Shortest Paths, Network Design and Associated Polyhedra

We study a specialized version of network design problems that arise in telecommunication, transportation and other industries. The problem, a generalization of the shortest path problem, is defined on an undirected network consisting of a set of arcs on which we can install (load), at a cost, a choice of up to three types of capacitated facilities. Our objective is to determine the configuration of facilities to load on each arc that will satisfy the demand of a single commodity at the lowest possible cost. Our results (i) demonstrate that the single-facility loading problem and certain "common breakeven point" versions of the two-facility and three-facility loading problems are polynomially solvable as a shortest path problem; (ii) show that versions of the twofacility loading problem are strongly NP-hard, but that a shortest path solution provides an asymptotically "good" heuristic; and (iii) characterize the optimal solution (that is, specify a linear programming formulation with integer solutions) of the common breakeven point versions of the two-facility and three-facility loading problems. In this development, we introduce two new families of facets, give geometric interpretations of our results, and demonstrate the usefulness of partitioning the space of the problem parameters to establish polyhedral integrality properties. Generalizations of our results apply to (i) multicommodity applications and (ii) situations with more than three facilities

Locations of Medians on Stochastic Networks

The definition of network medians is extended to the case where travel times on network links are random variables with known discrete probability distributions. Under a particular set of assumptions, it is shown that the well-known theorems of HAKIMI and of LEVY can be extended to such stochastic networks. The concepts are further extended to the case of stochastic oriented networks. A particular set of applications as well as formulations of the problem for solution using mathematical programming techniques are also discussed briefly

The Convex Hull of Two Core Capacitated Network Design Problems

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost. This paper studies two core subproblems of the NLP. The first problem, motivated by a Lagrangian relaxation approach for solving the problem, considers a multiple commodity, single arc capacitated network design problem. The second problem is a three node network; this specialized network arises in larger networks if we aggregate nodes. In both cases, we develop families of facets and completely characterize the convex hull of feasible solutions to the integer programming formulation of the problems. These results in turn strengthen the formulation of the NLP

User perceptions of the benefits of implementing an ERP system: A case study

Given the large time and fitiancial commitment that an ERP project requires and the potential benefits it can offer if successfidly implemented, it is important to understand the factors that facilitate and inhibit the success ofEP,P implementation. By means of a case study of a global energy company, we first examine the factors that facilitate and inhibit the success of their ERP implementation. We draw on the theory of business process change when analyzing the implementation process. Next, we examine the perceptions non-management professional users of the ERP system (who were not members of the ERP implementation team) have of the ERP system. The data for this part of the study was collected through a survey of nonmanagement professional users of an ERP system, 6 months after implementation

Heuristics, LPs, and Trees on Trees: Network Design Analyses

We study a class of models, known as overlay optimization problems, with a "base" subproblem and an "overlay" subproblem, linked by the requirement that the overlay solution be contained in the base solution. In some telecommunication settings, a feasible base solution is a spanning tree and the overlay solution is an embedded Steiner tree (or an embedded path). For the general overlay optimization problem, we describe a heuristic solution procedure that selects the better of two feasible solutions obtained by independently solving the base and overlay subproblems, and establish worst-case performance guarantees on both this heuristic and a LP relaxation of the model. These guarantees depend upon worst-case bounds for the heuristics and LP relaxations of the unlinked base and overlay problems. Under certain assumptions about the cost structure and the optimality of the subproblem solutions, both the heuristic and the LP relaxation of the combined overlay optimization model have performance guarantees of 4/3. We extend this analysis to multiple overlays on the same base solution, producing the first known worst-case bounds (approximately proportional to the square root of the number of commodities) for the uncapacitated multicommodity network design problem. In a companion paper, we develop heuristic performance guarantees for various new multi-tier. survivable network design models that incorporate both multiple facility types or technologies and differential node connectivity levels

Performance Evaluation of a Self-Organising Scheme for Multi-Radio Wireless Mesh Networks

Multi-Radio Wireless Mesh Networks (MR-WMN) can substantially increase the aggregate capacity of the Wireless Mesh Networks (WMN) if the channels are assigned to the nodes in an intelligent way so that the overall interference is limited. We propose a generic self-organisation algorithm that addresses the two key challenges of scalability and stability in a WMN. The basic approach is that of a distributed, light-weight, co-operative multiagent system that guarantees scalability. The usefulness of our algorithm is exhibited by the performance evaluation results that are presented for different MR-WMN node densities and typical topologies. In addition, our work complements the Task Group 802.11s Extended Service Set (ESS) Mesh networking project work that is in progress

Top Management Support, Collective Mindfulness, and Information Systems Performance

Mindfulness is a cognitive process that facilitates the discovery and correction of errors that might escalate. This study applies mindfulness theory to examine the impact of top management support for information systems on collective mindfulness, and that of collective mindfulness on IS performance. It treated such mindfulness in five dimensions, and top management support and IS performance as uni-dimensional. Forty-seven chief executive officers responded to a survey asking their perceptions of the constructs. Top management support predicted four of the dimensions with the strongest effect on sensitivity to IS operations. A negative path from support to commitment to IS resilience suggests a management predilection for planning over improvisation and adaptation. Sensitivity to IS operations alone predicted performance

A Topology Control-Based Self-Organisation in Wireless Mesh Networks

An algorithm for self-organisation that assigns the channels intelligently in multi-radio wireless mesh networks (MR-WMN) is important for the proper operation of MR-WMN. The aim of the self-organisation algorithm is to reduce the overall interference and increase the aggregate capacity of the network. In this paper, we have first proposed a generic self-organisation algorithm that addresses these two challenges. The basic approach is that of a distributed, light-weight, cooperative multiagent system that guarantees scalability. Second, we have evaluated the performance of the proposed self-organisation algorithm for two sets of initialisation schemes. The initialisation process results in a topology control of MR-WMN by way of spatial distribution of connectivity between the mesh nodes. The results have been obtained for realistic scenarios of MR-WMN node densities and topologies. We have shown in addition the need to develop non-transmit power control based algorithms to achieve a further increase in system capacity

Modeling and Solving the Capacitated Network Loading Problem

This paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry. In this problem, given point-topoint demand between various pairs of nodes of a network must be met by installing (loading) capacitated facilities on the arcs. The facilities are chosen from a small set of alternatives and loading a particular facility incurs an arc specific and facility dependent cost. The problem is to determine the configuration of facilities to be loaded on the arcs of the network that will satisfy the given demand at minimum cost. Since we need to install (load) facilities to carry the required traffic, we refer to the problem as the network loading problem. In this paper, we develop modeling and solution approaches for the problem. We consider two approaches for solving the underlying mixed integer programming model: (i) a Lagrangian relaxation strategy, and (ii) a cutting plane approach that uses three classes of valid inequalities that we identify for the problem. In particular, we show that a linear programming formulation that includes the valid inequalities always approximates the value of the mixed integer program at least as well as the Lagrangian relaxation bound (as measured by the gaps in the objective functions). We also examine the computational effectiveness of these inequalities on a set of prototypical telecommunications data. The computational results show that the addition of these inequalities considerably improves the gap between the integer programming formulation of the problem and its linear programming relaxation: for 6 - 15 node problems from an average of 25% to an average of 8%. These results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry