Optimizing invasive species management: A mixed-integer linear programming approach

• Published in: European journal of operational research Vol. 259; no. 1; pp. 308 - 321
• Main Authors: Kıbış, Eyyüb Y., Büyüktahtakın, İ. Esra
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16-05-2017
• Subjects: (S) Complexity theory; Big-M; Linearization; Mixed-integer programming (MIP); Spatially explicit large-scale optimization; Spatially explicit large-scale optimization; Mixed-integer programming (MIP); Big-M; (S) Complexity theory; Linearization
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2016.09.049

•We study a realistic linear integer model for controlling invasive species.•Linear model provides an exact optimal solution contrary to non-linear models.•The big-M value used to linearize the model impacts solution quality and time.•Results provide insights into spatial and dynamic allocation of control efforts.•Our model can be used as a decision-support tool in invasive species management.
Controlling invasive species is a highly complex problem. The intricacy of the problem stems from the nonlinearity that is inherent in biological systems, consequently impeding researchers to obtain timely and cost-efficient treatment strategies over a planning horizon. To cope with the complexity of the invasive species problem, we develop a mixed-integer programming (MIP) model that handles the problem as a full dynamic optimization model and solves it to optimality for the first time. We demonstrate the applicability of the model on a case study of sericea (Lespedeza cuneata) infestation by optimizing a spatially explicit model on a heterogeneous 10-by-10 grid landscape for a seven-year time period. We evaluate the solution quality of five different linearization methods that are used to obtain the MIP model. We also compare the model with its mixed-integer nonlinear programming (MINLP) equivalent and nonlinear programming (NLP) relaxation in terms of solution quality. The computational superiority and realism of the proposed MIP model demonstrate that our model has the potential to constitute the basis for future decision-support tools in invasive species management.