A Variational Approach to the Two-endpoint Boundary Value Problem of Route Location in Cost Heterogeneous Terrain - nan, nan; nan, nan (Iraqi Journal of Civil Engineering, 2010)
AbstractPresented in this paper is a variational solution of the two-endpoint boundary value problem of route location in cost heterogeneous terrain. The terrain consists of two cost subregions separated by a single straight cost boundary line. The integral concerning the total transportation cost is minimized to obtain the optimum route. The analytical solution developed on the basis of calculus of variations was applied to different cases of cost ratios using a computer program, which was written in MCAD language. A comparison is made between the developed analytical solution based on variational technique with that based on Snell’s law of light refraction and excellent agreement was obtained.