Reliable Location-Routing Design Under Probabilistic Facility Disruptions

postprin

Location and Location-Routing Problems with Disruption Risks

The academic literature on logistics network disruptions has increased sharply recently. Disruptions are random events that cause an element of a logistics network to stop functioning, either completely or partially, for a (typically random) given amount of time. Because of today's globalized threats such as, labor disruptions or failures resulting from harsh weather conditions, there has been a renewed interest in resilient facility location. Design of reliable logistics networks to avoid disruption can be accomplished by fortification of existing facilities and de�fining backup facilities. In this thesis, we will look at two components of a logistics system that can be affected by a disruption: the locations of the facilities, and the routes between a customer and a facility. We study the following three designs of logistics networks under disruption: (i) Reliable Capacitated Facility Location under Disruption, (ii) Shared Capacitated Reliable Facility Location in Presence of Disruption , and (iii) Reliable Facility Location and Routing in Logistics Network in presence of disruption considering backup sharing. A column generation approach is proposed to model and solve all three logistics problems. Results show the effectiveness of the decomposition schemes for solving exactly much larger facility location instances than in the literature. In addition, shared backup is shown to be a very effective scheme for the design of reliable facility locations/roads

Reliable design of interdependent service facility systems under correlated disruption risks

Facility location decisions lie at the center of planning many infrastructure systems. In many practice, public agencies (e.g., governments) and private companies (e.g., retailers) need to locate facilities to serve spatially distributed demands. For example, governments locate public facilities, e.g., hospitals, schools, fire stations, to provide public services; retail companies determine the locations of their warehouses and stores to provide business. The design of such facility systems involves considerations of investment of facility construction and transportation cost of serving demands, so as to maximize the system operational efficiency and profit. Recently, devastating infrastructure damages observed in real world show that infrastructure facilities may be subject to disruptions that compromise individual facility functionality as well as overall system performance. This emphasizes the necessity of taking facility disruptions into consideration during planning to balance between system efficiency and reliability. Furthermore, facility systems often exhibit complex interdependence when: (1) facilities are spatially correlated due to physical connections/interrelations, and (2) facilities provide combinatorial service under cooperation, competition and/or restrictions. These further complicate the facility location design. Therefore, facility location models need to be extended to tackle all these challenges and design a reliable interdependent facility system. This dissertation aims at investigating several important and challenging topics in the reliable facility location context, including facility correlations, facility combinations, and facility districting. The main work of this PhD research consist of: (1) establishing a new systematic methodological framework based on supporting stations and quasi-probabilities to describe and decompose facility correlations into succinct mathematical representations, which allows compact mathematical formulations to be developed for planning facility locations under correlated facility disruptions; (2) expanding the modeling framework to allow facilities to provide combinatorial service; e.g., in the context of sensor deployment problems, where sensors work in combinations to provide positioning/surveillance service via trilateration procedure; and (3) incorporating the concepts of spatial districting into the reliable facility location context, with the criteria of spatial contiguity, compactness, and demand balance being ensured. First, in many real-world facility systems, facility disruptions exhibit spatial correlations, which have strong impacts on the system performance, but are difficult to be described with succinct mathematical models. We first investigate facility systems with correlations caused by facilities’ share of network access points (e.g., bridges, railway crossings), which are required to be passed through by customers to visit facilities. We incorporate these network access points and their probabilistic failures into a joint optimization framework. A layer of supporting stations are added to represent the network access points, and are connected to facilities to indicate their real-world relationships. We then develop a compact mixed-integer mathematical model to optimize the facility location and customer assignment decisions. Lagrangian relaxation based algorithms are designed to effectively solve the model. Multiple case studies are constructed to test the model and algorithm, and to demonstrate their performance and applicability. Next, when there exists no real access points, facilities could also be correlated if they are exposed to shared hazards. We develop a virtual station structure framework to decompose these types of facility correlations. First, we define three probabilistic representations of correlated facility disruptions (i.e., with scenario, marginal, and conditional probabilities), derive pairwise transformations between them, and theoretically prove their equivalence. We then provide detailed formulas to transform these probabilistic representations into an equivalent virtual station structure, which enables the decomposition of any correlated facility disruptions into a compact network structure with only independent failures, and helps avoid enumerating an exponential number of disruption scenarios. Based on the augmented system, we propose a compact mixed-integer optimization program, and design several customized solution approaches based on Lagrangian relaxation to efficiently solve the model. We demonstrate our methodology on a series of numerical examples involving different correlation patterns and varying network and parameter settings. We then apply the reliable location modeling framework to sensor deployment problems, where multiple sensors work in combinations to provide combinatorial coverage service to customers via trilateration procedure. Since various sensor combinations may share common sensors, one combination is typically interrelated with some other combinations, which leads to internal correlations among the functionality of sensors and sensor combinations. We address the problem of where to deploy sensors, which sensor combinations are selected to use, and in what sequence and probability to use these combinations in case of disruptions. A compact mixed-integer mathematical model is developed to formulate the problem, by combining and extending the ideas of assigning back-up sensors and correlation decomposition via supporting stations. A customized solution algorithm based on Lagrangian relaxation and branch-and-bound is developed, together with several embedded approximation subroutines for solving subproblems. A series of numerical examples are investigated to illustrate the performance of the proposed methodology and to draw managerial insights. Finally, we develop an innovative reliable network districting framework to incorporate districting concepts into the reliable facility location context. Districting criteria including spatial contiguity, compactness, and demand balance are enforced for location design and extended in considerations of facility disruptions. The problem is modeled into a reliable network districting problem, in the form of a location-assignment based model. We develop customized solution approaches, including heuristics (i.e., constructive heuristic and neighborhood search) and set-cover based algorithms (e.g., district generation, lower bound estimation) to provide near-optimum solution with optimality gap. A series of hypothetical cases and an empirical full-scale application are presented to demonstrate the performance of our methodology for different network and parameter settings

What it takes to design a supply chain resilient to major disruptions and recurrent interruptions

Global supply chains are more than ever under threat of major disruptions caused by devastating natural and man-made disasters as well as recurrent interruptions caused by variations in supply and demand. This paper presents an optimization model for designing a supply chain resilient to (1) supply/demand interruptions and (2) facility disruptions whose probability of occurrence and magnitude of impact can be mitigated through fortification investments. Numerical results and managerial insights obtained from model implementation are presented. Our analysis focuses on how supply chain design decisions are influenced by facility fortification strategies, a decision maker’s conservatism degree, demand fluctuations, supply capacity variations, and budgetary constraints. Finally, examining the performance of the proposed model using a Monte Carlo simulation method provides additional insights and practical implications

A Bi-Objective Programming Model for Reliable Supply Chain Network Design Under Facility Disruption

Supply chain networks generally are composed of four main entity types: supplier, production centers, distribution centers and demand zones that consist of facilities whose activities involve the transformation of raw material into finished products that are later delivered from the suppliers to the end customers. Supply chain network design as the most important strategic decision in supply chain management plays an important role in the overall environmental and economic performance of the supply chain. The nature and complexity of today’s supply chains network make them vulnerable to various risks. One of the most important risks is disruption risk. Disruptions are costly and can be caused by internal or external sources to the supply chain, thus it is crucial that managers take appropriate measures of responses to reduce its negative effects. A recovery time of disrupted facilities and return it to the normal condition can be an important factor for members of the supply chain. In this paper, a bi-objective model is developed for reliable supply chain network design under facility disruption. To solve this model, we have applied two approaches, i.e., ε constraint method as an exact method and non- dominated sorting genetic algorithm (NSGAII) as a meta-heuristic method

Facility Location Planning Under Disruption

Facility Location Problems (FLPs) such as the Uncapacitated Facility Location (UFL) and the Capacitated Facility Location (CFL) along with the k-Shortest Path Problem (k-SPP) are important research problems in managing supply chain networks (SCNs) and related operations. In UFL, there is no limit on the facility serving capacity while in CFL such limit is imposed. FLPs aim to find the best facility locations to meet the customer demands within the available capacity with minimized facility establishment and transportation costs. The objective of the (k-SPP) is to find the k minimal length and partial overlapping paths between two nodes in a transport network graph. In the literature, many approaches are proposed to solve these problems. However, most of these approaches assume totally reliable facilities and do not consider the failure probability of the facilities, which can lead to notably higher cost. In this thesis, we investigate the reliable uncapacitated facility location (RUFL)and the reliable capacitated facility location (RCFL) problems, and the k-SPP where potential facilities are exposed to disruption then propose corresponding solution approaches to efficiently handle these problems. An evolutionary learning technique is elaborated to solve RUFL. Then, a non-linear integer programming model is introduced for the RCFL along with a solution approach involving the linearization of the model and its use as part of an iterative procedure leveraging CPLEX for facility establishment and customer assignment along with a knapsack implementation aiming at deriving the best facility fortification. In RUFL and RCFL, we assume heterogeneous disruption with respect to the facilities, each customer is assigned to primary and backup facilities and a fixed fortification budget allows to make a subset of the facilities totally reliable. Finally, we propose a hybrid approach based on graph partitioning and modified Dijkstra algorithm to find k partial overlapping shortest paths between two nodes on a transport network that is exposed to heterogeneous connected node failures. The approaches are illustrated via individual case studies along with corresponding key insights. The performance of each approach is assessed using benchmark results. For the k-SPP, the effect of preferred establishment locations is analyzed with respect to disruption scenarios, failure probability, computation time, transport costs, network size and partitioning parameters

Efficient Algorithms for Solving Facility Problems with Disruptions

This study investigates facility location problems in the presence of facility disruptions. Two types of problems are investigated. Firstly, we study a facility location problem considering random disruptions. Secondly, we study a facility fortification problem considering disruptions caused by random failures and intelligent attacks.We first study a reliable facility location problem in which facilities are faced with the risk of random disruptions. In the literature, reliable facility location models and solution methods have been proposed under different assumptions of the disruption distribution. In most of these models, the disruption distribution is assumed to be completely known, that is, the disruptions are known to be uncorrelated or to follow a certain distribution. In practice, we may have only limited information about the distribution. In this work, we propose a robust reliable facility location model that considers the worst-case distribution with incomplete information. Because the model imposes fewer distributional assumptions, it includes several important reliable facility location problems as special cases. We propose an effective cutting plane algorithm based on the supermodularity of the problem. For the case in which the distribution is completely known, we develop a heuristic algorithm called multi-start tabu search to solve very large instances.In the second part of the work, we study an r-interdiction median problem with fortification that simultaneously considers two types of disruption risks: random disruptions that happen probabilistically and disruptions caused by intentional attacks. The problem is to determine the allocation of limited facility fortification resources to an existing network. The problem is modeled as a bi-level programming model that generalizes the r-interdiction median problem with probabilistic fortification. The lower level problem, that is, the interdiction problem, is a challenging high-degree non-linear model. In the literature, only the enumeration method is applied to solve a special case of the problem. By exploring the special structure property of the problem, we propose an exact cutting plane method for the problem. For the fortification problem, an effective logic based Benders decomposition algorithm is proposed