Protected areas are a cornerstone in global conservation strategies. Constrained budgets for protected area management make it essential that protected area management plans take into account the heterogeneity of values, such as biodiversity and cultural sites, as well as dynamic threats.  Furthermore, there is a growing interest in joint management arrangements of protected areas to better integrate conservation on Indigenous lands and allow for traditional resource uses.  Therefore, better methods of accounting for complex objectives associated with these different types of management arrangements are needed.  We use Kakadu National Park, a world heritage site, as a case study and present a decision support tool designed specifically for the park which integrates dynamic aquatic weed and management models and mapped environmental and cultural values to evaluate the performance of different management strategies in a dynamic and uncertain future.  We present three invasive weed management scenarios for Kakadu's floodplains designed in collaboration with park staff and traditional owners which reflect different stakeholder values and priorities as well as real world constraints such as budgets.  For each scenario we evaluate the total costs of weed management and the benefits of management as the percentage lost or recovered of a range of biological and cultural assets.  We discuss the feasibility of each scenario and contrasting benefits and efficiencies that they present.