Uncertainty about future spread of invasive organisms hinders planning of effective response measures. We present a two-stage scenario optimization model that accounts for uncertainty about the spread of an invader, and determines survey and eradication strategies that minimize the expected program cost subject to a safety rule for eradication success. The safety rule includes a risk standard for the desired probability of eradication in each invasion scenario. Because the risk standard may not be attainable in every scenario, the safety rule defines a minimum proportion of scenarios with successful eradication. We apply the model to the problem of allocating resources to survey and eradicate the Asian longhorned beetle (ALB, Anoplophora glabripennis) after its discovery in the Greater Toronto Area, Ontario, Canada. We use historical data on ALB spread to generate a set of plausible invasion scenarios that characterizes the uncertainty of the beetle's extent. We use these scenarios in the model to find survey and tree removal strategies that minimize the expected program cost while satisfying the safety rule. We also identify strategies that reduce the risk of very high program costs. Our results reveal two alternative strategies: (i) delimiting surveys and subsequent tree removal based on the surveys' outcomes, or (ii) preventive host tree removal without referring to delimiting surveys. The second strategy is more likely to meet the stated objectives when the capacity to detect an invader is low or the aspirations to eradicate it are high. Our results provide practical guidelines to identify the best management strategy given aspirational targets for eradication and spending.