Vulnerability Assessment and Re-routing of Freight Trains Under Disruptions: A Coal Supply Chain Network Application

In this paper, we present a two-stage mixed integer programming (MIP) interdiction model in which an interdictor chooses a limited amount of elements to attack first on a given network, and then an operator dispatches trains through the residual network. Our MIP model explicitly incorporates discrete unit flows of trains on the rail network with time-variant capacities. A real coal rail transportation network is used in order to generate scenarios to provide tactical and operational level vulnerability assessment analysis including rerouting decisions, travel and delay costs analysis, and the frequency of interdictions of facilities for the dynamic rail system

Multiple Allocation Hub Interdiction and Protection Problems: Model Formulations and Solution Approaches

In this paper, we present computationally efficient formulations for the multiple allocation hub interdiction and hub protection problems, which are bilevel and trilevel mixed integer linear programs, respectively. In the hub interdiction problem, the aim is to identify a subset of r critical hubs from an existing set of p hubs that when interdicted results in the maximum post-interdiction cost of routing flows. We present two alternate ways of reducing the bilevel hub interdiction model to a single level optimization problem. The first approach uses the dual formulation of the lower level problem. The second approach exploits the structure of the lower level problem to replace it by a set of closest assignment constraints (CACs). We present alternate sets of CACs, study their dominance relationships, and report their computational performances. Further, we propose refinements to CACs that offer computational advantages of an order-of-magnitude compared to the one existing in the literature. Further, our proposed modifications offer structural advantages for Benders decomposition, which lead to substantial computational savings, particularly for large problem instances. Finally, we study and solve large scale instances of the trilevel hub protection problem exactly by utilizing the ideas developed for the hub interdiction problem

Prioritizing Satellite Payload Selection via Optimization

This thesis develops optimization models for prioritizing payloads for inclusion on satellite buses with volume, power, weight and budget constraints. The first model considers a single satellite launch for which the budget is uncertain and constellation requirements are not considered. Subsequently, we include constellation requirements and provide a more enhanced model. Both single-launch models provide a prioritized list of payloads to include on the launch before the budget is realized. The single-launch models are subsequently extended to a sequence of multiple launches in two cases, both of which incorporate an explicit dependence on the constellation composition at each launch epoch. The first case ignores future launches and solves a series of independent single-launch problems. The second case considers all launches simultaneously. The optimization models for single- and multiple-launch cases are evaluated through a computational study. It was found that, when the budget distribution is skewed, the prioritization model outperforms a greedy payload selection heuristic in the single-launch model. For the multiple-launch models, it was found that the consideration of future launches can significantly improve the objective function values

Network Interdiction under Uncertainty

We consider variants to one of the most common network interdiction formulations: the shortest path interdiction problem. This problem involves leader and a follower playing a zero-sum game over a directed network. The leader interdicts a set of arcs, and arc costs increase each time they are interdicted. The follower observes the leader\u27s actions and selects a shortest path in response. The leader\u27s optimal interdiction strategy maximizes the follower\u27s minimum-cost path. Our first variant allows the follower to improve the network after the interdiction by lowering the costs of some arcs, and the leader is uncertain regarding the follower\u27s cardinality budget restricting the arc improvements. We propose a multiobjective approach for this problem, with each objective corresponding to a different possible improvement budget value. To this end, we also present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem, and which tends to scale better than competing methods as the number of objectives grows. In our second variant, the leader selects a policy of randomized interdiction actions, and the follower uses the probability of where interdictions are deployed on the network to select a path having the minimum expected cost. We show that this continuous non-convex problem becomes strongly NP-hard when the cost functions are convex or when they are concave. After formally describing each variant, we present various algorithms for solving them, and we examine the efficacy of all our algorithms on test beds of randomly generated instances

Robust Design of Distribution Networks Considering Worst Case Interdictions

Multi-echelon facility location models are commonly employed to design transportation systems. While they provide cost-efficient designs, they are prone to severe financial loss in the event of the disruption of any of its facilities. Additionally, the recent crisis in the world motivates OR practitioners to develop models that better integrate disruptive event in the design phase of a distribution network. In this research, we propose a two-echelon capacitated facility location model under the risk of a targeted attack, which identifies the optimal location of intermediate facilities by minimizing the weighted sum of pre and post interdiction flow cost and the fixed cost of opening intermediate facilities. The developed model results in a tri-level Mixed Integer Programming (MIP) formulation, reformulated in a two-level MIP. Hence, we prescribe solution methods based on Bender Decomposition as well as two variants that enhance the speed performance of the algorithm. The results reveal the importance of selecting backup facilities and highlight that premium paid to design a robust distribution network is negligible given the benefit of reducing the post-interdiction cost when a disruptive event occurs

Locating and Protecting Facilities Subject to Random Disruptions and Attacks

Recent events such as the 2011 Tohoku earthquake and tsunami in Japan have revealed the vulnerability of networks such as supply chains to disruptive events. In particular, it has become apparent that the failure of a few elements of an infrastructure system can cause a system-wide disruption. Thus, it is important to learn more about which elements of infrastructure systems are most critical and how to protect an infrastructure system from the effects of a disruption. This dissertation seeks to enhance the understanding of how to design and protect networked infrastructure systems from disruptions by developing new mathematical models and solution techniques and using them to help decision-makers by discovering new decision-making insights. Several gaps exist in the body of knowledge concerning how to design and protect networks that are subject to disruptions. First, there is a lack of insights on how to make equitable decisions related to designing networks subject to disruptions. This is important in public-sector decision-making where it is important to generate solutions that are equitable across multiple stakeholders. Second, there is a lack of models that integrate system design and system protection decisions. These models are needed so that we can understand the benefit of integrating design and protection decisions. Finally, most of the literature makes several key assumptions: 1) protection of infrastructure elements is perfect, 2) an element is either fully protected or fully unprotected, and 3) after a disruption facilities are either completely operational or completely failed. While these may be reasonable assumptions in some contexts, there may exist contexts in which these assumptions are limiting. There are several difficulties with filling these gaps in the literature. This dissertation describes the discovery of mathematical formulations needed to fill these gaps as well as the identification of appropriate solution strategies

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