Design of capacitated network with tree configuration

Abstract

This thesis considers the problem of designing capacitated network with tree configuration (CTP). For a given set of nodes with their capacities, k types of link facilities with various characteristics, and wiring cost needed to connect each pair of nodes using each type of link facility, the problem is to find the tree network which satisfies the given traffic requirements between all pairs of nodes and minimizes total wiring cost. We formulate (CTP) as an integer programming problem using path variables. To solve the linear programming relaxation which has exponentially many variables, we develop a polynomial-time column generation procedure. Moreover, to tighten the formulation, an efficient preprocessing procedure is devised and some classes of valid inequalities are found. Using the results, we develop a branch-and-cut algorithm with column generation where an efficient branching rule is adopted. Computational results show that the algorithm can solve practically-sized problems to optimality within reasonable time.