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Planning for disaster - Designing robust coverage networks to hedge against worst-case facility losses

01 Nov 2008-
TL;DR: In this paper, a location-interdiction covering model was developed to maximize a combination of 1) initial coverage given p facilities and 2) the minimum coverage level following the loss of any subset of facilities r < p. In order to design a coverage-type service network that is robust to the worst instances of facility loss, a decomposition algorithm was presented.
Abstract: The potential for long-term facility loss has important implications for the reliability of service/supply networks. In order to design a coverage-type service network that is robust to the worst instances of facility loss, we develop a location-interdiction covering model that maximizes a combination of 1) initial coverage given p facilities and 2) the minimum coverage level following the loss of any subset of facilities r < p. The problem is formulated both as a mixed integer program and as a bilevel mixed integer program. To solve the bilevel program optimally, a decomposition algorithm is presented, whereby the original bilevel program is decoupled into an upper level master problem and a lower level subproblem. After sequentially solving these problems, information is fed back to the upper level master by appending supervalid inequalities, which attempt to force the upper level master away from clearly dominated solutions. Supervalid inequalities, unlike standard valid inequalities used in cutting plane algorithms, cut away parts of the feasible region but are guaranteed not to remove all optimal solutions unless an optimal solution has already been found. Computational results show that when solved to optimality, bilevel decomposition is up to several orders of magnitude faster than performing branch and bound on the mixed integer program. All interested are welcome – For further information, please visit http://www.math.hkbu.edu.hk/ICM, or call 34115056.

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Citations
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Journal ArticleDOI
TL;DR: A review of the OR/MS literature on supply chain disruptions can be found in this paper, where the authors provide an overview of the research questions that have been addressed and a discussion of future research directions.
Abstract: We review the OR/MS literature on supply chain disruptions in order to take stock of the research to date and to provide an overview of the research questions that have been addressed. We first place disruptions in the context of other forms of supply uncertainty and discuss common modeling approaches. We then discuss nearly 150 scholarly works on the topic, organized into six categories: evaluating supply disruptions; strategic decisions; sourcing decisions; contracts and incentives; inventory; and facility location. We conclude with a discussion of future research directions.

553 citations

Journal ArticleDOI
TL;DR: This survey tries to review all aspects of the covering problems by stressing the works after Schilling, Jayaraman, and Barkhi (1993).

540 citations

Posted Content
TL;DR: An automated text-analysis of an extended list of papers published on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary is performed.
Abstract: Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community. Only limited work exists on bilevel problems using evolutionary computation techniques; however, recently there has been an increasing interest due to the proliferation of practical applications and the potential of evolutionary algorithms in tackling these problems. This paper provides a comprehensive review on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary. A number of potential application problems are also discussed. To offer the readers insights on the prominent developments in the field of bilevel optimization, we have performed an automated text-analysis of an extended list of papers published on bilevel optimization to date. This paper should motivate evolutionary computation researchers to pay more attention to this practical yet challenging area.

268 citations

Journal ArticleDOI
TL;DR: This work considers the problem of optimally protecting a capacitated median system with a limited amount of protective resources subject to disruptions, and provides a tri-level formulation of the problem and an exact solution algorithm which makes use of a tree-search procedure to identify which facilities to protect.
Abstract: Supply systems are subject to disruptions whose impact may not remain confined, but might actually propagate across the network. We consider the problem of optimally protecting a capacitated median system with a limited amount of protective resources subject to disruptions. Specifically, the type of disruption studied is characterized by correlation effects between the facilities, and may result in partial or complete disruption of the facilities involved. The model optimizes protection plans in the face of large area disruptions; i.e., disruptions that affect regions rather than single elements of the system. Examples may be earthquakes, storms, floods, fires, hurricanes, droughts, the spread of diseases, the spread of chemical agents, and cascading failures. The model is also a general framework for the family of fortification problems in the context of location analysis, as it includes uncapacitated facilities and single-target disruptions as special cases. We provide a tri-level formulation of the problem, and we propose an exact solution algorithm which makes use of a tree-search procedure to identify which facilities to protect. The procedure is enhanced by a dual-based pruning rule. The underlying disruption problem is reformulated as a single-level mixed-integer program. The algorithm has been tested on a dataset based on the 2009 L’Aquila earthquake. We verify empirically the efficiency of the pruning rule, and we provide an evaluation of the importance of considering propagation effects in the disruptions.

177 citations

Journal ArticleDOI
TL;DR: This model optimally allocates defensive resources among facilities to minimize the worst-case impact of an intentional disruption and proposes pre-processing techniques based on the computation of valid lower and upper bounds to expedite the solution of instances of realistic size.

167 citations

References
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Journal ArticleDOI
01 Jan 1974
TL;DR: The use of a maximal service distance as a measure of the value of a given locational configuration has been discussed at length by Toregas and ReVelle 1 who show that it is an important surrogate measurement for the value.
Abstract: The belief that mathematical location modeling can identify "optimal" location patterns rests on the basis that some realistic objective can be identified and by some measure quantified. For example, in the area of private facilities location analysis, a reasonably accurate statement of the objective of locating warehouses is to minimize the costs of manufacturing and distribution. Since most cost elements included in the objectives of private facility location can be reasonably estimated, the models can picture with some degree of accuracy the real location problem they are designed to solve. Unlike private facility location analysis, the objectives of public facility location analysis are more difficult to embrace and to quantify. The difficulty in defining direct measures of public objectives has resulted in a search for some surrogate measure with which the decision maker may be comfortable. Two different surrogate measures which have received attention in location models are: (1) total weighted distance or time for travel to the facilities, and (2) the distance or time that the user most distant from a facility would have to travel to reach that facility, that is, the maximal service distance.* The use of a maximal service distance as a measure of the value of a given locational configuration has been discussed at length by Toregas and ReVelle 1 who show that it is an important surrogate measurement for the value of a given locational configuration. For a given location solution, the maximum distance which any user would have to travel to reach a facility would reflect the worst possible performance of the system. In the regional location of emergency facilities such as fire stations or ambulance dispatching stations, the concept of the maximal service distance is well established. ~,3 The maximal service distance concept appears in the Location Set Covering

2,080 citations

Book
01 May 1995
TL;DR: The second edition of Network and Discrete Location: Models, Algorithms, and Applications as discussed by the authors provides a taxonomy of location problems and models, as well as a full range of exercises to equip readers with an understanding of the basic facility location model types.
Abstract: Thoroughly updated and revised, Network and Discrete Location: Models, Algorithms, and Applications, Second Edition remains the go-to guide on facility location modeling. The book offers a unique introduction to methodological tools for solving location models and provides insight into when each approach is useful and what information can be obtained. The Second Edition focuses on real-world extensions of the basic models used in locating facilities, including production and distribution systems, location-inventory models, and defender-interdictor problems. A unique taxonomy of location problems and models is also presented. Featuring examples using the author’s own software—SITATION, MOD-DIST, and MENU-OKF—as well as Microsoft Office Excel, the book provides: • A theoretical and applied perspective on location models and algorithms• An intuitive presentation of the uses and limits of modeling techniques• An introduction to integrated location-inventory modeling and defender-interdictor models for the design of reliable facility location systems• A full range of exercises to equip readers with an understanding of the basic facility location model types Network and Discrete Location: Models, Algorithms, and Applications, Second Edition is an essential resource for practitioners in applied and discrete mathematics, operations research, industrial engineering, and quantitative geography. The book is also a useful textbook for upper-level undergraduate, graduate, and MBA courses.

1,534 citations

Journal ArticleDOI
TL;DR: In this article, the authors extended the maximum covering location model to account for the chance that when a demand arrives at the system it will not be covered since all facilities capable of covering the demand are engaged serving other demands.
Abstract: The maximum covering location model has been used extensively in analyzing locations for public service facilities. The model is extended to account for the chance that when a demand arrives at the system it will not be covered since all facilities capable of covering the demand are engaged serving other demands. An integer programming formulation of the new problem is presented. Several properties of the formulation are proven. A heuristic solution algorithm is presented and computational results with the algorithm are discussed. Directions for future study are also discussed.

763 citations

Journal ArticleDOI
TL;DR: The properties of the Stackelberg solution in static and dynamic nonzero-sum two-player games are investigated in this paper, and necessary and sufficient conditions for its existence are derived.
Abstract: The properties of the Stackelberg solution in static and dynamic nonzero-sum two-player games are investigated, and necessary and sufficient conditions for its existence are derived. Several game problems, such as games where one of the two players does not know the other’s performance criterion or games with different speeds in computing the strategies, are best modeled and solved within this solution concept. In the case of dynamic games, linear-quadratic problems are formulated and solved in a Hilbert space setting. As a special case, nonzero-sum linear-quadratic differential games are treated in detail, and the open-loop Stackelberg solution is obtained in terms of Riccati-like matrix differential equations. The results are applied to a simple nonzero-sum pursuit-evasion problem.

720 citations

Journal ArticleDOI
TL;DR: This paper forms reliability models based on both the PMP and the UFLP and presents an optimal Lagrangian relaxation algorithm to solve them, and discusses how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account.
Abstract: Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that, once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost, while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account, and we use these trade-off curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.

703 citations