This paper considers the constrained inverse problem based on the nonlinear convection-diffusion equation in the multiphase porous media flow. To solve this problem, a widely convergent homotopy method is introduced and proposed. To evaluate the performance of the mentioned method, two numerical examples are presented. This method turns out to have wide convergence region and strong anti-noise ability.

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In this study, we developed a vehicle allocation model that can meet the requirements and cost best, the data related to the number of calls in each zone, and the variability required to respond to different types of calls. First, several indicators are extracted to quantify the advantages of station construction in each zone, and the hierarchical analysis method and TOPSIS are used to score each zone, and then select the stations that need to be built according to the score. Subsequently, according to the call requirements of each zone, its distance from the site, the amount of resources owned, etc, we develop a vehicle allocation model based on integer programming.