Abstract There is an urgent need to design management strategies to reduce invasive species spread and impact, but the large spatial and temporal scales of most biological invasions make them challenging environments in which to conduct field studies. In this context, simulation models can play a key role in informing invasive species management. Woody plants are among the most harmful invaders, yet an evidence base to support different management objectives for these species remains poorly developed. Pines (Pinus) have been intensively studied, in terms of demography, dispersal, spread and impact, which makes them an ideal study system to model invasions. Using a multiyear database of observations of an invasive population, we employed an approximate Bayesian computation to fit an individual‐based spatially explicit model to compare management strategies to reduce the spread, population size and impact of a woody invader, Pinus contorta (pine hereafter), on grasslands in Patagonia. We simulated a pine population spreading from a plantation into a grassland over 50 years. Annual control actions in the grasslands started as soon as pines started spreading (when the pines from the plantation become reproductive) or were delayed at 10‐year intervals. For control actions, we targeted different pine life stages, prioritized different locations in the landscape and explored a wide range of available budgets. Removing saplings was the most cost‐effective way to reduce pine spread and population size, whereas reducing management delay had a stronger effect on minimizing pine invasion impact on native grassland productivity. Focusing only on invasive adults was ineffective because it was costly, and it allowed a build‐up in the population size of other stages which soon became adults (and started spreading seeds). Synthesis and applications: Our highest‐ranking strategies represent management actions to start implementing in the field as part of an adaptive management plan that iteratively evaluates the validity of our simulation model and updates the management recommendations. Our study can be applied to guide management of invasive pines and replicated with any invasive woody species with sufficient data.