The Center Of Gravity Location Problem And Its Inverse Problem

Location Problem is a classic and important problem in Operational Research literature.In the combinatorial optimization problem,location problem has important theoretical significance to research and extensive practical background.It has involved in economy,politics,humanities, management,psychology and engineering geology,etc.But along with the society's development,in order to adapt the different actual situation,new questions emerge one after another incessantly.In this article,the character 1 introduces some classic location models:continuous location problems and discrete location problems.In the discrete location problems,p-median problem and p-center problem are the two models that are researched deeply.In this character,simply introduces the development and research status of the two location problems,and present the mathematical models of the two problems.In character 2,we mainly study the 1-median problem and its inverse problem,2-median problem and its inverse problem on the tree.The 1-median problem and its inverse problem with non-negative weights have effective algorithm.The inverse 1-median problem can be solved by greedy algorithm. The 2-median problem on a tree with non-negative weights can be solved by solve the 1-median problem on its sub tree,and the inverse 2-median problem can be translated in to a linear programming model,which could be solved by an effective algorithm.In character 3,the stochastic location problems are studied.Introduce two different two stage stochastic location and give their mathematical models.We mainly study the median problem under uncertainty.Along with the expansion of the scale of production,we will add the number of the facilities in the future(add up to q).Assume that the number of new facilities we will add in the future is r,(0≤r≤q),we need to locate p facilities at the present time,and the p facilities are the p-median of the network.The solution to the p-median problem under uncertainty with q=1 is equivalent to solving n p-median problems each based on n nodes.The 2-median problem under uncertainty on a tree with q=1 has effective algorithm.