Abstract
This paper investigates optimal maintenance of equipment under uncertainty and the options of scrapping versus keeping the equipment as a back up (at a cost). This set up is used to analyze three points. The first observation is that the continuous, deterministic and even the unconstrained stochastic problem allow for closed form analytical solutions, realistic constraints require numerical means to solve the corresponding stochastic managerial problem. Second, the possibility to switch at negligible costs between different modes (here running or mothballing the equipment) depending on current states requires a condition in addition to the familiar value matching and smooth pasting conditions, namely continuity of the second derivative of the value function (or super contact). Equipped with these findings the analysis turns to the third point of quantifying numerically the value of keeping equipments as a back-up instead of scrapping.
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Wirl, F. Optimal maintenance and scrapping versus the value of back ups. Comput Manage Sci 5, 379–392 (2008). https://doi.org/10.1007/s10287-007-0059-7
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DOI: https://doi.org/10.1007/s10287-007-0059-7