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Markov decision models (MDM) used in practical applications are most oftenless complex than the underlying `true' MDM. The reduction of model complexityis performed for several reasons. However, it is obviously of interest to knowwhat kind of model reduction is reasonable (in regard to the optimal value) andwhat kind is not. In this article we propose a way how to address thisquestion. We introduce a sort of derivative of the optimal value as a functionof the transition probabilities, which can be used to measure the (first-order)sensitivity of the optimal value w.r.t.\ changes in the transitionprobabilities. `Differentiability' is obtained for a fairly broad class ofMDMs, and the `derivative' is specified explicitly. Our theoretical findingsare illustrated by means of optimization problems in inventory control andmathematical finance.

First-order sensitivity of the optimal value in a Markov decision model with respect to deviations in the transition probability function