Two-stage network design in humanitarian logistics.

Natural disasters such as floods and earthquakes can cause multiple deaths, injuries, and severe damage to properties. In order to minimize the impact of such disasters, emergency response plans should be developed well in advance of such events. Moreover, because different organizations such as non-governmental organizations (NGOs), governments, and militaries are involved in emergency response, the development of a coordination scheme is necessary to efficiently organize all the activities and minimize the impact of disasters. The logistics network design component of emergency management includes determining where to store emergency relief materials, the corresponding quantities and distribution to the affected areas in a cost effective and timely manner. In a two-echelon humanitarian relief chain, relief materials are pre-positioned first in regional rescue centers (RRCs), supply sources, or they are donated to centers. These materials are then shipped to local rescue centers (LRCs) that distribute these materials locally. Finally, different relief materials will be delivered to demand points (also called affected areas or AAs). Before the occurrence of a disaster, exact data pertaining to the origin of demand, amount of demand at these points, availability of routes, availability of LRCs, percentage of usable pre-positioned material, and others are not available. Hence, in order to make a location-allocation model for pre-positioning relief material, we can estimate data based on prior events and consequently develop a stochastic model. The outputs of this model are the location and the amount of pre-positioned material at each RRC as well as the distribution of relief materials through LRCs to demand points. Once the disaster occurs, actual values of the parameters we seek (e.g., demand) will be available. Also, other supply sources such as donation centers and vendors can be taken into account. Hence, using updated data, a new location-allocation plan should be developed and used. It should be mentioned that in the aftermath of the disaster, new parameters such as reliability of routes, ransack probability of routes and priority of singular demand points will be accessible. Therefore, the related model will have multiple objectives. In this dissertation, we first develop a comprehensive pre-positioning model that minimizes the total cost while considering a time limit for deliveries. The model incorporates shortage, transportation, and holding costs. It also considers limited capacities for each RRC and LRC. Moreover, it has the availability of direct shipments (i.e., shipments can be done from RRCs directly to AAs) and also has service quality. Because this model is in the class of two-stage stochastic facility location problems, it is NP-hard and should be solved heuristically. In order to solve this model, we propose using Lagrangian Heuristic that is based on Lagrangian Relaxation. Results from the first model are amounts and locations of pre-positioned relief materials as well as their allocation plan for each possible scenario. This information is then used as a part of the input for the second model, where the facility location problem will be formulated using real data. In fact, with pre-positioned items in hand, other supplies sources can be considered as necessary. The resulting multi-objective problem is formulated based on a widely used method called lexicography goal programming. The real-time facility location model of this dissertation is multi-product. It also considers the location problem for LRCs using real-time data. Moreover, it considers the minimization of the total cost as one of the objectives in the model and it has the availability of direct shipments. This model is also NP-hard and is solved using the Lagrangian Heuristic. One of the contributions of this dissertation is the development of Lagrangian Heuristic method for solving the pre-positioning and the real- time models. Based on the results of Lagrangian Heuristic for the pre-positioning model, almost all the deviations from optimal values are below 5%, which shows that the Heuristics works acceptably for the problem. Also, the execution times are no more than 780 seconds for the largest test instances. Moreover, for the real-time model, though not directly comparable, the solutions are fairly close to optimal and the execution time for the largest test instance is below 660 seconds. Hence, the efficiency of the heuristic for real-time model is satisfactory

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

A hybrid multi-objective approach to capacitated facility location with flexible store allocation for green logistics modeling

We propose an efficient evolutionary multi-objective optimization approach to the capacitated facility location–allocation problem (CFLP) for solving large instances that considers flexibility at the allocation level, where financial costs and CO2 emissions are considered simultaneously. Our approach utilizes suitably adapted Lagrangian Relaxation models for dealing with costs and CO2 emissions at the allocation level, within a multi-objective evolutionary framework at the location level. Thus our method assesses the robustness of each location solution with respect to our two objectives for customer allocation. We extend our exploration of selected solutions by considering a range of trade-offs for customer allocation

Location-allocation models for relief distribution and victim evacuation after a sudden-onset natural disaster

Quick response to natural disasters is vital to reduce loss of and negative impact to human life. The response is more crucial in the presence of sudden-onset, difficult-to-predict natural disasters, especially in the early period of those events. On-site actions are part of such response, some of which are determination of temporary shelters and/ or temporary medical facility locations, the evacuation process of victims and relief distribution to victims. These activities of last-mile disaster logistics are important as they are directly associated with sufferers, the main focus of any alleviation of losses caused by any disaster. This research deals with the last-mile site positioning of relief supplies and medical facilities in response to a sudden-onset, difficult-to-predict disaster event, both dynamically and in a more coordinative way during a particular planning time horizon. Four mathematical models which reflect the situation in Padang Pariaman District after the West Sumatera earthquake were built and tested. The models are all concerned with making decisions in a rolling time horizon manner, but differ in coordinating the operations and in utilization of information about future resource availability. Model I is a basic model representing the current practice with relief distribution and victim evacuation performed separately and decisions made only considering the resources available at the time. Model II considers coordination between the two operations and conducts them with the same means of transport. Model III takes into account future information keeping the two operations separate. Model IV combines the features of Models II and III. The four models are approached both directly and by using various heuristics. The research shows that conducting relief distribution and victim evacuation activities by using shared vehicles and/or by taking into account future information on resource availability improves the current practice . This is clearly demonstrated by the experimental results on small problems. For large problems, experiments show that it is not practical to directly solve the models, especially the last three, and that the solution quality is poor when the solution process is limited to a reasonable time. Experiments also show that the heuristics help improve the solution quality and that the performances of the heuristics are different for different models. When each model is solved using its own best heuristic, the conclusions from results of large problems get very close to those from small problems. Finally, deviation of future information on resource availability is considered in the study, but is shown not to affect the performance of model III and model IV in carrying out relief distribution and victim evacuation. This indicates that it is always worthwhile to take into account the future information, even if the information is not perfect, as long as it is reasonably reliable

Locating and Protecting Facilities Subject to Random Disruptions and Attacks

Recent events such as the 2011 Tohoku earthquake and tsunami in Japan have revealed the vulnerability of networks such as supply chains to disruptive events. In particular, it has become apparent that the failure of a few elements of an infrastructure system can cause a system-wide disruption. Thus, it is important to learn more about which elements of infrastructure systems are most critical and how to protect an infrastructure system from the effects of a disruption. This dissertation seeks to enhance the understanding of how to design and protect networked infrastructure systems from disruptions by developing new mathematical models and solution techniques and using them to help decision-makers by discovering new decision-making insights. Several gaps exist in the body of knowledge concerning how to design and protect networks that are subject to disruptions. First, there is a lack of insights on how to make equitable decisions related to designing networks subject to disruptions. This is important in public-sector decision-making where it is important to generate solutions that are equitable across multiple stakeholders. Second, there is a lack of models that integrate system design and system protection decisions. These models are needed so that we can understand the benefit of integrating design and protection decisions. Finally, most of the literature makes several key assumptions: 1) protection of infrastructure elements is perfect, 2) an element is either fully protected or fully unprotected, and 3) after a disruption facilities are either completely operational or completely failed. While these may be reasonable assumptions in some contexts, there may exist contexts in which these assumptions are limiting. There are several difficulties with filling these gaps in the literature. This dissertation describes the discovery of mathematical formulations needed to fill these gaps as well as the identification of appropriate solution strategies

Models, Theoretical Properties, and Solution Approaches for Stochastic Programming with Endogenous Uncertainty

In a typical optimization problem, uncertainty does not depend on the decisions being made in the optimization routine. But, in many application areas, decisions affect underlying uncertainty (endogenous uncertainty), either altering the probability distributions or the timing at which the uncertainty is resolved. Stochastic programming is a widely used method in optimization under uncertainty. Though plenty of research exists on stochastic programming where decisions affect the timing at which uncertainty is resolved, much less work has been done on stochastic programming where decisions alter probability distributions of uncertain parameters. Therefore, we propose methodologies for the latter category of optimization under endogenous uncertainty and demonstrate their benefits in some application areas. First, we develop a data-driven stochastic program (integrates a supervised machine learning algorithm to estimate probability distributions of uncertain parameters) for a wildfire risk reduction problem, where resource allocation decisions probabilistically affect uncertain human behavior. The nonconvex model is linearized using a reformulation approach. To solve a realistic-sized problem, we introduce a simulation program to efficiently compute the recourse objective value for a large number of scenarios. We present managerial insights derived from the results obtained based on Santa Fe National Forest data. Second, we develop a data-driven stochastic program with both endogenous and exogenous uncertainties with an application to combined infrastructure protection and network design problem. In the proposed model, some first-stage decision variables affect probability distributions, whereas others do not. We propose an exact reformulation for linearizing the nonconvex model and provide a theoretical justification of it. We designed an accelerated L-shaped decomposition algorithm to solve the linearized model. Results obtained using transportation networks created based on the southeastern U.S. provide several key insights for practitioners in using this proposed methodology. Finally, we study submodular optimization under endogenous uncertainty with an application to complex system reliability. Specifically, we prove that our stochastic program\u27s reliability maximization objective function is submodular under some probability distributions commonly used in reliability literature. Utilizing the submodularity, we implement a continuous approximation algorithm capable of solving large-scale problems. We conduct a case study demonstrating the computational efficiency of the algorithm and providing insights

A Two-Echelon Location-inventory Model for a Multi-product Donation-demand Driven Industry

This study involves a joint bi-echelon location inventory model for a donation-demand driven industry in which Distribution Centers (DC) and retailers (R) exist. In this model, we confine the variables of interest to include; coverage radius, service level, and multiple products. Each retailer has two classes of product flowing to and from its assigned DC i.e. surpluses and deliveries. The proposed model determines the number of DCs, DC locations, and assignments of retailers to those DCs so that the total annual cost including: facility location costs, transportation costs, and inventory costs are minimized. Due to the complexity of problem, the proposed model structure allows for the relaxation of complicating terms in the objective function and the use of robust branch-and-bound heuristics to solve the non-linear, integer problem. We solve several numerical example problems and evaluate solution performance

Facility Location Problems: Models, Techniques, and Applications in Waste Management

This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for e�ective and e�cient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP

The design of effective and robust supply chain networks

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2009-2010Pour faire face aux risques associés aux aléas des opérations normales et aux périls qui menacent les ressources d'un réseau logistique, une méthodologie générique pour le design de réseaux logistiques efficaces et robustes en univers incertain est développée dans cette thèse. Cette méthodologie a pour objectif de proposer une structure de réseau qui assure, de façon durable, la création de valeur pour l'entreprise pour faire face aux aléas et se prémunir contre les risques de ruptures catastrophiques. La méthodologie s'appuie sur le cadre de prise de décision distribué de Schneeweiss et l'approche de modélisation mathématique qui y est associée intègre des éléments de programmation stochastique, d'analyse de risque et de programmation robuste. Trois types d'événements sont définis pour caractériser l'environnement des réseaux logistiques: des événements aléatoires (ex. la demande, les coûts et les taux de changes), des événements hasardeux (ex. les grèves, les discontinuités d'approvisionnement des fournisseurs et les catastrophes naturelles) et des événements profondément incertains (ex. les actes de sabotage, les attentats et les instabilités politiques). La méthodologie considère que l'environnement futur de l'entreprise est anticipé à l'aide de scénarios, générés partiellement par une méthode Monte-Carlo. Cette méthode fait partie de l'approche de solution et permet de générer des replications d'échantillons de petites tailles et de grands échantillons. Elle aide aussi à tenir compte de l'attitude au risque du décideur. L'approche générique de solution du modèle s'appuie sur ces échantillons de scénarios pour générer des designs alternatifs et sur une approche multicritère pour l'évaluation de ces designs. Afin de valider les concepts méthodologiques introduits dans cette thèse, le problème hiérarchique de localisation d'entrepôts et de transport est modélisé comme un programme stochastique avec recours. Premièrement, un modèle incluant une demande aléatoire est utilisé pour valider en partie la modélisation mathématique du problème et étudier, à travers plusieurs anticipations approximatives, la solvabilité du modèle de design. Une approche de solution heuristique est proposée pour ce modèle afin de résoudre des problèmes de taille réelle. Deuxièmement, un modèle incluant les aléas et les périls est utilisé pour valider l'analyse de risque, les stratégies de resilience et l'approche de solution générique. Plusieurs construits mathématiques sont ajoutés au modèle de base afin de refléter différentes stratégies de resilience et proposer un modèle de décision sous risque incluant l'attitude du décideur face aux événements extrêmes. Les nombreuses expérimentations effectuées, avec les données d'un cas réaliste, nous ont permis de tester les concepts proposés dans cette thèse et d'élaborer une méthode de réduction de complexité pour le modèle générique de design sans compromettre la qualité des solutions associées. Les résultats obtenus par ces expérimentations ont pu confirmer la supériorité des designs obtenus en appliquant la méthodologie proposée en termes d'efficacité et de robustesse par rapport à des solutions produites par des approches déterministes ou des modèles simplifiés proposés dans la littérature