In this paper, we establish a novel duality relationship between node-capacitated multiflows and tree-shaped facility locations. We prove that the maximum value of a tree-distance-weighted maximum node-capacitated multiflow problem is equal to the minimum value of the problem of locating subtrees in a tree, and the maximum is attained by a half-integral multiflow. Utilizing this duality, we sho...

We study the polyhedral structure of two primal relaxations of a class of specially structured mixed integer programming problems. This class includes the generalized capacitated plant location problem and a production scheduling problem as special cases. We show that for this class of problems two polyhedra constructed from the constraint sets in two difl‘erent primal relaxations are identical...

In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present two facility location problems with stochastic demand and exponential servers, respectively inventory. We present a (1 + , 1)-reduction of the facility location problem with subadditive costs to a soft capacitated facility location problem, which i...

This thesis is a critical investigation into the development, application and evaluation of ant colony optimisation metaheuristics, with a view to solving a class of capacitated facility location problems. The study is comprised of three phases. The first sets the scene and motivation for research, which includes; key concepts of ant colony optimisation, a review of published academic materials...

This article introduces a new problem called the Capacity and Distance Constrained Plant Location Problem. It is an extension of the discrete capacitated plant location problem, where the customers assigned to each plant have to be packed in groups that will be served by one vehicle each. The paper addresses different modeling aspects of the problem. It describes a tabu search algorithm for its...

Location Routing is a fundamental planning problem in logistics, which strategic location decisions on the placement of facilities (depots, distribution centers, warehouses etc.) are taken based accurate estimates operational routing costs. We present an approximation algorithm, i.e., algorithm with proven worst-case guarantees both terms running time and solution quality, for general capacitat...

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide ran...