Routing and scheduling of vehicles and crews: The state of the art

This paper is intended as a survey in the area of network synthesis and optimum network design, which, in view of the importance and variety of the underlying applications, has attraced, since the early 1960s, much interest in the Operations Research community. Indeed, if the first models were studied in connection with telecommunication networks, the range of applications kept on getting broader and broader, including transportation networks, computer and teleprocessing networks, energy transport systems, water distribution networks, etc. However, beyond the apparent diversity of practical situations involved, most of these applications can be accounted for (modulo possibly a few minor adaptations), by a rather limited number of basic models. One of the main purposes of this paper is to provide the reader with a relevant classification of the area which will help him identify the fundamental structure of the problem (if any) he has to cope with, and relate it to already published work. In order to obtain a fairly good coverage of the matter, we have thus been led to identify three basic models aroung which the whole paper is organized: a general model using minimum cost multicommodity flows (Section 2); models in terms of tree-like networks (Section 3); models using nonsmultaneous single-commodity or multicommodity flows (Section 4). In each bcase the most important variants of the basic models have been surveyed with the purpose of providing as much information as possible concerning (a) the various contexts of applications from which the problem arose; (b) the main computational methods proposed in the literature for solving it, with emphasis on those techniques which appear at present, to be most efficient or promising.

Networks synthesis and optimum network design problems: Models, solution methods and applications

In recent years we have evidenced an extensive effort in the development of computer communication networks. One of the important aspects of the network design process is the solution of the topological design questions involved in establishing a communication network. In this article, formulations are presented for a variety of centralized network design problems such as the minimal spanning tree problem, capacitated and degree constrained minimal spanning tree problems, The Telpak problem, and, heterogeneous network design problems. The applicability of these formulations to algorithmic development is demonstrated by developing an efficient algorithm for solving the degree constrained minimal spanning tree problem. Computational results are reported for 630 test problems. A Bender's decomposition procedure is developed and tested for the capacitated minimal spanning tree problem with less favorable results.

Topological design of centralized computer networks—formulations and algorithms

We examine the complexity of a classical problem related to the design of centralized computer networks. Under very broad assumptions the problem is shown to be NP-complete, and hence most probably intractable. The same result holds for the “Euclidean” case of the problem; however, in the latter case a simple algorithm produces solutions with relative error almost certainly arbitrarily close to zero.

The complexity of the capacitated tree problem

Computer communication networks and telecommunication systems are growing at an explosive rate. Some of the major factors influencing this phenomenal growth rate have been technology driven, deregulation of the telecommunication industry and the breakup of AT&T, product and service introductions and competition, new application areas, price reductions and improved services. Corporations have discovered how to use telecommunication-based systems and computer networks as a strategic competitive weapon. Modern computer networks consist of backbone networks which serve as major highways to transfer large volumes of communication traffic, and local access networks which feed traffic between the backbone network and end user nodes. The design of the local access network is a complex process which builds on many difficult combinatorial optimization problems. This paper surveys many of the problems, presents the state of the art in solving them, and demonstrates a variety of solution procedures. The paper concludes with a list of open problems and areas open for further investigation.

Topological design of telecommunication networks-local access design methods

The capacitated minimum spanning tree is an offspring of the minimum spanning tree and network flow problems. It has application in the design of multipoint linkages in elementary teleprocessing tree networks. Some theorems are used in conjunction with Little's branch and bound algorithm to obtain optimal solutions. Computational results are provided to show that the problem is tractable.

Tachen Lo

Papers

The Capacitated Minimum Spanning Tree