Dynamical monge-kantorovich mass transportation problem model with water permeability term

Abstract

This research focuses on the development of mass transportation problem model in urban planning. This study highlights the dynamical Monge-Kantorovich mass transportation problem model particularly on water permeability potential. It started from the problem that occurs when there is a decrease in the capability of water to infiltrate into the soil whenever there is an increase in population density in an area. This situation occurs when the development of the area is poorly planned such that the coverage of surface area disturbs the existing water infiltration process. Thus, this study aims to develop a model by considering the issues outlined above based on the dynamic Monge-Kantorovich mass transportation model, strengthened by theoretical analysis and support. Here, a new model is developed by extending the basic dynamical Monge-Kantorovich mass transportation model by incorporating a water permeability term. The resulting model shows that it satisfies a system of optimality and uniqueness conditions effectively. Also, the stability estimation of the new model are derived. In addition, the proximal splitting method specifically Douglas-Rachford method is implemented to solve the new model. The model is able to successfully identify areas suitable for development using its converged solution. As a conclusion, this investigation leads to an extension of the basic dynamical Monge-Kantorovich mass transportation model into a model with appended water permeability term, assessed and supported by theorems and propositions for validation. This model is useful for future research especially on the development of models in the field of water permeability.