Decomposition Algorithms in Stochastic Integer Programming: Applications and Computations.

In this dissertation we focus on two main topics. Under the first topic, we develop a new framework for stochastic network interdiction problem to address ambiguity in the defender risk preferences. The second topic is dedicated to computational studies of two-stage stochastic integer programs. More specifically, we consider two cases. First, we develop some solution methods for two-stage stochastic integer programs with continuous recourse; second, we study some computational strategies for two-stage stochastic integer programs with integer recourse. We study a class of stochastic network interdiction problems where the defender has incomplete (ambiguous) preferences. Specifically, we focus on the shortest path network interdiction modeled as a Stackelberg game, where the defender (leader) makes an interdiction decision first, then the attacker (follower) selects a shortest path after the observation of random arc costs and interdiction effects in the network. We take a decision-analytic perspective in addressing probabilistic risk over network parameters, assuming that the defender\u27s risk preferences over exogenously given probabilities can be summarized by the expected utility theory. Although the exact form of the utility function is ambiguous to the defender, we assume that a set of historical data on some pairwise comparisons made by the defender is available, which can be used to restrict the shape of the utility function. We use two different approaches to tackle this problem. The first approach conducts utility estimation and optimization separately, by first finding the best fit for a piecewise linear concave utility function according to the available data, and then optimizing the expected utility. The second approach integrates utility estimation and optimization, by modeling the utility ambiguity under a robust optimization framework following \cite{armbruster2015decision} and \cite{Hu}. We conduct extensive computational experiments to evaluate the performances of these approaches on the stochastic shortest path network interdiction problem. In third chapter, we propose partition-based decomposition algorithms for solving two-stage stochastic integer program with continuous recourse. The partition-based decomposition method enhance the classical decomposition methods (such as Benders decomposition) by utilizing the inexact cuts (coarse cuts) induced by a scenario partition. Coarse cut generation can be much less expensive than the standard Benders cuts, when the partition size is relatively small compared to the total number of scenarios. We conduct an extensive computational study to illustrate the advantage of the proposed partition-based decomposition algorithms compared with the state-of-the-art approaches. In chapter four, we concentrate on computational methods for two-stage stochastic integer program with integer recourse. We consider the partition-based relaxation framework integrated with a scenario decomposition algorithm in order to develop strategies which provide a better lower bound on the optimal objective value, within a tight time limit

DECENTRALIZED ALGORITHMS FOR NASH EQUILIBRIUM PROBLEMS – APPLICATIONS TO MULTI-AGENT NETWORK INTERDICTION GAMES AND BEYOND

Nash equilibrium problems (NEPs) have gained popularity in recent years in the engineering community due to their ready applicability to a wide variety of practical problems ranging from communication network design to power market analysis. There are strong links between the tools used to analyze NEPs and the classical techniques of nonlinear and combinatorial optimization. However, there remain significant challenges in both the theoretical and algorithmic analysis of NEPs. This dissertation studies certain special classes of NEPs, with the overall purpose of analyzing theoretical properties such as existence and uniqueness, while at the same time proposing decentralized algorithms that provably converge to solutions. The subclasses are motivated by relevant application examples

Games for the Optimal Deployment of Security Forces

In this thesis, we develop mathematical models for the optimal deployment of security forces addressing two main challenges: adaptive behavior of the adversary and uncertainty in the model. We address several security applications and model them as agent-intruder games. The agent represents the security forces which can be the coast guard, airport control, or military assets, while the intruder represents the agent's adversary such as illegal fishermen, terrorists or enemy submarines. To determine the optimal agent's deployment strategy, we assume that we deal with an intelligent intruder. This means that the intruder is able to deduce the strategy of the agent. To take this into account, for example by using randomized strategies, we use game theoretical models which are developed to model situations in which two or more players interact. Additionally, uncertainty may arise at several aspects. For example, there might be uncertainty in sensor observations, risk levels of certain areas, or travel times. We address this uncertainty by combining game theoretical models with stochastic modeling, such as queueing theory, Bayesian beliefs, and stochastic game theory. This thesis consists of three parts. In the first part, we introduce two game theoretical models on a network of queues. First, we develop an interdiction game on a network of queues where the intruder enters the network as a regular customer and aims to route to a target node. The agent is modeled as a negative customer which can inspect the queues and remove intruders. By modeling this as a queueing network, stochastic arrivals and travel times can be taken into account. The second model considers a non-cooperative game on a queueing network where multiple players decide on a route that minimizes their sojourn time. We discuss existence of pure Nash equilibria for games with continuous and discrete strategy space and describe how such equilibria can be found. The second part of this thesis considers dynamic games in which information that becomes available during the game plays a role. First, we consider partially observable agent-intruder games (POAIGs). In these types of games, both the agent and the intruder do not have full information about the state space. However, they do partially observe the state space, for example by using sensors. We prove the existence of approximate Nash equilibria for POAIGs with an infinite time horizon and provide methods to find (approximate) solutions for both POAIGs with a finite time horizon and POAIGs with an infinite time horizon. Second, we consider anti-submarine warfare operations with time dependent strategies where parts of the agent's strategy becomes available to the intruder during the game. The intruder represents an enemy submarine which aims to attack a high value unit. The agent is trying to prevent this by the deployment of both frigates and helicopters. In the last part of this thesis we discuss games with restrictions on the agent's strategy. We consider a special case of security games dealing with the protection of large areas for a given planning period. An intruder decides on which cell to attack and an agent selects a patrol route visiting multiple cells from a finite set of patrol routes, such that some given operational conditions on the agent's mobility are met. First, this problem is modeled as a two-player zero-sum game with probabilistic constraints such that the operational conditions are met with high probability. Second, we develop a dynamic variant of this game by using stochastic games. This ensures that strategies are constructed that consider both past actions and expected future risk levels. In the last chapter, we consider Stackelberg security games with a large number of pure strategies. In order to construct operationalizable strategies we limit the number of pure strategies that is allowed in the optimal mixed strategy of the agent. We investigate the cost of these restrictions by introducing the price of usability and develop algorithmic approaches to calculate such strategies efficiently

Prevention of terrorism : an assessment of prior POM work and future potentials

© 2020 Production and Operations Management Society In this study, we review POM-based research related to prevention of terrorism. According to the Federal Emergency Management Agency (FEMA) terrorist attacks have the potential to be prevented. Consequently, the focus of this study is on security enhancement and improving the resiliency of a nation to prevent terrorist attacks. Accordingly, we review articles from the 25 top journals, [following procedures developed by Gupta et al. (2016)], in the fields of Production and Operations Management, Operations Research, Management Science, and Supply Chain Management. In addition, we searched some selected journals in the fields of Information Sciences, Political Science, and Economics. This literature is organized and reviewed under the following seven core capabilities defined by the Department of Homeland Security (DHS): (1) Intelligence and Information Sharing, (2) Planning, (3) Interdiction and Disruption, (4) Screening, Search, and Detection, (5) Forensics and Attribution, (6) Public Information and Warning, and (7) Operational Coordination. We found that POM research on terrorism is primarily driven by the type of information that a defending country and a terrorist have about each other. Game theory is the main technique that is used in most research papers. Possible directions for future research are discussed

The golden age of social science

Social science is entering a golden age, marked by the confluence of explosive growth in new data and analytic methods, interdisciplinary approaches, and a recognition that these ingredients are necessary to solve the more challenging problems facing our world. We discuss how developing a “lingua franca” can encourage more interdisciplinary research, providing two case studies (social networks and behavioral economics) to illustrate this theme. Several exemplar studies from the past 12 y are also provided. We conclude by addressing the challenges that accompany these positive trends, such as career incentives and the search for unifying frameworks, and associated best practices that can be employed in response

Supporting Virtual Enterprise Systems Using Agent Coordination

International audienceOpen environments like the Internet or corporate intranets enable a large number of interested enterprises to access, filter, process, and present information on an as-needed basis. These environments support modern applications, such as virtual enterprises and inter-organizational workflow management systems, which involve a number of heterogeneous resources, services, and processes. However, any execution of a virtual enterprise system would yield to disjoining and error-prone behavior without appropriate techniques to coordinate the various business processes. This paper reports on the design and implementation of a flexible agent-based framework for supporting the coordination of virtual enterprises and workflow management systems. The paper also shows how an agent coordination infrastructure, which is explained by social constraints, can impact on the engineering of highly dynamic virtual enterprises and workflow management systems by presenting a simple case study