A multi-objective mixed-integer dynamic optimization approach to oil spill response planning

Catastrophic oil spills, such as the recent Deepwater Horizon/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 oil-spill 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 of great importance to integrate the response planning model with the oil transport and weathering model. In this work, we propose a bi-criterion optimization approach that seamlessly integrates the oil-spill response planning decisions with the oil transport and weathering process under the economic and responsiveness criteria. The economic criterion is measured by the total response cost, and responsiveness is measured by the time span of the entire response operations. A mixed-integer 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, variational operational window, and regulatory constraints. To solve the MIDO problem effectively, we reformulated it as a mixed-integer nonlinear programming (MINLP) problem using orthogonal collocation on finite elements. We also developed an approximate mixed-integer linear programming (MILP) model for the initialization for solving the nonconvex MINLP problem. The results of the multi-objective optimization problem yield a Pareto-optimal curve, which reveals how the optimal total cost, oil spill cleanup operations, and coastal protection plans change under different specifications of the response time span. The application of the proposed optimization approach is illustrated through an case study based on the Deepwater Horizon/BP oil spill.