AbstractAim Decision‐support models have considerable potential for guiding management strategies when problems are complex. The robustness of such decision‐making processes is rarely evaluated, and the influence of decision criteria (or factors) in management decisions is seldom considered. We present a framework for a spatially‐explicit sensitivity analysis by using a scheme developed to provide objective guidelines, in the form of static priority maps, for managing woody invasive alien plants (IAPs).Location The Cape Floristic Region, South Africa.Methods The model included seven factors related to management history, fire risk, and the age, identity, density and spread of IAPs. Each factor had a weight associated that reflected its relative importance in prioritizing areas for clearing. We changed these factor weights using three approaches of sensitivity analysis and assessed the effect of these changes on the spatial structure of the resulting priority maps in three different management regions.Results Different outcomes arose depending on the importance given to different factors. Priority maps were most sensitive to the fire‐related factors, suggesting that fire is both a crucial driver of invasion in fynbos and an overriding determinant of management options. The factor ‘area burnt recently’ provided crucial information for the effective clearing of IAPs. The sensitivity of the model to changes in other factors was more context specific: levels of sensitivity were highly dependent on different features of the landscape, especially the spatial heterogeneity of particular factors.Main conclusions By clarifying the importance of factors in shaping priority maps, the sensitivity analysis framework enabled us to identify the necessary factors to produce outcomes matching a pre‐selected management strategy. This is important for cost‐efficient management, as acquisition and curation of data is expensive. This spatially‐explicit sensitivity analysis is, thus, recommended to evaluate the robustness and generality of selected management strategies, and validate the assumptions derived from decision‐making protocols.