Solving the p -Median Problem with a Semi-Lagrangian Relaxation

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median proble

LP-Based Algorithms for Capacitated Facility Location

Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of algorithmic methodologies, such as LP-rounding and primal-dual method, have been applied to and evolved from algorithms for this problem. Unfortunately, this collection of powerful algorithmic techniques had not yet been applicable to the more general capacitated facility location problem. In fact, all of the known algorithms with good performance guarantees were based on a single technique, local search, and no linear programming relaxation was known to efficiently approximate the problem. In this paper, we present a linear programming relaxation with constant integrality gap for capacitated facility location. We demonstrate that the fundamental theories of multi-commodity flows and matchings provide key insights that lead to the strong relaxation. Our algorithmic proof of integrality gap is obtained by finally accessing the rich toolbox of LP-based methodologies: we present a constant factor approximation algorithm based on LP-rounding.Comment: 25 pages, 6 figures; minor revision

Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network

Matheuristics:survey and synthesis

In integer programming and combinatorial optimisation, people use the term matheuristics to refer to methods that are heuristic in nature, but draw on concepts from the literature on exact methods. We survey the literature on this topic, with a particular emphasis on matheuristics that yield both primal and dual bounds (i.e., upper and lower bounds in the case of a minimisation problem). We also make some comments about possible future developments

Park-and-Ride Facilities Design for Special Events Using Space-Time Network Models

abstract: Given that more and more planned special events are hosted in urban areas, during which travel demand is considerably higher than usual, it is one of the most effective strategies opening public rapid transit lines and building park-and-ride facilities to allow visitors to park their cars and take buses to the event sites. In the meantime, special event workforce often needs to make balances among the limitations of construction budget, land use and targeted travel time budgets for visitors. As such, optimizing the park-and-ride locations and capacities is critical in this process of transportation management during planned special event. It is also known as park-and-ride facility design problem. This thesis formulates and solves the park-and-ride facility design problem for special events based on space-time network models. The general network design process with park-and-ride facilities location design is first elaborated and then mathematical programming formulation is established for special events. Meanwhile with the purpose of relax some certain hard constraints in this problem, a transformed network model which the hard park-and-ride constraints are pre-built into the new network is constructed and solved with the similar solution algorithm. In doing so, the number of hard constraints and level of complexity of the studied problem can be considerable reduced in some cases. Through two case studies, it is proven that the proposed formulation and solution algorithms can provide effective decision supports in selecting the locations and capabilities of park-and-ride facilities for special events.Dissertation/ThesisMasters Thesis Civil and Environmental Engineering 201

Performance Appraisal Research: A Critical Review of Work on “The Social Context and Politics of Appraisal”

This paper reviews existing literatures on the analysis of performance appraisal (PA) paying special attention to those which try to take into account the “social context” of appraisal systems and processes. The special place of political action within these processes is underlined and the different levels at which politics need to be considered in research are outlined. Research on politics is considered and shown to lack an adequate consideration of the social relations involved in the reciprocal interactions between PA tools and processes and users interpretation and manipulation of them.Performance appraisal; Social context; Politics

Accelerating Benders' Decomposition: Algorithmic Enhancements and Model Selection Criteria

Not AvailableThis research was supported by the U.S. Department of Transportation under Contract DOT-TSC-1058, Transportation Advanced Research Program (TARP)

File Allocation and Join Site Selection Problem in Distributed Database Systems.

There are two important problems associated with the design of distributed database systems. One is the file allocation problem, and the other is the query optimization problem. In this research a methodology that considers both these aspects is developed that determines the optimal location of files and join sites for given queries simultaneously. Using this methodology, three different mixed integer programming models that describe three cases of the file allocation and join site selection problem are developed. Dual-based procedures are developed for each of the three mixed integer programming models. Extensive computational testing is performed which shows that the dual-based algorithms developed are able to generate solutions which are very close to the optimal. Also, these near optimal solutions are found very quickly, even for large scale problems

Large-scale optimization for data placement problem

Large-scale optimization of combinatorial problems is one of the most challenging areas. These problems are characterized by large sets of data (variables and constraints). In this thesis, we study large-scale optimization of the data placement problem with zero storage cost. The goal in the data placement problem is to find the placement of data objects in a set of fixed capacity caches in a network to optimize the latency of access. Data placement problem arises naturally in the design of content distribution networks. We report on an empirical study of the upper bound and the lower bound of this problem for large sized instances. We also study a semi-Lagrangean relaxation of a closely related k-median problem. In this thesis, we study the theory and practice of approximation algorithm for the data placement problem and the k-median problem