Network design under uncertainty and demand elasticity

Network design covers a large class of fundamental problems ubiquitous in the fields of transportation and communication. These problems are modelled mathematically using directed graphs and capture the trade-off between initial investment in infrastructure and operational costs. This thesis presents the use of mixed integer programming theory and algorithms to solve network design problems and their extensions. We focus on two types of network design problems, the first is a hub location problem in which the initial investments are in the form of fixed costs for installing infrastructure at nodes for them to be equipped for the transhipment of commodities. The second is a fixed-charge multicommodity network design problem in which investments are in the form of installing infrastructure on arcs so that they may be used to transport commodities. We first present an extension of the hub location problem where both demand and transportation cost uncertainty are considered. We propose mixed integer linear programming formulations and a branch-and-cut algorithm to solve robust counterparts for this problem. Comparing the proposed models' solutions to those obtained from a commensurate stochastic counterpart, we note that their performance is similar in the risk-neutral setting while solutions from the robust counterparts are significantly superior in the risk-averse setting. We next present exact algorithms based on Benders decomposition capable of solving large-scale instances of the classic uncapacitated fixed-charge multicommodity network design problem. The method combines the use of matheuristics, general mixed integer valid inequalities, and a cut-and-solve enumeration scheme. Computational experiments show the proposed approaches to be up to three orders of magnitude faster than the state-of-the-art general purpose mixed integer programming solver. Finally, we extend the classic fixed-charge multicommodity network design problem to a profit-oriented variant that accounts for demand elasticity, commodity selection, and service commitment. An arc-based and a path-based formulation are proposed. The former is a mixed integer non-convex problem solved with a general purpose global optimization solver while the latter is an integer linear formulation with exponentially many variables solved with a hybrid matheuristic. Further analysis shows the impact of considering demand elasticity to be significant in strategic network design

The production-assembly-distribution system design problem: modeling and solution approaches

This dissertation, which consists of four parts, is to (i) present a mixed integer programming model for the strategic design of an assembly system in the international business environment established by the North American Free Trade Agreement (NAFTA) with the focus on modeling the material flow network with assembly operations, (ii) compare different decomposition schemes and acceleration techniques to devise an effective branch-and-price solution approach, (iii) introduce a generalization of Dantzig-Wolf Decomposition (DWD), and (iv) propose a combination of dual-ascent and primal drop heuristics. The model deals with a broad set of design issues (bill-of-materials restrictions, international financial considerations, and material flows through the entire supply chain) using effective modeling devices. The first part especially focuses on modeling material flows in such an assembly system. The second part is to study several schemes for applying DWD to the productionassembly- distribution system design problem (PADSDP). Each scheme exploits selected embedded structures. The research objective is to enhance the rate of DWD convergence in application to PADSDP through formulating a rationale for decomposition by analyzing potential schemes, adopting acceleration techniques, and assessing the impacts of schemes and techniques computationally. Test results provide insights that may be relevant to other applications of DWD. The third part proposes a generalization of column generation, reformulating the master problem with fewer variables at the expense of adding more constraints; the subproblem structure does not change. It shows both analytically and computationally that the reformulation promotes faster convergence to an optimal solution in application to a linear program and to the relaxation of an integer program at each node in the branchand- bound tree. Further, it shows that this reformulation subsumes and generalizes prior approaches that have been shown to improve the rate of convergence in special cases. The last part proposes two dual-ascent algorithms and uses each in combination with a primal drop heuristic to solve the uncapacitated PADSDP, which is formulated as a mixed integer program. Computational results indicate that one combined heuristic finds solutions within 0.15% of optimality in most cases and within reasonable time, an efficacy suiting it well for actual large-scale applications

Infrastructure Design for Electric and Autonomous Vehicles

This thesis focuses on infrastructure design for the disruptive transportation technologies of electric vehicles (EVs) and autonomous vehicles (AVs) to enable their adoption at large scale. Particularly, two EV-related problem frameworks concerning the spatial distribution of charging stations and their respective capacity levels are studied, and a new problem is introduced to determine the optimal deployment of AV lanes and staging facilities to enable shared autonomous transportation in urban areas. The first problem is centered around determining optimal locations of fast-charging stations to enable long-distance transportation with EVs. A new mathematical model is developed to address this problem. This model not only determines optimal facility locations but also finds optimal routes for every origin-destination (OD) trip which follows the path that leads to the minimum total en route recharging. Through computational experiments, this model is shown to outperform the widely used maximum and set cover problem settings in the literature in terms of several routing-related performance measures. A Benders decomposition algorithm is developed to solve large-scale instances of the problem. Within this algorithm, a novel subproblem solution methodology is developed to accelerate the performance of the classical Benders implementation. Computational experiments on real-world transportation networks demonstrate the value of this methodology as it turns out to speed the classical Benders up to 900 times and allows solving instances with up to 1397 nodes. The second problem extends the previous one by seeking to determine EV charging station locations and capacities under stochastic vehicle flows and charging times. It also considers the route choice behavior of EV users by means of a bilevel optimization model. This model incorporates a probabilistic service requirement on the waiting time to charge, and it is studied under a framework where charging stations operate as M/M/c queuing systems. A decomposition-based solution methodology, that uses a logic-based Benders algorithm for the location-only problem, is developed to solve the proposed bilevel model. This methodology is designed to be versatile enough to be tailored for the cooperative or uncooperative EV user behavior. Computational experiments are conducted on real-life highway networks to evaluate how service level requirements, deviation tolerance levels, and route choice behavior affect the location and sizing decisions of charging stations. The third problem entails the staging facility location and AV lane deployment problem for shared autonomous transportation. The proposed problem aims to find the optimal locations of staging facilities utilizing a bi-objective model that minimizes total travel distance and the total AV travel not occurring on AV lanes with respect to a given AV lane deployment budget and a number of staging facilities to locate. A Benders decomposition algorithm with Pareto-optimal cuts is developed and the trade-offs with optimal solutions on benchmark instances are evaluated. Computational experiments are performed to analyze the effects of AV lane budget, staging facility count, and the objective preferences of decision makers on optimal solutions

Designing robust railroad blocking plans

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1998.Includes bibliographical references (leaves 121-130).On major domestic railroads, a typical general merchandise shipment, or commodity, may pass through many classification yards on its route from origin to destination. At these yards, the incoming traffic, which may consist of several shipments, is reclassified (sorted and grouped together) to be placed on outgoing trains. On average, each reclassification results in an one day delay for the shipment. In addition, the classification process is labor and capital intensive. To prevent shipments from being reclassified at every yard they pass through, several shipments may be grouped together to form a block. The blocking problem consists of choosing the set of blocks to be built at each terminal (the blocking plan) and assigning each commodity to a series of blocks that will take it from origin to destination. It is one of the most important problems in railroad freight transportation since a good blocking plan can reduce the number of reclassifications of the shipments, thus reducing operating costs and delays associated with excess reclassifications. We provide a variety of model formulations that attain the minimum costs for different problem instances. The deterministic model identifies the blocking plan for the problems with certainty in problem inputs. Static stochastic models provide blocking plans that are feasible for all possible realizations of uncertainties in demand and supply. Dynamic stochastic models generate blocking plans that balance flow costs and plan change costs for possible realizations of uncertainties. We adopt Lagrangian relaxation techniques to decompose the resulting huge mixed integer programming models into two smaller subproblems. This reduces storage requirements and computational efforts to solve these huge problems. We propose other enhancements to reduce computational burden, such as adding a set of valid inequalities and using advanced start dual solutions. These enhancements help tighten the lower bounds and facilitate the generation of high quality feasible solutions. We test the proposed models and solution approaches using the data from a major railroad. Compared to current blocking plans, the solutions from our model reduce the total number of classifications significantly, leading to potential savings of millions of dollars annually. We also investigate various problem aggregation techniques to determine the appropriate ways of generating satisfactory blocking plans with different levels of computational resources. We illustrate the benefits of robust planning by comparing the total costs of our robust plans with those of our deterministic plans. The experiments show that the the realized costs can be reduced by around 50% using robust blocking plans.by Hong Jin.Ph.D

Mixed integer programming approaches to problems combining network design and facility location

Viele heutzutage über das Internet angebotene Dienstleistungen benötigen wesentlich höhere Bandbreiten als von bestehenden lokalen Zugangsnetzen bereitgestellt werden. Telekommunikationsanbieter sind daher seit einigen Jahren bestrebt, ihre zum Großteil auf Kupferkabeln basierenden Zugangsnetze entsprechend zu modernisieren. Die gewünschte Erweiterung der bereitgestellten Bandbreiten wird oftmals erzielt, indem ein Teil des Kupfernetzes durch Glasfaser ersetzt wird. Dafür sind Versorgungsstandorte notwendig, an welchen die optischen und elektrischen Signale jeweils in einander umgewandelt werden. In der Praxis gibt es mehrere Strategien für die Installation von optischen Zugangsnetzen. Fiber-to-the-Home bezeichnet Netze, in denen jeder Haushalt direkt per Glasfaser angebunden wird. Wird je Wohngebäude eine optische Verbindung bereitgestellt, nennt man dies Fiber-to-the-Building. Endet die Glasfaserverbindung an einem Versorgungsstandort, welcher die Haushalte eines ganzen Wohnviertels durch Kupferkabel versorgt, bezeichnet man dies als Fiber-to-the-Curb. Inhalt dieser Dissertation sind mathematische Optimierungsmodelle für die kosteneffiziente Planung von auf Glasfaser basierenden lokalen Zugangsnetzen. Diese Modelle decken mehrere Aspekte der Planung ab, darunter die Fiber-to-the-Curb-Strategie mit zusätzlichen Restriktionen betreffend Ausfallssicherheit, gemischte Fiber-to-the-Home und Fiber-to-the-Curb-Netze sowie die Kapazitätenplanung von Fiber-to-the-Curb-Netzen. Ergebnis dieser Dissertation sind die theoretische Analyse der beschriebenen Modelle sowie effiziente Lösungsalgorithmen. Es kommen Methoden der kombinatorischen Optimierung zum Einsatz, darunter Umformulierungen auf erweiterten Graphen, zulässige Ungleichungen und Branch-and-Cut-Verfahren.In recent years, telecommunication service providers started to adapt their local access networks to the steadily growing demand for bandwidth of internet-based services. Most existing local access networks are based on copper cable and offer a limited bandwidth to customers. A common approach to increase this bandwidth is to replace parts of the network by fiber-optic cable. This requires the installation of facilities, where the optical signal is transformed into an electrical one and vice versa. Several strategies are commonly used to deploy fiber-optic networks. Connecting each customer via a fiber-optic link is referred to as Fiber-to-the-Home. If there is a fiber-optic connection for every building this is commonly referred to as Fiber-to-the-Building. If a fiber-optic connection leads to each facility that serves an entire neighborhood, this is referred to as Fiber-to-the-Curb. In this thesis we propose mathematical optimization models for the cost-efficient design of local access networks based on fiber-optic cable. These models cover several aspects, including the Fiber-to-the-Curb strategy under additional reliability constraints, mixed Fiber-to-the-Home and Fiber-to-the-Curb strategies and capacity planning of links and facilities for Fiber-to-the-Curb networks. We provide a theoretical analysis of the proposed models and develop efficient solution algorithms. We use state-of-the-art methods from combinatorial optimization including polyhedral comparisons, reformulations on extended graphs, valid inequalities and branch-and-cut procedures

On High-Performance Benders-Decomposition-Based Exact Methods with Application to Mixed-Integer and Stochastic Problems

RÉSUMÉ : La programmation stochastique en nombres entiers (SIP) combine la difficulté de l’incertitude et de la non-convexité et constitue une catégorie de problèmes extrêmement difficiles à résoudre. La résolution efficace des problèmes SIP est d’une grande importance en raison de leur vaste applicabilité. Par conséquent, l’intérêt principal de cette dissertation porte sur les méthodes de résolution pour les SIP. Nous considérons les SIP en deux étapes et présentons plusieurs algorithmes de décomposition améliorés pour les résoudre. Notre objectif principal est de développer de nouveaux schémas de décomposition et plusieurs techniques pour améliorer les méthodes de décomposition classiques, pouvant conduire à résoudre optimalement divers problèmes SIP. Dans le premier essai de cette thèse, nous présentons une revue de littérature actualisée sur l’algorithme de décomposition de Benders. Nous fournissons une taxonomie des améliorations algorithmiques et des stratégies d’accélération de cet algorithme pour synthétiser la littérature et pour identifier les lacunes, les tendances et les directions de recherche potentielles. En outre, nous discutons de l’utilisation de la décomposition de Benders pour développer une (méta- )heuristique efficace, décrire les limites de l’algorithme classique et présenter des extensions permettant son application à un plus large éventail de problèmes. Ensuite, nous développons diverses techniques pour surmonter plusieurs des principaux inconvénients de l’algorithme de décomposition de Benders. Nous proposons l’utilisation de plans de coupe, de décomposition partielle, d’heuristiques, de coupes plus fortes, de réductions et de stratégies de démarrage à chaud pour pallier les difficultés numériques dues aux instabilités, aux inefficacités primales, aux faibles coupes d’optimalité ou de réalisabilité, et à la faible relaxation linéaire. Nous testons les stratégies proposées sur des instances de référence de problèmes de conception de réseau stochastique. Des expériences numériques illustrent l’efficacité des techniques proposées. Dans le troisième essai de cette thèse, nous proposons une nouvelle approche de décomposition appelée méthode de décomposition primale-duale. Le développement de cette méthode est fondé sur une reformulation spécifique des sous-problèmes de Benders, où des copies locales des variables maîtresses sont introduites, puis relâchées dans la fonction objective. Nous montrons que la méthode proposée atténue significativement les inefficacités primales et duales de la méthode de décomposition de Benders et qu’elle est étroitement liée à la méthode de décomposition duale lagrangienne. Les résultats de calcul sur divers problèmes SIP montrent la supériorité de cette méthode par rapport aux méthodes classiques de décomposition. Enfin, nous étudions la parallélisation de la méthode de décomposition de Benders pour étendre ses performances numériques à des instances plus larges des problèmes SIP. Les variantes parallèles disponibles de cette méthode appliquent une synchronisation rigide entre les processeurs maître et esclave. De ce fait, elles souffrent d’un important déséquilibre de charge lorsqu’elles sont appliquées aux problèmes SIP. Cela est dû à un problème maître difficile qui provoque un important déséquilibre entre processeur et charge de travail. Nous proposons une méthode Benders parallèle asynchrone dans un cadre de type branche-et-coupe. L’assouplissement des exigences de synchronisation entraine des problèmes de convergence et d’efficacité divers auxquels nous répondons en introduisant plusieurs techniques d’accélération et de recherche. Les résultats indiquent que notre algorithme atteint des taux d’accélération plus élevés que les méthodes synchronisées conventionnelles et qu’il est plus rapide de plusieurs ordres de grandeur que CPLEX 12.7.----------ABSTRACT : Stochastic integer programming (SIP) combines the difficulty of uncertainty and non-convexity, and constitutes a class of extremely challenging problems to solve. Efficiently solving SIP problems is of high importance due to their vast applicability. Therefore, the primary focus of this dissertation is on solution methods for SIPs. We consider two-stage SIPs and present several enhanced decomposition algorithms for solving them. Our main goal is to develop new decomposition schemes and several acceleration techniques to enhance the classical decomposition methods, which can lead to efficiently solving various SIP problems to optimality. In the first essay of this dissertation, we present a state-of-the-art survey of the Benders decomposition algorithm. We provide a taxonomy of the algorithmic enhancements and the acceleration strategies of this algorithm to synthesize the literature, and to identify shortcomings, trends and potential research directions. In addition, we discuss the use of Benders decomposition to develop efficient (meta-)heuristics, describe the limitations of the classical algorithm, and present extensions enabling its application to a broader range of problems. Next, we develop various techniques to overcome some of the main shortfalls of the Benders decomposition algorithm. We propose the use of cutting planes, partial decomposition, heuristics, stronger cuts, and warm-start strategies to alleviate the numerical challenges arising from instabilities, primal inefficiencies, weak optimality/feasibility cuts, and weak linear relaxation. We test the proposed strategies with benchmark instances from stochastic network design problems. Numerical experiments illustrate the computational efficiency of the proposed techniques. In the third essay of this dissertation, we propose a new and high-performance decomposition approach, called Benders dual decomposition method. The development of this method is based on a specific reformulation of the Benders subproblems, where local copies of the master variables are introduced and then priced out into the objective function. We show that the proposed method significantly alleviates the primal and dual shortfalls of the Benders decomposition method and it is closely related to the Lagrangian dual decomposition method. Computational results on various SIP problems show the superiority of this method compared to the classical decomposition methods as well as CPLEX 12.7. Finally, we study parallelization of the Benders decomposition method. The available parallel variants of this method implement a rigid synchronization among the master and slave processors. Thus, it suffers from significant load imbalance when applied to the SIP problems. This is mainly due to having a hard mixed-integer master problem that can take hours to be optimized. We thus propose an asynchronous parallel Benders method in a branchand- cut framework. However, relaxing the synchronization requirements entails convergence and various efficiency problems which we address them by introducing several acceleration techniques and search strategies. In particular, we propose the use of artificial subproblems, cut generation, cut aggregation, cut management, and cut propagation. The results indicate that our algorithm reaches higher speedup rates compared to the conventional synchronized methods and it is several orders of magnitude faster than CPLEX 12.7