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

Motivated 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 ℓp-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.Fonds de la Recherche Scientique - FNRSMinisterio de Economía y CompetitividadFondo Europeo de Desarrollo Regiona

Optimization Approaches To Protect Transportation Infrastructure Against Strategic and Random Disruptions

Past and recent events have proved that critical infrastructure are vulnerable to natural catastrophes, unintentional accidents and terrorist attacks. Protecting these systems is critical to avoid loss of life and to guard against economical upheaval. A systematic approach to plan security investments is paramount to guarantee that limited protection resources are utilized in the most effcient manner. This thesis provides a detailed review of the optimization models that have been introduced in the past to identify vulnerabilities and protection plans for critical infrastructure. The main objective of this thesis is to study new and more realistic models to protect transportation infrastructure such as railway and road systems against man made and natural disruptions. Solution algorithms are devised to effciently solve the complex formulations proposed. Finally, several illustrative case studies are analysed to demonstrate how solving these models can be used to support effcient protection decisions

Determining the most vulnerable components in a transportatıon network

Transportation networks belong to the class of critical infrastructure networks since a small deterioration in the service provision has the potential to cause considerable negative consequences on everyday activities. Among the reasons for the deterioration we can mention the shutdown of a subway station, the closure of one or more lanes on a bridge, the operation of an airport at a much reduced capacity. In order to measure the vulnerability of transportation network, it is necessary to determine the maximum possible disruption by assuming that there is an intelligent attacker wishing to give damage to the components of the network including the stations/stops and linkages. Identifying the worst disruptions can be realized by using interdiction models that are formulated by a bilevel mathematical programming model involving two decision makers: leader and follower. In this paper, we develop such a model referred to as attacker-operator model, where the leader is a virtual attacker who wants to cause the maximum possible disruption in the transportation network by minimizing the amount of flow among the nodes of the network, while the follower is the system operator who tries to reorganize the flow in the most effective way by maximizing the flow after the disruption. The benefit of such a model to the system operator is to determine the most vulnerable stations and linkages in the transportation network on one hand, and to take precautions in preventing the negative effects of the disruption on the other hand.TUBİTAK Sponsorlu YayınWOS:000458617100002Emerging Sources Citation IndexArticleOcak2018YÖK - 2017-1

Optimizing dynamic investment decisions for railway systems protection

Past and recent events have shown that railway infrastructure systems are particularly vulnerable to natural catastrophes, unintentional accidents and terrorist attacks. Protection investments are instrumental in reducing economic losses and preserving public safety. A systematic approach to plan security investments is paramount to guarantee that limited protection resources are utilized in the most efficient manner. In this article, we present an optimization model to identify the railway assets which should be protected to minimize the impact of worst case disruptions on passenger flows. We consider a dynamic investment problem where protection resources become available over a planning horizon. The problem is formulated as a bilevel mixed-integer model and solved using two different decomposition approaches. Random instances of different sizes are generated to compare the solution algorithms. The model is then tested on the Kent railway network to demonstrate how the results can be used to support efficient protection decisions

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

Multi-Level Multi-Objective Programming and Optimization for Integrated Air Defense System Disruption

The U.S. military\u27s ability to project military force is being challenged. This research develops and demonstrates the application of three respective sensor location, relocation, and network intrusion models to provide the mathematical basis for the strategic engagement of emerging technologically advanced, highly-mobile, Integrated Air Defense Systems. First, we propose a bilevel mathematical programming model for locating a heterogeneous set of sensors to maximize the minimum exposure of an intruder\u27s penetration path through a defended region. Next, we formulate a multi-objective, bilevel optimization model to relocate surviving sensors to maximize an intruder\u27s minimal expected exposure to traverse a defended border region, minimize the maximum sensor relocation time, and minimize the total number of sensors requiring relocation. Lastly, we present a trilevel, attacker-defender-attacker formulation for the heterogeneous sensor network intrusion problem to optimally incapacitate a subset of the defender\u27s sensors and degrade a subset of the defender\u27s network to ultimately determine the attacker\u27s optimal penetration path through a defended network

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

Improving estimates for reliability and cost in microgrid investment planning models

This paper develops a new microgrid investment planning model that determines cost-optimal investment and operation of distributed energy resources (DERs) in a microgrid. We formulate the problem in a bilevel framework, using particle swarm optimization to determine investment and the DER-CAM model (Distributed Energy Resources Customer Adoption Model) to determine operation. The model further uses sequential Monte Carlo simulation to explicitly simulate power outages and integrates time-varying customer damage functions to calculate interruption costs from outages. The model treats nonlinearities in reliability evaluation directly, where existing linear models make critical simplifying assumptions. It combines investment, operating, and interruption costs together in a single objective function, thereby treating reliability endogenously and finding the cost-optimal trade-off between cost and reliability - two competing objectives. In benchmarking against a version of the DER-CAM model that treats reliability through a constraint on minimum investment, our new model improves estimates of reliability (the loss of load expectation) by up to 600%, of the total system cost by 6%-18%, of the investment cost by 32%-50%, and of the economic benefit of investing 27%-47%. Improvements stem from large differences in investment of up to 56% for natural gas generators, solar photovoltaics, and battery energy storage