Bilevel models on the competitive facility location problem

Facility location and allocation problems have been a major area of research for decades, which has led to a vast and still growing literature. Although there are many variants of these problems, there exist two common features: finding the best locations for one or more facilities and allocating demand points to these facilities. A considerable number of studies assume a monopolistic viewpoint and formulate a mathematical model to optimize an objective function of a single decision maker. In contrast, competitive facility location (CFL) problem is based on the premise that there exist competition in the market among different firms. When one of the competing firms acts as the leader and the other firm, called the follower, reacts to the decision of the leader, a sequential-entry CFL problem is obtained, which gives rise to a Stackelberg type of game between two players. A successful and widely applied framework to formulate this type of CFL problems is bilevel programming (BP). In this chapter, the literature on BP models for CFL problems is reviewed, existing works are categorized with respect to defined criteria, and information is provided for each work.WOS:000418225000002Scopus - Affiliation ID: 60105072Book Citation Index- Science - Book Citation Index- Social Sciences and HumanitiesArticle; Book ChapterOcak2017YÖK - 2016-1

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Integer Bilevel Linear Programming Problems: New Results and Applications

Integer Bilevel Linear Programming Problems: New Results and Application

Multilevel decision-making: A survey

© 2016 Elsevier Inc. All rights reserved. Multilevel decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a multiple level hierarchy. Significant efforts have been devoted to understanding the fundamental concepts and developing diverse solution algorithms associated with multilevel decision-making by researchers in areas of both mathematics/computer science and business areas. Researchers have emphasized the importance of developing a range of multilevel decision-making techniques to handle a wide variety of management and optimization problems in real-world applications, and have successfully gained experience in this area. It is thus vital that a high quality, instructive review of current trends should be conducted, not only of the theoretical research results but also the practical developments in multilevel decision-making in business. This paper systematically reviews up-to-date multilevel decision-making techniques and clusters related technique developments into four main categories: bi-level decision-making (including multi-objective and multi-follower situations), tri-level decision-making, fuzzy multilevel decision-making, and the applications of these techniques in different domains. By providing state-of-the-art knowledge, this survey will directly support researchers and practical professionals in their understanding of developments in theoretical research results and applications in relation to multilevel decision-making techniques

Linear bilevel problems:Genericity results and an efficient method for computing local minima

The paper is concerned with linear bilevel problems. These nonconvex problems are known to be NP-complete. So, no theoretically efficient method for solving the global bilevel problem can be expected. In this paper we give a genericity analysis of linear bilevel problems and present a new algorithm for efficiently computing local minimizers. The method is based on the given structural analysis and combines ideas of the Simplex method with projected gradient steps

Joint Design and Pricing of Intermodal Port - Hinterland Network Services: Considering Economies of Scale and Service Time Constraints

Maritime container terminal operating companies have extended their role from node operators to that of multimodal transport network operators. They have extended the gates of their seaport terminals to the gates of inland terminals in their network by means of frequent services of high capacity transport modes such as river vessels (barges) and trains.

Un algoritmo basado en la búsqueda dispersa para resolver el problema de producción distribución de una cadena de suministro

En este trabajo nosotros consideramos el problema de planeación de producción y distribución de una cadena de suministro en una red, que consiste de un conjunto de centros de distribución que buscan dar servicio a un conjunto de minoristas, y dichos centros de distribución abastecidos por un conjunto de plantas, buscando minimizar los costos de transportación en la red y de operación en las plantas, basado en el problema propuesto por Herminia y Calvete en 2011. El problema es formulado como un programa matemático binivel donde el nivel superior (líder) consiste en fijar las rutas de distribución de productos enviados de los centros de distribución a los minoristas, satisfaciendo sus demandas sin exceder de un tiempo límite de duración de cada ruta. Por otro lado, en el nivel inferior (seguidor) se reciben las órdenes de cada centro de distribución y se deciden cuales plantas producirán estas órdenes satisfaciendo las demandas allí conjuntadas sin sobrepasar las capacidades de producción de las plantas. La función objetivo del nivel superior minimiza los costos incurridos en el envío de los productos desde los centros de distribución hacia los minoristas y los costos asociados al envío desde las plantas hasta los centros de distribución considerando un costo de descarga por artículo. En el nivel inferior se busca minimizar los costos de operación en las plantas. En este trabajo proponemos un algoritmo heurístico basado en el equilibrio de Stackelberg y la Búsqueda Dispersa. El algoritmo propuesto consiste en aplicar la búsqueda dispersa en las variables del nivel superior encontrando la mejor respuesta del nivel inferior para cada solución obtenida por la búsqueda dispersa obteniendo así un equilibrio entre estos dos niveles. Nuestro algoritmo ha mostrado ser competitivo y brinda buenos resultados comparados con los publicados por Herminia y Calvete en 2011

An investigation of models for identifying critical components in a system.

Lai, Tsz Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 193-207).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Overview --- p.1Chapter 1.2 --- Contributions --- p.2Chapter 1.3 --- Organization --- p.2Chapter 2 --- Literature Review --- p.4Chapter 2.1 --- Taxonomy --- p.4Chapter 2.2 --- Design of Infrastructure --- p.6Chapter 2.2.1 --- Facility Location Models --- p.7Chapter 2.2.1.1 --- Random Breakdowns --- p.7Chapter 2.2.1.2 --- Deliberate Attacks --- p.8Chapter 2.2.2 --- Network Design Models --- p.9Chapter 2.3 --- Protection of Existing Components --- p.10Chapter 2.3.1 --- Interdiction Models --- p.11Chapter 2.3.2 --- Facility Location Models --- p.12Chapter 2.3.2.1 --- Random Breakdowns --- p.12Chapter 2.3.2.2 --- Deliberate Attacks --- p.12Chapter 2.3.3 --- Network Design Models --- p.14Chapter 3 --- Identifying Critical Facilities: Median Problem --- p.16Chapter 3.1 --- Introduction --- p.16Chapter 3.2 --- Problem Formulation --- p.18Chapter 3.2.1 --- The p-Median Problem --- p.18Chapter 3.2.1.1 --- A Toy Example --- p.19Chapter 3.2.1.2 --- Problem Definition --- p.21Chapter 3.2.1.3 --- Mathematical Model --- p.22Chapter 3.2.2 --- The r-Interdiction Median Problem --- p.24Chapter 3.2.2.1 --- The Toy Example --- p.24Chapter 3.2.2.2 --- Problem Definition --- p.27Chapter 3.2.2.3 --- Mathematical Model --- p.28Chapter 3.2.3 --- The r-Interdiction Median Problem with Fortification --- p.29Chapter 3.2.3.1 --- The Toy Example --- p.30Chapter 3.2.3.2 --- Problem Definition --- p.32Chapter 3.2.3.3 --- Mathematical Model --- p.33Chapter 3.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.35Chapter 3.2.4.1 --- Mathematical Model --- p.36Chapter 3.3 --- Solution Methodologies --- p.38Chapter 3.3.1 --- Model Reduction --- p.38Chapter 3.3.2 --- Variable Consolidation --- p.40Chapter 3.3.3 --- Implicit Enumeration --- p.45Chapter 3.4 --- Results and Discussion --- p.48Chapter 3.4.1 --- Data Sets --- p.48Chapter 3.4.1.1 --- Swain --- p.48Chapter 3.4.1.2 --- London --- p.49Chapter 3.4.1.3 --- Alberta --- p.49Chapter 3.4.2 --- Computational Study --- p.50Chapter 3.4.2.1 --- The p-Median Problem --- p.50Chapter 3.4.2.2 --- The r-Interdiction Median Problem --- p.58Chapter 3.4.2.3 --- The r-Interdiction Median Problem with Fortification --- p.63Chapter 3.4.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.68Chapter 3.5 --- Summary --- p.76Chapter 4 --- Hybrid Approaches --- p.79Chapter 4.1 --- Framework --- p.80Chapter 4.2 --- Tabu Assisted Heuristic Search --- p.81Chapter 4.2.1 --- A Tabu Assisted Heuristic Search Construct --- p.83Chapter 4.2.1.1 --- Search Space --- p.84Chapter 4.2.1.2 --- Initial Trial Solution --- p.85Chapter 4.2.1.3 --- Neighborhood Structure --- p.85Chapter 4.2.1.4 --- Local Search Procedure --- p.86Chapter 4.2.1.5 --- Form of Tabu Moves --- p.88Chapter 4.2.1.6 --- Addition of a Tabu Move --- p.88Chapter 4.2.1.7 --- Maximum Size of Tabu List --- p.89Chapter 4.2.1.8 --- Termination Criterion --- p.89Chapter 4.3 --- Hybrid Simulated Annealing Search --- p.90Chapter 4.3.1 --- A Hybrid Simulated Annealing Construct --- p.91Chapter 4.3.1.1 --- Random Selection of Immediate Neighbor --- p.92Chapter 4.3.1.2 --- Cooling Schedule --- p.93Chapter 4.3.1.3 --- Termination Criterion --- p.94Chapter 4.4 --- Hybrid Genetic Search Algorithm --- p.95Chapter 4.4.1 --- A Hybrid Genetic Search Construct --- p.99Chapter 4.4.1.1 --- Search Space --- p.99Chapter 4.4.1.2 --- Initial Population --- p.100Chapter 4.4.1.3 --- Selection --- p.104Chapter 4.4.1.4 --- Crossover --- p.105Chapter 4.4.1.5 --- Mutation --- p.106Chapter 4.4.1.6 --- New Population --- p.108Chapter 4.4.1.7 --- Termination Criterion --- p.109Chapter 4.5 --- Further Assessment --- p.109Chapter 4.6 --- Computational Study --- p.114Chapter 4.6.1 --- Parameter Selection --- p.115Chapter 4.6.1.1 --- Tabu Assisted Heuristic Search --- p.115Chapter 4.6.1.2 --- Hybrid Simulated Annealing Approach --- p.121Chapter 4.6.1.3 --- Hybrid Genetic Search Algorithm --- p.124Chapter 4.6.2 --- Expected Performance --- p.128Chapter 4.6.2.1 --- Tabu Assisted Heuristic Search --- p.128Chapter 4.6.2.2 --- Hybrid Simulated Annealing Approach --- p.138Chapter 4.6.2.3 --- Hybrid Genetic Search Algorithm --- p.146Chapter 4.6.2.4 --- Overall Comparison --- p.150Chapter 4.7 --- Summary --- p.153Chapter 5 --- A Special Case of the Median Problems --- p.156Chapter 5.1 --- Introduction --- p.157Chapter 5.2 --- Problem Formulation --- p.158Chapter 5.2.1 --- The r-Interdiction Covering Problem --- p.158Chapter 5.2.1.1 --- Problem Definition --- p.159Chapter 5.2.1.2 --- Mathematical Model --- p.160Chapter 5.2.2 --- The r-Interdiction Covering Problem with Fortification --- p.162Chapter 5.2.2.1 --- Problem Definition --- p.163Chapter 5.2.2.2 --- Mathematical Model --- p.164Chapter 5.2.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.167Chapter 5.2.3.1 --- Mathematical Model --- p.168Chapter 5.3 --- Theoretical Relationship --- p.170Chapter 5.4 --- Solution Methodologies --- p.172Chapter 5.5 --- Results and Discussion --- p.175Chapter 5.5.1 --- The r-Interdiction Covering Problem --- p.175Chapter 5.5.2 --- The r-Interdiction Covering Problem with Fortification --- p.178Chapter 5.5.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.182Chapter 5.6 --- Summary --- p.187Chapter 6 --- Conclusion --- p.189Chapter 6.1 --- Summary of Our Work --- p.189Chapter 6.2 --- Future Directions --- p.19