A MATHEMATICAL FRAMEWORK FOR OPTIMIZING DISASTER RELIEF LOGISTICS

In today's society that disasters seem to be striking all corners of the globe, the importance of emergency management is undeniable. Much human loss and unnecessary destruction of infrastructure can be avoided with better planning and foresight. When a disaster strikes, various aid organizations often face significant problems of transporting large amounts of many different commodities including food, clothing, medicine, medical supplies, machinery, and personnel from several points of origin to a number of destinations in the disaster areas. The transportation of supplies and relief personnel must be done quickly and efficiently to maximize the survival rate of the affected population. The goal of this research is to develop a comprehensive model that describes the integrated logistics operations in response to natural disasters at the operational level. The proposed mathematical model integrates three main components. First, it controls the flow of several relief commodities from sources through the supply chain until they are delivered to the hands of recipients. Second, it considers a large-scale unconventional vehicle routing problem with mixed pickup and delivery schedules for multiple transportation modes. And third, following FEMA's complex logistics structure, a special facility location problem is considered that involves four layers of temporary facilities at the federal and state levels. Such integrated model provides the opportunity for a centralized operation plan that can effectively eliminate delays and assign the limited resources in a way that is optimal for the entire system. The proposed model is a large-scale mixed integer program. To solve the model, two sets of heuristic algorithms are proposed. For solving the multi-echelon facility location problem, four heuristic approaches are proposed. Also four heuristic algorithms are proposed to solve the general integer vehicle routing problem. Overall, the proposed heuristics could efficiently find optimal or near optimal solution in minutes of CPU time where solving the same problems with a commercial solver needed hours of computation time. Numerical case studies and extensive sensitivity analysis are conducted to evaluate the properties of the model and solution algorithms. The numerical analysis indicated the capabilities of the model to handle large-scale relief operations with adequate details. Solution algorithms were tested for several random generated cases and showed robustness in solution quality as well as computation time

Recent Trends and Innovations in Modelling City Logistics

AbstractThere are many challenges associated with moving goods within cities as urban areas become larger and elderly residents require more healthcare in their homes. Air quality is also impacted by urban freight vehicles. This paper presents a review of recent trends and innovations in modelling city logistics. New techniques for modelling city logistics developed in the areas of emissions, healthcare and mega-cities are outlined. This paper describes the formulation, solution methodologies and applications of these models

New and simple algorithms for stable flow problems

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting-path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocation as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kir\'{a}ly and Pap. The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is NP-complete to decide whether an integral solution exists

Exposure to Stressful Environments: Strategy of Adaptive Responses

Any new natural environment may generate a number of stresses (such as hypoxia, water lack, and heat exposure), each of which can produce strains in more than a single organ system. Every strain may in turn stimulate the body to adapt in multiple ways. Nevertheless, a general strategy of the various adaptive responses emerges when the challenges are divided into three groups. The first category includes conditions that affect the supply of essential molecules, while the second is made up by those stresses that prevent the body from regulating properly the output of waste products, such as CO2 and heat. In both classes, there is a small number of responses, similar in principle, regardless of the specific situation. The third unit is created by environments that disrupt body transport systems. Problems may arise when there is a conflict between two stresses requiring conflicting adaptive changes. An alternative to adaptation, creation of micro-environment, is often favored by the animal

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

Rail-Road terminal locations: aggregation errors and best potential locations on large networks

In network location problems, the number of potential locations is often too large in order to find a solution in a reasonable computing time. That is why aggregation techniques are often used to reduce the number of nodes. This reduction of the size of the location problems makes them more computationally tractable, but aggregation introduces errors into the solutions. Some of these errors will be estimated in this paper. A method that helps to isolate the best potential locations for rail-road terminals embedded in a hub-and-spoke network will further be outlined. Hub location problems arise when it is desirable to consolidate flows at certain locations called hubs. The basic idea is to use the flows of commodities and their geographic spreading as input to determine a set of potential locations for hub terminals. The exercise will be done for the trans-European networks. These potential locations can then further be used as input by an optimal location method