Oil Spill Response Planning with MINLP

Catastrophic oil spills [1], such as the recent Deepwater BP oil spill in the Gulf of Mexico [2], have demonstrated the importance of developing responsive and effective oil spill response planning strategies for the oil industry and the government. Although a few models have been developed for oil-spill response planning, response operations and the oil weathering process are usually considered separately [3, 5, 4]. Yet significant interactions between them exist throughout the response. Oil-spill cleanup activities change the volume and area of the oil slick and in turn affect the oil transport and weathering process, which also affects coastal protection activities and cleanup operations (e.g., performance degradation and operational window of cleanup facilities). Therefore, it is critical to integrate the response planning model with the oil transport and weathering model, although this integration has not been addressed in the existing literature to the best of our knowledge. The objective of this note is to develop an optimization approach for seamlessly integrating the planning of oil-spill response operations with the oil transport and weathering process. A mixedinteger dynamic optimization (MIDO) model is proposed that simultaneously predicts the time trajectories of the oil volume and slick area and the optimal response cleanup schedule and coastal protection plan, by taking into account the time-dependent oil physiochemical properties, spilled amount, hydrodynamics, weather conditions, facility availability, performance degradation, cleanup operational window, and regulatory constraints. To solve the MIDO problem, we reformulated it as a mixed-integer nonlinear programming (MINLP) problem using orthogonal collocation on finite elements. We also developed a mixed-integer linear programming (MILP) model to obtain a good starting point for solving the nonconvex MINLP problem. The application of the proposed integrated optimization approach is illustrated through a case study based on the Deepwater BP oil spill.