Algorithms For Constrained Multiple Interactive Facilities Location Problem

For solving the classical multi-source Weber problem(MWP), each iteration of the well-know location-allocation heuristic algorithm consists of a location phase and an allocation phase. The task of the location phase is to solve finitely many single-source sub-problems, which are reduced by the heuristic of nearest center reclassification for the customers in the previous allocation phase. In this thesis, we are interested in two locaiton problems which are more general and practical than MWP..For the first problem, we are concerned about the every demand point to multiple facilities for service.The locational constraints on facilities and the interactive transportation between facilities are considered in locating the new facilities. For the second problem, every demand point is only assigned to its nearest facility while the other conditions are the same as the first one. The first problem is convex, but the second problem is nonconvex, which is solved by the location-allocation heuristic algorithm in the paper, and the solving process of the first problem is the location phase of the second one. We make the subproblem of the location phase for the two problem transform into a linear variational inequality(LVI) problem, and we put forward two kinds of new projection-contraction(PC) methods to solve the two problem, respectively. The Global convergence of the PC method is proved under some mild assumptions as well as the convergence of the new location-allocation heuristic algorithm. Some preliminary numerical results are reported which are used to verify the effectiveness of the proposed PC method and the heuristic algorithm.