Algorithm for the ATM switching node location problem

Abstract

This thesis considers an optimization model for the ATM Switching node location problem, where each ATM Switching node consists of one hub facility (HSN) and five remote facilities (RSN). The problem is to find an optimal configuration of hub facilities and remote facilities such that each user should be connected to a hub node via a remote node in order to satisfy the demand of the user. Each hub (remote) node may have multiple facilities. Costs include installation cost of facilities and connection costs. The connection cost between a user node and a remote node arises when a user node is connected to remote facilities on the remote node. The connection cost between a remote node and a hub node arises when the facilities on the remote node are connected to the facilities on the hub node. We propose two integer programming models. First, we formulate this problem with path variables. To solve this model, we propose a preprocessing procedure and consider the integer knapsack polytope and derive some valid inequalities. To solve this problem to optimality, we develop a branch-and-cut algorithm. Second, we decompose the problem into master problem and subproblem and formulate the master problem using tree variables. To solve this model, we develop a branch-and-price algorithm. These two algorithms are tested on several sets of test problems. The branch-and-cut algorithm can solve the practically sized problems to optimality within reasonable time, whereas it takes more time to solve the problems using the branch-and-price algorithm.