Jeff Kennington

A Survey of Linear Cost Multicommodity Network Flows

This exposition presents a state-of-the-art survey of results and algorithms for linear multicommodity network flow problems.

The asymmetric m-traveling salesman problem: A duality based branch-and-bound algorithm

Abstract This paper presents a new model and branch-and-bound algorithm for the asymmetric m-travelling salesmen problem. The algorithm uses a Lagrangean relaxation, a subgradient algorithm to solve the Lagrangean dual, a greedy algorthim for obtaining minimal m-trees, penalties to strengthen the lower bounds on candidate problems, and a new concept known as staged optimization. Computational experience for problems having up to 100 cities is presented.

The equal flow problem

Abstract This paper presents a new algorithm for the solution of a network problem with equal flow side constraints. The solution technique is motivated by the desire to exploit the special structure of the side constraints and to maintain as much of the characteristics of pure network problems as possible. The proposed algorithm makes use of Lagrangean relaxation to obtain a lower bound and decomposition by right-hand-side allocation to obtain upper bounds. The lagrangean dual serves not only to provide a lower bound used to assist in termination criteria for the upper bound, but also allows an initial allocation of equal flows for the upper bound. The algorithm has been tested on problems with up to 1500 nodes and 6000 arcs. Computational experience indicates that solutions whose objective function value is well within 1% of the optimum can be obtained in 1%–65% of the MPSX time depending on the amount of imbalance inherent in the problem. Incumbent integer solutions which are within 99.99% feasible and well within 1% of the proven lower bound are obtained in a straightforward manner requiring, on the average, 30% of the MPSX time required to obtain a linear optimum.

The Fixed-Charge Transportation Problem: A Computational Study with a Branch-and-Bound Code

Abstract This paper presents the computational experience obtained with an experimental branch-and-bound code for the fixed-charged transportation problem. The code calculates simple penalties and uses a modern transportation routine to solve the linear programming relaxation. The findings of the investigation are as follows: (i) the solution times for problems with similar variable and fixed arc costs are highly variable, but performance definately worsens as fixed costs increase relative to variable costs with demands remaining constant, (ii) computational times decrease as total supply increases if other variables are held constant, (iii) computational times tend to vary inversely with the ratio of number of destinations to number of sources for ratios greater than unity if other variables are held constant, and (iv) problems with about 200 arcs may be solved if the fixed costs do not play too large a role, while problems with fewer than 100 arcs may blow up. We found no way to predict solution time as...

An Efficient Procedure for Implementing a Dual Simplex Network Flow Algorithm

Abstract This paper shows that for linear programming formulations of network flow problems, the nonzero components of rows of the basis inverse are identical. A simple algorithm for identifying these nonzero components is given along with a suggested data structure for implementation. The algorithm requires only one bit of storage for each node plus one additional bit. Finally we indicate how these ideas may be used in the development of a dual simplex code for network flow problems.

Design Strategies for Meeting Unavailability Targets Using Dedicated Protection in DWDM Networks

Service providers operating dense-wavelength-division-multiplexed networks are often faced with the problem of designing their networks such that a certain level of service availability can be delivered to their customers. This paper introduces optimization-based algorithms that address this problem efficiently and effectively. For a given network topology, specified by existing dark-fiber links, our algorithms determine a cost-effective solution consisting of the size and location of equipment needed to satisfy the desired amount of point-to-point traffic demands. In addition, the solution approach discussed in this paper delivers estimates for the service unavailability probability of each traffic-demand pair and enables the service provider to programmatically determine which and how many supplemental node-disjoint protection paths are required in order to attain a prespecified demand-pair unavailability target. To the best of our knowledge, these algorithms provide the user with the most detailed design created by any optimization-based design tool to date. The efficiency and effectiveness of the proposed network-design algorithms is studied using an empirical analysis

Introduction to Optimization in Wireless Networks

Wireless communications have progressed tremendously from the days of Marconi and Tesla. It is hard to imagine life without the comforts enabled by wireless technologies, which has impacted several facets of society.

Optimization Based WLAN Modeling and Design

This chapter describes strategies, software tools, and optimization models that may be used to design wireless local area networks. While most small scale WLAN deployments can be designed in an ad-hoc fashion, medium to large scale networks can benefit from a more methodical design approach. In one design strategy, RF signal strength data are sampled at various locations within a site. Measurements are then used to determine transmitter locations that ensure site wide coverage. This chapter describes approaches that belong to an alternate strategy, which relies on using special purpose software tools. These tools most often attempt to solve an underlying optimization problem maximizing either coverage or capacity. Some coverage models are simple and can be solved with existing commercial optimization software. Solution procedures for sophisticated capacity models with integer variables and nonlinear constraints are not solvable using current commercial optimization software. Therefore, many industrial and academic research groups rely upon metaheuristics for problem solution. The chapter concludes with a discussion of computational results that illustrate the application of two widely known metaheuristics to the WLAN design problem.

Optimizing Cash Management for Large Scale Bank Operations

The Federal Reserve System (Fed) provides currency services to banks, including sorting currency into fit and non-fit bills and repackaging bills for redistribution. To reduce the cost of currency management operations, many banks make Fed deposits and withdrawals of the same denomination each week. In July 2007, the Fed introduced fees for making both deposits and withdrawals during a given Monday through Friday. Recognizing an opportunity, Fiserv Corporation initiated a project to optimize bank vault inventories across time and space. This article presents the integer programming model developed to assist Fiserv clients reduce the logistics cost component of cash management. The model is implemented in software using OPL. The underlying configuration is a time-space multi-commodity network with a fixed-charge cost structure. The authors report on a successful pilot study and present an efficient heuristic procedure that can be used to reduce computational solution times from hours to a few minutes.

Comments on A Suggested Computation for Maximal Multi-Commodity Network Flows

T L. R. Ford Jr. and D. R. Fulkerson paper, “Suggested Computation for Maximal MultiCommodity Network Flows” (Management Science 1958), is a foundation study for two important developments in the management sciences. One is applied and the other is theoretical. The basic theory for single-commodity network flows was developed primarily by Ford, Fulkerson, and Dantzig and documented in a series of publications in the late 1950s and two famous books (Flows in Networks by Ford and Fulkerson and Linear Programming and Extensions by Dantzig). This Management Science 1958 manuscript introduced the concept of multiple commodities sharing the same capacitated network. In the introduction they state the major differences between the multicommodity version and its single-commodity cousin.