Mixed‐integer dynamic optimization for oil‐spill response planning with integration of a dynamic oil weathering model

Catastrophic oil spills, such as the recent Deepwater BP oil spill in the Gulf of Mexico, 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 oilspill response planning, response operations and the oil weathering process are usually considered separately. 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 mixed-integer dynamic optimization (MIDO) model is proposed that simultaneously predicts the time trajectories of the oil volume and slick area, the 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 for an oil spill in Gulf of Mexico. The tradeoff between response cost and the response time span has also been examined and illustrated through the case study. The rest of this note is organized as follows. The problem statement is presented in the next section. It is then followed by the detailed model formulation and the solution approach. Computational results for a case study and the conclusions are given at the end of this note.