New models for the location of controversial facilities: A bilevel programming approach

International audienceMotivated by recent real-life applications in Location Theory in which the location decisions generate controversy, we propose a novel bilevel location model in which, on the one hand, there is a leader that chooses among a number of fixed potential locations which ones to establish. Next, on the second hand, there is one or several followers that, once the leader location facilities have been set, chooses his location points in a continuous framework. The leader's goal is to maximize some proxy to the weighted distance to the follower's location points, while the follower(s) aim is to locate his location points as close as possible to the leader ones. We develop the bilevel location model for one follower and for any polyhedral distance, and we extend it for several followers and any p-norm, p ∈ Q, p ≥ 1. We prove the NP-hardness of the problem and propose different mixed integer linear programming formulations. Moreover, we develop alternative Benders decomposition algorithms for the problem. Finally, we report some computational results comparing the formulations and the Benders decompositions on a set of instances

OPTIMIZATION OF RAILWAY TRANSPORTATION HAZMATS AND REGULAR COMMODITIES

Transportation of dangerous goods has been receiving more attention in the realm of academic and scientific research during the last few decades as countries have been increasingly becoming industrialized throughout the world, thereby making Hazmats an integral part of our life style. However, the number of scholarly articles in this field is not as many as those of other areas in SCM. Considering the low-probability-and-high-consequence (LPHC) essence of transportation of Hazmats, on the one hand, and immense volume of shipments accounting for more than hundred tons in North America and Europe, on the other, we can safely state that the number of scholarly articles and dissertations have not been proportional to the significance of the subject of interest. On this ground, we conducted our research to contribute towards further developing the domain of Hazmats transportation, and sustainable supply chain management (SSCM), in general terms. Transportation of Hazmats, from logistical standpoint, may include all modes of transport via air, marine, road and rail, as well as intermodal transportation systems. Although road shipment is predominant in most of the literature, railway transportation of Hazmats has proven to be a potentially significant means of transporting dangerous goods with respect to both economies of scale and risk of transportation; these factors, have not just given rise to more thoroughly investigation of intermodal transportation of Hazmats using road and rail networks, but has encouraged the competition between rail and road companies which may indeed have some inherent advantages compared to the other medium due to their infrastructural and technological backgrounds. Truck shipment has ostensibly proven to be providing more flexibility; trains, per contra, provide more reliability in terms of transport risk for conveying Hazmats in bulks. In this thesis, in consonance with the aforementioned motivation, we provide an introduction into the hazardous commodities shipment through rail network in the first chapter of the thesis. Providing relevant statistics on the volume of Hazmat goods, number of accidents, rate of incidents, and rate of fatalities and injuries due to the incidents involving Hazmats, will shed light onto the significance of the topic under study. As well, we review the most pertinent articles while putting more emphasis on the state-of-the-art papers, in chapter two. Following the discussion in chapter 3 and looking at the problem from carrier company’s perspective, a mixed integer quadratically constraint problem (MIQCP) is developed which seeks for the minimization of transportation cost under a set of constraints including those associating with Hazmats. Due to the complexity of the problem, the risk function has been piecewise linearized using a set of auxiliary variables, thereby resulting in an MIP problem. Further, considering the interests of both carrier companies and regulatory agencies, which are minimization of cost and risk, respectively, a multiobjective MINLP model is developed, which has been reduced to an MILP through piecewise linearization of the risk term in the objective function. For both single-objective and multiobjective formulations, model variants with bifurcated and nonbifurcated flows have been presented. Then, in chapter 4, we carry out experiments considering two main cases where the first case presents smaller instances of the problem and the second case focuses on a larger instance of the problem. Eventually, in chapter five, we conclude the dissertation with a summary of the overall discussion as well as presenting some comments on avenues of future work

Contributions to robust and bilevel optimization models for decision-making

Los problemas de optimización combinatorios han sido ampliamente estudiados en la literatura especializada desde mediados del siglo pasado. No obstante, en las últimas décadas ha habido un cambio de paradigma en el tratamiento de problemas cada vez más realistas, en los que se incluyen fuentes de aleatoriedad e incertidumbre en los datos, múltiples criterios de optimización y múltiples niveles de decisión. Esta tesis se desarrolla en este contexto. El objetivo principal de la misma es el de construir modelos de optimización que incorporen aspectos inciertos en los parámetros que de nen el problema así como el desarrollo de modelos que incluyan múltiples niveles de decisión. Para dar respuesta a problemas con incertidumbre usaremos los modelos Minmax Regret de Optimización Robusta, mientras que las situaciones con múltiples decisiones secuenciales serán analizadas usando Optimización Binivel. En los Capítulos 2, 3 y 4 se estudian diferentes problemas de decisión bajo incertidumbre a los que se dará una solución robusta que proteja al decisor minimizando el máximo regret en el que puede incurrir. El criterio minmax regret analiza el comportamiento del modelo bajo distintos escenarios posibles, comparando su e ciencia con la e ciencia óptima bajo cada escenario factible. El resultado es una solución con una eviciencia lo más próxima posible a la óptima en el conjunto de las posibles realizaciones de los parámetros desconocidos. En el Capítulo 2 se estudia un problema de diseño de redes en el que los costes, los pares proveedor-cliente y las demandas pueden ser inciertos, y además se utilizan poliedros para modelar la incertidumbre, permitiendo de este modo relaciones de dependencia entre los parámetros. En el Capítulo 3 se proponen, en el contexto de la secuenciación de tareas o la computación grid, versiones del problema del camino más corto y del problema del viajante de comercio en el que el coste de recorrer un arco depende de la posición que este ocupa en el camino, y además algunos de los parámetros que de nen esta función de costes son inciertos. La combinación de la dependencia en los costes y la incertidumbre en los parámetros da lugar a dependencias entre los parámetros desconocidos, que obliga a modelar los posibles escenarios usando conjuntos más generales que los hipercubos, habitualmente utilizados en este contexto. En este capítulo, usaremos poliedros generales para este cometido. Para analizar este primer bloque de aplicaciones, en el Capítulo 4, se analiza un modelo de optimización en el que el conjunto de posibles escenarios puede ser alterado mediante la realización de inversiones en el sistema. En los problemas estudiados en este primer bloque, cada decisión factible es evaluada en base a la reacción más desfavorable que pueda darse en el sistema. En los Capítulos 5 y 6 seguiremos usando esta idea pero ahora se supondrá que esa reacción a la decisión factible inicial está en manos de un adversario o follower. Estos dos capítulos se centran en el estudio de diferentes modelos binivel. La Optimización Binivel aborda problemas en los que existen dos niveles de decisión, con diferentes decisores en cada uno ellos y la decisión se toma de manera jerárquica. En concreto, en el Capítulo 5 se estudian distintos modelos de jación de precios en el contexto de selección de carteras de valores, en los que el intermediario nanciero, que se convierte en decisor, debe jar los costes de invertir en determinados activos y el inversor debe seleccionar su cartera de acuerdo a distintos criterios. Finalmente, en el Capítulo 6 se estudia un problema de localización en el que hay distintos decisores, con intereses contrapuestos, que deben determinar secuencialmente la ubicación de distintas localizaciones. Este modelo de localización binivel se puede aplicar en contextos como la localización de servicios no deseados o peligrosos (plantas de reciclaje, centrales térmicas, etcétera) o en problemas de ataque-defensa. Todos estos modelos se abordan mediante el uso de técnicas de Programación Matemática. De cada uno de ellos se analizan algunas de sus propiedades y se desarrollan formulaciones y algoritmos, que son examinados también desde el punto de vista computacional. Además, se justica la validez de los modelos desde un enfoque de las aplicaciones prácticas. Los modelos presentados en esta tesis comparten la peculiaridad de requerir resolver distintos problemas de optimización encajados.Combinatorial optimization problems have been extensively studied in the specialized literature since the mid-twentieth century. However, in recent decades, there has been a paradigm shift to the treatment of ever more realistic problems, which include sources of randomness and uncertainty in the data, multiple optimization criteria and multiple levels of decision. This thesis concerns the development of such concepts. Our objective is to study optimization models that incorporate uncertainty elements in the parameters de ning the model, as well as the development of optimization models integrating multiple decision levels. In order to consider problems under uncertainty, we use Minmax Regret models from Robust Optimization; whereas the multiplicity and hierarchy in the decision levels is addressed using Bilevel Optimization. In Chapters 2, 3 and 4, we study di erent decision problems under uncertainty to which we give a robust solution that protects the decision-maker minimizing the maximum regret that may occur. This robust criterion analyzes the performance of the system under multiple possible scenarios, comparing its e ciency with the optimum one under each feasible scenario. We obtain, as a result, a solution whose e ciency is as close as possible to the optimal one in the set of feasible realizations of the uncertain parameters. In Chapter 2, we study a network design problem in which the costs, the pairs supplier-customer, and the demands can take uncertain values. Furthermore, the uncertainty in the parameters is modeled via polyhedral sets, thereby allowing relationships among the uncertain parameters. In Chapter 3, we propose time-dependent versions of the shortest path and traveling salesman problems in which the costs of traversing an arc depends on the relative position that the arc occupies in the path. Moreover, we assume that some of the parameters de ning these costs can be uncertain. These models can be applied in the context of task sequencing or grid computing. The incorporation of time-dependencies together with uncertainties in the parameters gives rise to dependencies among the uncertain parameters, which require modeling the possible scenarios using more general sets than hypercubes, normally used in this context. In this chapter, we use general polyhedral sets with this purpose. To nalize this rst block of applications, in Chapter 4, we analyze an optimization model in which the set of possible scenarios can be modi ed by making some investments in the system. In the problems studied in this rst block, each feasible decision is evaluated based on the most unfavorable possible reaction of the system. In Chapters 5 and 6, we will still follow this idea, but assuming that the reaction to the initial feasible decision will be held by a follower or an adversary, instead of assuming the most unfavorable one. These two chapters are focused on the study of some bilevel models. Bilevel Optimization addresses optimization problems with multiple decision levels, di erent decision-makers in each level and a hierarchical decision order. In particular, in Chapter 5, we study some price setting problems in the context of portfolio selection. In these problems, the nancial intermediary becomes a decisionmaker and sets the transaction costs for investing in some securities, and the investor chooses her portfolio according to di erent criteria. Finally, in Chapter 6, we study a location problem with several decision-makers and opposite interests, that must set, sequentially, some location points. This bilevel location model can be applied in practical applications such as the location of semi-obnoxious facilities (power or electricity plants, waste dumps, etc.) or interdiction problems. All these models are stated from a Mathematical Programming perspective, analyzing their properties and developing formulations and algorithms, that are tested from a computational point of view. Furthermore, we pay special attention to justifying the validity of the models from the practical applications point of view. The models presented in this thesis share the characteristic of involving the resolution of nested optimization problems.Premio Extraordinario de Doctorado U

Mathematical models for the design and planning of transportation on demand in urban logistics networks

Falta palabras claveThe freight-transport industry has made enormous progress in the development and application of logistics techniques that has transformed its operation, giving raise to impressive productivity gains and improved responsiveness to its consumers. While the separation of passenger and freight traffic is a relatively new concept in historic terms, recent approaches point out that most freight-logistics techniques are transferable to the passenger-transport industry. In this sense, passenger logistics can be understood as the application of logistics techniques in urban contexts to the passenger-transport industry. The design of an urban logistic network integrates decisions about the emplacement, number and capacities of the facilities that will be located, the flows between them, demand patterns and cost structures that will validate the profitability of the process. This strategic decision settles conditions and constraints of latter tactical and operative decisions. In addition, different criteria are involved during the whole process so, in general terms, it is essential an exhaustive analysis, from the mathematical point of view, of the decision problem. The optimization models resulting from this analysis require techniques and mathematical algorithms in constant development and evolution. Such methods demand more and more a higher number of interrelated elements due to the increase of scale used in the current logistics and transportation problems. This PhD dissertation explores different topics related to Mathematical models for the design and planning of transportation on demand in urban logistics networks. The contributions are divided into six main chapters since and, in addition, Chapter 0 offers a basic background for the contents that are presented in the remaining six chapters. Chapter 1 deals with the Transit Network Timetabling and Scheduling Problem (TNTSP) in a public transit line. The TNTSP aims at determining optimal timetables for each line in a transit network by establishing departure and arrival times of each vehicle at each station. We assume that customers know departure times of line runs offered by the system. However, each user, traveling later of before their desired travel time, will give rise to an inconvenience cost, or a penalty cost if that user cannot be served according to the scheduled timetable. The provided formulation allocates each user to the best possible timetable considering capacity constraints. The problem is formulated using a p-median based approach and solved using a clustering technique. Computational results that show useful applications of this methodology are also included. Chapter 2 deals with the TNTSP in a public transit network integrating in the model the passengers' routings. The current models for planning timetables and vehicle schedules use the knowledge of passengers' routings from the results of a previous phase. However, the actual route a passenger will take strongly depends on the timetable, which is not yet known a priori. The provided formulation guarantees that each user is allocated to the best possible timetable ensuring capacity constraints. Chapter 3 deals with the rescheduling problem in a transit line that has suffered a eet size reduction. We present different modelling possibilities depending on the assumptions that need to be included in the modelization and we show that the problem can be solved rapidly by using a constrained maxcost- ow problem whose coe_cient matrix we prove is totally unimodular. We test our results in a testbed of random instances outperforming previous results in the literature. An experimental study, based on a line segment of the Madrid Regional Railway network, shows that the proposed approach provides optimal reassignment decisions within computation times compatible with real-time use. In Chapter 4 we discuss the multi-criteria p-facility median location problem on networks with positive and negative weights. We assume that the demand is located at the nodes and can be different for each criterion under consideration. The goal is to obtain the set of Pareto-optimal locations in the graph and the corresponding set of non-dominated objective values. To that end, we first characterize the linearity domains of the distance functions on the graph and compute the image of each linearity domain in the objective space. The lower envelope of a transformation of all these images then gives us the set of all non-dominated points in the objective space and its preimage corresponds to the set of all Pareto-optimal solutions on the graph. For the bicriteria 2-facility case we present a low order polynomial time algorithm. Also for the general case we propose an efficient algorithm, which is polynomial if the number of facilities and criteria is fixed. In Chapter 5, Ordered Weighted Average optimization problems are studied from a modeling point of view. Alternative integer programming formulations for such problems are presented and their respective domains studied and compared. In addition, their associated polyhedra are studied and some families of facets and new families of valid inequalities presented. The proposed formulations are particularized for two well-known combinatorial optimization problems, namely, shortest path and minimum cost perfect matching, and the results of computational experiments presented and analyzed. These results indicate that the new formulations reinforced with appropriate constraints can be effective for efficiently solving medium to large size instances. In Chapter 6, the multiobjective Minimum cost Spanning Tree Problem (MST) is studied from a modeling point of view. In particular, we use the ordered median objective function as an averaging operator to aggregate the vector of objective values of feasible solutions. This leads to the Ordered Weighted Average Spanning Tree Problem (OWASTP), which we study in this work. To solve the problem, we propose different integer programming formulations based in the most relevant MST formulations and in a new one. We analyze several enhancements for these formulations and we test their performance over a testbed of random instances. Finally we show that an appropriate choice will allow us to solve larger instances with more objectives than those previously solved in the literature.Premio Extraordinario de Doctorado U