assumptions that lead to different types of cost functions. We then use these results as a building block to characterize the optimal policy for a generalized cost function. When there is a penalty for upgrading outside an overhaul moment, we propose a dynamic programming approach that efficiently determines the optimal upgrade policy by using our analytical results. We also prove that as this penalty increases, the optimal policy can only change to one where the number of upgrades not jointly executed with overhauls is reduced. However, the optimal number of upgrades is a nonincreasing function of this penalty. Also, surprisingly, more overhauls may lead to a smaller number of upgrades under the optimal policy.
Original languageEnglish
Pages (from-to)212-232
Number of pages21
JournalService Science
Issue number3
Publication statusPublished - 1 Sept 2023


Funding:This publication is part of the project “Maritime Remote Control Tower for Service Logistics Innovation (MARCONI)” (project 439.18.309) of the research program “Integrator-Logistics as Enabler for Enhancing Society,” which is (partly) financed by the Dutch Research Council (NWO).

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek


    • age-dependent cost functions
    • maintenance
    • obsolescence
    • technology advancement
    • upgrade policy


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