An exact approach for the reliable fixed-charge location problem with capacity constraints

Introducing capacities in the reliable fixed charge location problem is a complex task since successive failures might yield in high facility overloads. Ideally, the goal consists in minimizing the total cost while keeping the expected facility overloads under a given threshold. Several heuristic approaches have been proposed in the literature for dealing with this goal. In this paper, we present the first exact approach for this problem, which is based on a cutting planes algorithm. Computational results illustrate its good performancePostprint (published version

Finding optimal Stackelberg production strategies: How to produce in times of war?

Inspired by a military context, we study a Stackelberg production game where a country's government, the leader, wants to maximize the production of military assets. The leader does so by allocating his resources among a set of production facilities. His opponent, the follower, observes this allocation and tries to destroy the associated production as much as possible by allocating his destructive resources, for example bombs, among these facilities. In this paper, we identify a follower's optimal strategy. For the leader, we show that an optimal production strategy can be found in the class of so-called seried-balanced strategies. We present a linear time algorithm that finds an optimal strategy in this class

Reliable Location Allocation Routing Design under Disruption: An Improved Column Generation Decomposition Approach

Every year, various human actions (e.g., terrorist attacks, strikes, etc.) and natural disasters (e.g., earthquakes, hurricanes, and etc.) cause disruptions in supply networks, and as the result, huge financial and humanitarian loss. Not only they brought loss of services to the system, they, depending on the type, partial or complete, may result in facility failures, roads failures or both, simultaneously. Therefore, having reliable systems are essential in order to reduce risks as well as cost in case of failures. Motivated by the importance of considering the failure in design level, we, in this thesis, focused on problem of locating facilities, allocating demand points to the facilities, and defining the rout among them while considering the complete failure in the elements of the network. The Reliable Location/ Allocation/ Routing Problem (RLARP) formulation which is Mixed Integer Programming model is proposed, taking into account failures in facilities and routs in different scenarios as failure sets. Along with bringing in trustworthy systems, we also contribute an exact decomposition methodology and propose a Column Generation model to tackle the complexity. The idea is to define a supply chain network at the design level to be robust against worst case failures and disruptions scenarios. To the best of author’s knowledge, the Column Generation technique has not been applied previously to solve RLARP problems in the literature. In addition, we consider the facility and transportation method failures in our model, despite the fact that mostly either facility failures or transportation failures are taken into account in the literature. Various data sets designated for validating Column Generation and RLARP formulation proposed in this thesis. Eventually, we compare the performance of CG and RLARP models over a range of instances. Results suggests that CG technique performs significantly better than solving the RLARP model with a general optimization solver (CPLEX) in terms of computational time and the size of instances that can be solved

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

Disaster management from a POM perspective : mapping a new domain

We have reviewed disaster management research papers published in major operations management, management science, operations research, supply chain management and transportation/ logistics journals. In reviewing these papers our objective is to assess and present the macro level “architectural blue print” of disaster management research with the hope that it will attract new researchers and motivate established researchers to contribute to this important field. The secondary objective is to bring this disaster research to the attention of disaster administrators so that disasters are managed more efficiently and more effectively. We have mapped the disaster management research on the following five attributes of a disaster: (1) Disaster Management Function (decision making process, prevention and mitigation, evacuation, humanitarian logistics, casualty management, and recovery and restoration), (2) Time of Disaster (before, during and after), (3) Type of Disaster (accidents, earthquakes, floods, hurricanes, landslides, terrorism and wildfires etc.), (4) Data Type (Field and Archival data, Real data and Hypothetical data), and (5) Data Analysis Technique (bidding models, decision analysis, expert systems, fuzzy system analysis, game theory, heuristics, mathematical programming, network flow models, queuing theory, simulation and statistical analysis). We have done cross tabulations of data among these five parameters to gain greater insights in disaster research. Recommendations for future research are provided

An exact solution approach for the interdiction median problem with fortification

Systematic approaches to security investment decisions are crucial for improved homeland security. We present an optimization modeling approach for allocating protection resources among a system of facilities so that the disruptive effects of possible intentional attacks to the system are minimized. This paper is based upon the p-median service protocol for an operating set of p facilities. The primary objective is to identify the subset of q facilities which, when fortified, provides the best protection against the worst-case loss of r non-fortified facilities. This problem, known as the r-interdiction median problem with fortification (IMF), was first formulated as a mixed-integer program by Church and Scaparra [R.L. Church, M.P. Scaparra, Protecting critical assets: The r-interdiction median problem with fortification, Geographical Analysis 39 (2007) 129-146]. In this paper, we reformulate the IMF as a maximal covering problem with precedence constraints, which is amenable to a new solution approach. This new approach produces good approximations to the best fortification strategies. Furthermore, it provides upper and lower bounds that can be used to reduce the size of the original model. The reduced model can readily be solved to optimality by general-purpose MIP solvers. Computational results on two geographical data sets with different structural characteristics show the effectiveness of the proposed methodology for solving IMF instances of considerable size

An exact solution approach for the interdiction median problem with fortification

Systematic approaches to security investment decisions are crucial for improved homeland security. We present an optimization modeling approach for allocating protection resources among a system of facilities so that the disruptive effects of possible intentional attacks to the system are minimized. This paper is based upon the p-median service protocol for an operating set of p facilities. The primary objective is to identify the subset of q facilities which, when fortified, provides the best protection against the worst-case loss of r non-fortified facilities. This problem, known as the r-interdiction median problem with fortification (IMF), was first formulated as a mixed-integer program by Church and Scaparra [R.L. Church, M.P. Scaparra, Protecting critical assets: The r-interdiction median problem with fortification, Geographical Analysis 39 (2007) 129-146]. In this paper, we reformulate the IMF as a maximal covering problem with precedence constraints, which is amenable to a new solution approach. This new approach produces good approximations to the best fortification strategies. Furthermore, it provides upper and lower bounds that can be used to reduce the size of the original model. The reduced model can readily be solved to optimality by general-purpose MIP solvers. Computational results on two geographical data sets with different structural characteristics show the effectiveness of the proposed methodology for solving IMF instances of considerable size.

Analytical approaches to protection planning in rail-truck intermodal transportation

A significant volume of traffic uses a rail-truck intermodal transportation network, making it the preferred transportation medium for customers. Thus, the associated infrastructure of rail-truck intermodal transportation should be considered critical, i.e., systems and assets whose destruction (or disruption) would have a crippling effect on security, economy, public health, and safety. Disruptions could be induced by nature such as hurricane Katrina in 2005, or man-made disturbances such as the 9/11 terrorist attacks in the United States. This thesis proposes an analytical approach to preserve, as much as possible, the functionality of a rail-truck intermodal transportation system in the wake of worst-case attacks. As such, it will serves as an aid to the top managers to compare the cost of implementing protective measures with the benefits that such measures could bring. A tri-level Defender-Attacker-Defender (DAD) approach is proposed to model this situation, where the outermost problem belongs to the network operator with a limited budget to protect some of the terminals, the middle level problem belongs to the attacker with enough resources to interdict some of the un-protected terminals, and the innermost problem belongs to the intermodal operator who attempts to meet the demand on a reduced network with the minimum cost. Since the resulting model is very difficult to solve by any optimization package, efficient solution techniques have been developed for solving this model. Finally, the proposed framework is applied to the rail-truck intermodal transportation network of a Class I railroad operator in North America to discover the optimal way to protect the system

Responsive Contingency Planning for Supply Chain Disruption Risk Mitigation

Contingent sourcing from a backup resource is an effective risk mitigation strategy under major disruptions. The production volumes and speeds of the backup resource are important protection design considerations, as they affect recovery. The objective of this dissertation is to show that cost-effective protection of existing supply networks from major disruptions result from planning appropriate volume and response speeds of a backup production facility prior to the disruptive event by considering operational aspects such as congestion that may occur at facilities. Contingency strategy are more responsive and disruption recovery periods can be shortened through such prior planning. The dissertation focuses on disruption risk arising from intelligent or pre-meditated attacks on supply facilities. An intelligent attacker has the capability to create worst case loss depending on the protection strategy of a given network. Since the attacker seeks the maximum loss and the designer tries to identify the protection scheme which minimizes this maximum loss, there exists an interdependence between attack and protection decisions. Ignoring this characteristic leads to suboptimal mitigation solutions under such disruptions. We therefore develop a mathematical model which utilizes a game theoretic framework of attack and defense involving nested optimization problems. The model is used to decide optimal selection of backup production volume and the response speeds, the facilities to build such capability within the available budget. The reallocation of demands from a disrupted facility to an undisrupted facility in a contingency strategy leads to congestion of the undisrupted facility, which may result in longer lead times and reduced throughput during disruption periods, thereby limiting the effectiveness of a contingency strategy. In the second part of the dissertation, we therefore analyze congestion effects in responsive contingency planning. The congestion cost function is modeled and integrated into the mathematical model of responsive contingency planning developed in the first part of the dissertation. The main contribution of this dissertation is that a decision tool has been developed to plan protection of an existing supply networks considering backup sourcing through gradual capacity acquisition. The solution methodology involving recursive search tree has been implemented which allows exploring protection solutions under a given budget of protection and multiple combinations of response speeds and production capacities of a backup facility. The results and analysis demonstrate the value of planning for responsive contingency in supply chains subject to risks of major disruptions and provide insights to aid managerial decision making

Exact Algorithms for Mixed-Integer Multilevel Programming Problems

We examine multistage optimization problems, in which one or more decision makers solve a sequence of interdependent optimization problems. In each stage the corresponding decision maker determines values for a set of variables, which in turn parameterizes the subsequent problem by modifying its constraints and objective function. The optimization literature has covered multistage optimization problems in the form of bilevel programs, interdiction problems, robust optimization, and two-stage stochastic programming. One of the main differences among these research areas lies in the relationship between the decision makers. We analyze the case in which the decision makers are self-interested agents seeking to optimize their own objective function (bilevel programming), the case in which the decision makers are opponents working against each other, playing a zero-sum game (interdiction), and the case in which the decision makers are cooperative agents working towards a common goal (two-stage stochastic programming). Traditional exact approaches for solving multistage optimization problems often rely on strong duality either for the purpose of achieving single-level reformulations of the original multistage problems, or for the development of cutting-plane approaches similar to Benders\u27 decomposition. As a result, existing solution approaches usually assume that the last-stage problems are linear or convex, and fail to solve problems for which the last-stage is nonconvex (e.g., because of the presence of discrete variables). We contribute exact finite algorithms for bilevel mixed-integer programs, three-stage defender-attacker-defender problems, and two-stage stochastic programs. Moreover, we do not assume linearity or convexity for the last-stage problem and allow the existence of discrete variables. We demonstrate how our proposed algorithms significantly outperform existing state-of-the-art algorithms. Additionally, we solve for the first time a class of interdiction and fortification problems in which the third-stage problem is NP-hard, opening a venue for new research and applications in the field of (network) interdiction