Conditional facility location problems with continuous demand and a polygonal barrier

We consider facility location problems where n facilities are present in a convex polygon the rectilinear plane, over which continuous and uniform demand is distributed within polygonal barrier located (removing all preventing travel barrier), optimal for an additional sought. start with in-depth analysis of representation bisectors two affected by how it position facility. Following this, detailed investigation into changes structure Voronoi diagram caused movement this facility, governs form objective function numerous problems, yields set linear constraints general that partitions market space finite number regions exact solution can be found polynomial time. This allows us to formulate algorithm makes use triangular decomposition incremental first order optimality conditions.