Comput Manage Sci (2008) 5:379–392 DOI 10.1007/s10287-007-0059-7 ORIGINAL PAPER Optimal maintenance and scrapping versus the value of back ups Franz Wirl Published online: 18 April 2007 © Springer-Verlag 2007 Abstract This paper investigates optimal maintenance of equipment under uncer- tainty 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 match- ing 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. Keywords Itô-process · Stopping · Switching · Super contact · Real option 1 Introduction This paper addresses the following points within managerial decisions requiring dynamic and stochastic optimizations: 1. Theoretical analysis and computation are often complementary. More precisely, in the context of stochastic dynamic optimization brute force numerics (i.e., trying to solve numerically directly the partial differential equations resulting from the Hamilton–Jacobi–Bellman equations) fails. On the other hand, analytical solutions F. Wirl (B ) Faculty of Business, Economics and Statistics, University of Vienna, Brünnerstr. 72, 1210 Vienna, Austria e-mail: franz.wirl@univie.ac.at URL:http://www.univie.ac.at/bwl/ieu/ 123