A mathematical model for P-hub median location problem to multiple assignment between non-hub to hub nodes under fuzzy environment مقاله

One group of the optimization problems is Hub location problem. Hub facilities are used in transportation network which are provided transfer of products, information, passengers and postal package through of intermediate node instead of direct transfer. One main group of these problems is discrete hub median location that seeks to minimize total transportation cost. In this paper, we present hub median location problem with multiple allocation of non-hub nodes to hub nodes, moreover it is possible to connect non-hub nodes directly with considering a penalty coefficient. The numerical example for CAB25data set -which is related to flow and distance between 25 cities in America- with establishment cost under fuzzy circumstance solved and presented.

A mathematical model for P-hub median location problem to multiple assignment between non-hub to hub nodes under fuzzy environment Mohammad Bagher Fakhrzad1, Amir-Mohammad Golmohammadi2*, Farzaneh Bagheri3 1Assistance profesor, Depatment of Industrial Engineering, Universiy of Yazd, Yazd, Iran. In this paper, we present hub median location problem with multiple allocation of non-hub nodes to hub nodes, moreover it is possible to connect non-hub nodes directly with considering a penalty coefficient. P-hub Median Problem In this model, the number of p-hub is determined and the objective of this model is minimizing total cost (time, distance, etc. P-hub Center Problem The objective of this model is minimizing the maximum cost (travel time, distance, etc) so that should be a connection between each pair of n node. Hub Location with Fixed Cost In this model minimizing the total cost (time, distance, or etc) to transport is considered. 2. The Models This paper introduces multiple hub median problem which the direct connections between non-hub nodes are allowed. three objectives: a) Optimal number of hubs b) Optimal location of hubs c) Optimal allocation of non-hub to hub nodes O’Kelly presented a new quadratic integer formulation of single allocation p-hub median problem. Sue Abdinnour-Helm proposed a hybrid genetic and tabu search algorithm for solving the problem so that genetic algorithm finds the number and location of hubs and uses tabu search for finding the optimal allocation of non- hub nodes to hubs. In this model the costs of direct connection between non-hub nodes are also considered.