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Controlling invasive species is a highly complex problem defined by the biological characteristics of the organisms, the landscape context, and a management objective of minimizing invasion damages given limited financial resources. While bio-economic optimization models provide a promising approach for invasive species control, current spatio-temporal optimization models omit key ecological details such as age structures-which could be essential to predict how populations grow and spread spatially over time and determine the most effective control strategies. We develop a novel age-structured optimization model as a spatial-dynamic decision framework for controlling invasive species. In particular, we propose a new carrying capacity sub-model, which allows us to take into account the biological competition among different age classes within the population. The potential use of the model is demonstrated on controlling the invasion of sericea (Lespedeza cuneata), a perennial legume threatening native grasslands in the Great Plains. The results show that incorporating age-structure into the model captures important biological characteristics of the species and leads to unexpected results such as multilogistic population growth with multiple, sequential, and overlapping phases of logistic form. These new findings can contribute to understanding time-lags and invasion growth dynamics. Additionally, given budget constraints, utilizing control measures every 2-3 years is found to be more effective than yearly control because of the time to reproductive maturity. Results of the bioeconomic optimization approach provide both ecological and economic insights into the control of invasive species. Furthermore, while the proposed model is specific enough to capture biological realism, it also has the potential to be generalized to a wide range of invasive plant and animal species under various management scenarios in order to identify the most efficient control strategies for managing invasive species.

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The multi-attribute biomass and food production (BFP) problem facing farmers and cooperatives is further complicated by uncertainties in crop yield and prices. In this paper, we present a two-stage stochastic mixed-integer programming (MIP) model that maximizes the economic and environmental benefits of food and biofuel production. The uncertain parameters of yield amount and price level are calculated using real data. Economic aspects include revenue obtained from biomass and food crop sales as well as costs related to seeding, production, harvesting, and transportation operations at the farm level. Environmental effects include greenhouse gas (GHG) emissions, carbon sequestration, soil erosion, and nitrogen leakage to water. The first-stage variables define binary decisions for allocating various land types to food and energy crops, while the second-stage variables are operational decisions related to harvesting, budget allocation, and amounts of different yield types. We present a decomposition algorithm, which is enhanced with specialized Benders cuts for solving this stochastic MIP problem. The computational efficiency of the proposed model and approach is demonstrated by applying it to a real case study involving switchgrass and corn production in the state of Kansas. We measure the solution quality and speed of the decomposition method over stochastic and deterministic models. Results indicate the significant benefit of using the stochastic yield-level information in an optimization model. The proposed stochastic MIP model provides important strategies and insights into decision making for biofuel and food production under uncertainty.