Conditional p-maxian problem on network

This article investigates the problem of conditional p-maxian on the networks. Assume a network like G = (V,E) that the weight in each of its vertices vi is positive wi . In a p-maxian problem, the goal is to find a set contains p as the vertice of the set and as a facility; in a way that the sum of maximum of weighted distance of other point is the highest one from the set. In the problem of conditional p-maxian, we assume that some facilities are already existed and there is need to add other p ones. In this article, other new algorithms are presented to solve the problem of conditional p-maxian and their results (e.g. their solution time in finding the optimum points) are compared. One of the applications of this article is to determine an optimum place for landfill wastes. The wastes must be in the farthest distance of the demand (areas that people live) and it must be in the appropriate places to serve the requests.