Stability and resource allocation in project planning.

The majority of resource-constrained project scheduling efforts assumes perfect information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule is executed. In reality, project activities are subject to considerable uncertainty, which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed resource allocation problem. We report on computational results obtained on a set of benchmark problems.Constraint satisfaction; Information; Model; Planning; Problems; Project management; Project planning; Project scheduling; Resource allocati; Scheduling; Stability; Uncertainty; Variability;

COMPUTATIONALLY TRACTABLE STOCHASTIC INTEGER PROGRAMMING MODELS FOR AIR TRAFFIC FLOW MANAGEMENT

A primary objective of Air Traffic Flow Management (ATFM) is to ensure the orderly flow of aircraft through airspace, while minimizing the impact of delays and congestion on airspace users. A fundamental challenge of ATFM is the vulnerability of the airspace to changes in weather, which can lower the capacities of different regions of airspace. Considering this uncertainty along with the size of the airspace system, we arrive at a very complex problem. The development of efficient algorithms to solve ATFM problems is an important and active area of research. Responding to predictions of bad weather requires the solution of resource allocation problems that assign a combination of ground delay and route adjustments to many flights. Since there is much uncertainty associated with weather predictions, stochastic models are necessary. We address some of these problems using integer programming (IP). In general, IP models can be difficult to solve. However, if "strong" IP formulations can be found, then problems can be solved quickly by state of the art IP solvers. We start by describing a multi-period stochastic integer program for the single airport stochastic dynamic ground holding problem. We then show that the linear programming relaxation yields integer optimal solutions. This is a fairly unusual property for IP formulations that can significantly reduce the complexity of the corresponding problems. The proof is achieved by defining a new class of matrices with the Monge property and showing that the formulation presented belongs to this class. To further improve computation times, we develop alternative compact formulations. These formulations are extended to show that they can also be used to model different concepts of equity and fairness as well as efficiency. We explore simple rationing methods and other heuristics for these problems both to provide fast solution times, but also because these methods can embody inherent notions of fairness. The initial models address problems that seek to restrict flow into a single airport. These are extended to problems where stochastic weather affects en route traffic. Strong formulations and efficient solutions are obtained for these problems as well

OPTIMIZATION MODELS AND METHODOLOGIES TO SUPPORT EMERGENCY PREPAREDNESS AND POST-DISASTER RESPONSE

This dissertation addresses three important optimization problems arising during the phases of pre-disaster emergency preparedness and post-disaster response in time-dependent, stochastic and dynamic environments. The first problem studied is the building evacuation problem with shared information (BEPSI), which seeks a set of evacuation routes and the assignment of evacuees to these routes with the minimum total evacuation time. The BEPSI incorporates the constraints of shared information in providing on-line instructions to evacuees and ensures that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. A mixed-integer linear program is formulated for the BEPSI and an exact technique based on Benders decomposition is proposed for its solution. Numerical experiments conducted on a mid-sized real-world example demonstrate the effectiveness of the proposed algorithm. The second problem addressed is the network resilience problem (NRP), involving an indicator of network resilience proposed to quantify the ability of a network to recover from randomly arising disruptions resulting from a disaster event. A stochastic, mixed integer program is proposed for quantifying network resilience and identifying the optimal post-event course of action to take. A solution technique based on concepts of Benders decomposition, column generation and Monte Carlo simulation is proposed. Experiments were conducted to illustrate the resilience concept and procedure for its measurement, and to assess the role of network topology in its magnitude. The last problem addressed is the urban search and rescue team deployment problem (USAR-TDP). The USAR-TDP seeks an optimal deployment of USAR teams to disaster sites, including the order of site visits, with the ultimate goal of maximizing the expected number of saved lives over the search and rescue period. A multistage stochastic program is proposed to capture problem uncertainty and dynamics. The solution technique involves the solution of a sequence of interrelated two-stage stochastic programs with recourse. A column generation-based technique is proposed for the solution of each problem instance arising as the start of each decision epoch over a time horizon. Numerical experiments conducted on an example of the 2010 Haiti earthquake are presented to illustrate the effectiveness of the proposed approach

Multi-period, multi-product production planning in an uncertain manufacturing environment

Les travaux de cette thèse portent sur la planification de la production multi-produits, multi-périodes avec des incertitudes de la qualité de la matière première et de la demande. Un modèle de programmation stochastique à deux étapes avec recours est tout d'abord proposé pour la prise en compte de la non-homogénéité de la matière première, et par conséquent, de l'aspect aléatoire des rendements de processus. Ces derniers sont modélisés sous forme de scénarios décrits par une distribution de probabilité stationnaire. La méthodologie adoptée est basée sur la méthode d'approximation par moyenne d'échantillonnage. L'approche est appliquée pour planifier la production dans une unité de sciage de bois et le modèle stochastique est validé par simulation de Monte Carlo. Les résultats numériques obtenus dans le cas d'une scierie de capacité moyenne montrent la viabilité de notre modèle stochastique, en comparaison au modèle équivalent déterministe. Ensuite, pour répondre aux préoccupations du preneur de décision en matière de robustesse, nous proposons deux modèles d'optimisation robuste utilisant chacun une mesure de variabilité du niveau de service différente. Un cadre de décision est développé pour choisir parmi les deux modèles d'optimisation robuste, en tenant compte du niveau du risque jugé acceptable quand à la variabilité du niveau de service. La supériorité de l'approche d'optimisation robuste, par rapport à la programmation stochastique, est confirmée dans le cas d'une usine de sciage de bois. Finalement, nous proposons un modèle de programmation stochastique qui tient compte à la fois du caractère aléatoire de la demande et du rendement. L'incertitude de la demande est modélisée par un processus stochastique dynamique qui est représenté par un arbre de scénarios. Des scénarios de rendement sont ensuite intégrés dans chaque noeud de l'arbre de scénarios de la demande, constituant ainsi un arbre hybride de scénarios. Nous proposons un modèle de programmation stochastique multi-étapes qui utilise un recours complet pour les scénarios de la demande et un recours simple pour les scénarios du rendement. Ce modèle est également appliqué au cas industriel d'une scierie et les résultats numériques obtenus montrent la supériorité du modèle stochastique multi- étapes, en comparaison avec le modèle équivalent déterministe et le modèle stochastique à deux étapes

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Optimization Approaches for Electricity Generation Expansion Planning Under Uncertainty

In this dissertation, we study the long-term electricity infrastructure investment planning problems in the electrical power system. These long-term capacity expansion planning problems aim at making the most effective and efficient investment decisions on both thermal and wind power generation units. One of our research focuses are uncertainty modeling in these long-term decision-making problems in power systems, because power systems\u27 infrastructures require a large amount of investments, and need to stay in operation for a long time and accommodate many different scenarios in the future. The uncertainties we are addressing in this dissertation mainly include demands, electricity prices, investment and maintenance costs of power generation units. To address these future uncertainties in the decision-making process, this dissertation adopts two different optimization approaches: decision-dependent stochastic programming and adaptive robust optimization. In the decision-dependent stochastic programming approach, we consider the electricity prices and generation units\u27 investment and maintenance costs being endogenous uncertainties, and then design probability distribution functions of decision variables and input parameters based on well-established econometric theories, such as the discrete-choice theory and the economy-of-scale mechanism. In the adaptive robust optimization approach, we focus on finding the multistage adaptive robust solutions using affine policies while considering uncertain intervals of future demands. This dissertation mainly includes three research projects. The study of each project consists of two main parts, the formulation of its mathematical model and the development of solution algorithms for the model. This first problem concerns a large-scale investment problem on both thermal and wind power generation from an integrated angle without modeling all operational details. In this problem, we take a multistage decision-dependent stochastic programming approach while assuming uncertain electricity prices. We use a quasi-exact solution approach to solve this multistage stochastic nonlinear program. Numerical results show both computational efficient of the solutions approach and benefits of using our decision-dependent model over traditional stochastic programming models. The second problem concerns the long-term investment planning with detailed models of real-time operations. We also take a multistage decision-dependent stochastic programming approach to address endogenous uncertainties such as generation units\u27 investment and maintenance costs. However, the detailed modeling of operations makes the problem a bilevel optimization problem. We then transform it to a Mathematic Program with Equilibrium Constraints (MPEC) problem. We design an efficient algorithm based on Dantzig-Wolfe decomposition to solve this multistage stochastic MPEC problem. The last problem concerns a multistage adaptive investment planning problem while considering uncertain future demand at various locations. To solve this multi-level optimization problem, we take advantage of affine policies to transform it to a single-level optimization problem. Our numerical examples show the benefits of using this multistage adaptive robust planning model over both traditional stochastic programming and single-level robust optimization approaches. Based on numerical studies in the three projects, we conclude that our approaches provide effective and efficient modeling and computational tools for advanced power systems\u27 expansion planning

Learning-Based Matheuristic Solution Methods for Stochastic Network Design

Cette dissertation consiste en trois études, chacune constituant un article de recherche. Dans tous les trois articles, nous considérons le problème de conception de réseaux multiproduits, avec coût fixe, capacité et des demandes stochastiques en tant que programmes stochastiques en deux étapes. Dans un tel contexte, les décisions de conception sont prises dans la première étape avant que la demande réelle ne soit réalisée, tandis que les décisions de flux de la deuxième étape ajustent la solution de la première étape à la réalisation de la demande observée. Nous considérons l’incertitude de la demande comme un nombre fini de scénarios discrets, ce qui est une approche courante dans la littérature. En utilisant l’ensemble de scénarios, le problème mixte en nombre entier (MIP) résultant, appelé formulation étendue (FE), est extrêmement difficile à résoudre, sauf dans des cas triviaux. Cette thèse vise à faire progresser le corpus de connaissances en développant des algorithmes efficaces intégrant des mécanismes d’apprentissage en matheuristique, capables de traiter efficacement des problèmes stochastiques de conception pour des réseaux de grande taille. Le premier article, s’intitulé "A Learning-Based Matheuristc for Stochastic Multicommodity Network Design". Nous introduisons et décrivons formellement un nouveau mécanisme d’apprentissage basé sur l’optimisation pour extraire des informations concernant la structure de la solution du problème stochastique à partir de solutions obtenues avec des combinaisons particulières de scénarios. Nous proposons ensuite une matheuristique "Learn&Optimize", qui utilise les méthodes d’apprentissage pour déduire un ensemble de variables de conception prometteuses, en conjonction avec un solveur MIP de pointe pour résoudre un problème réduit. Le deuxième article, s’intitulé "A Reduced-Cost-Based Restriction and Refinement Matheuristic for Stochastic Network Design". Nous étudions comment concevoir efficacement des mécanismes d’apprentissage basés sur l’information duale afin de guider la détermination des variables dans le contexte de la conception de réseaux stochastiques. Ce travail examine les coûts réduits associés aux variables hors base dans les solutions déterministes pour guider la sélection des variables dans la formulation stochastique. Nous proposons plusieurs stratégies pour extraire des informations sur les coûts réduits afin de fixer un ensemble approprié de variables dans le modèle restreint. Nous proposons ensuite une approche matheuristique utilisant des techniques itératives de réduction des problèmes. Le troisième article, s’intitulé "An Integrated Learning and Progressive Hedging Method to Solve Stochastic Network Design". Ici, notre objectif principal est de concevoir une méthode de résolution capable de gérer un grand nombre de scénarios. Nous nous appuyons sur l’algorithme Progressive Hedging (PHA), ou les scénarios sont regroupés en sous-problèmes. Nous intégrons des methodes d’apprentissage au sein de PHA pour traiter une grand nombre de scénarios. Dans notre approche, les mécanismes d’apprentissage developpés dans le premier article de cette thèse sont adaptés pour résoudre les sous-problèmes multi-scénarios. Nous introduisons une nouvelle solution de référence à chaque étape d’agrégation de notre ILPH en exploitant les informations collectées à partir des sous problèmes et nous utilisons ces informations pour mettre à jour les pénalités dans PHA. Par conséquent, PHA est guidé par les informations locales fournies par la procédure d’apprentissage, résultant en une approche intégrée capable de traiter des instances complexes et de grande taille. Dans les trois articles, nous montrons, au moyen de campagnes expérimentales approfondies, l’intérêt des approches proposées en termes de temps de calcul et de qualité des solutions produites, en particulier pour traiter des cas très difficiles avec un grand nombre de scénarios.This dissertation consists of three studies, each of which constitutes a self-contained research article. In all of the three articles, we consider the multi-commodity capacitated fixed-charge network design problem with uncertain demands as a two-stage stochastic program. In such setting, design decisions are made in the first stage before the actual demand is realized, while second-stage flow-routing decisions adjust the first-stage solution to the observed demand realization. We consider the demand uncertainty as a finite number of discrete scenarios, which is a common approach in the literature. By using the scenario set, the resulting large-scale mixed integer program (MIP) problem, referred to as the extensive form (EF), is extremely hard to solve exactly in all but trivial cases. This dissertation is aimed at advancing the body of knowledge by developing efficient algorithms incorporating learning mechanisms in matheuristics, which are able to handle large scale instances of stochastic network design problems efficiently. In the first article, we propose a novel Learning-Based Matheuristic for Stochastic Network Design Problems. We introduce and formally describe a new optimizationbased learning mechanism to extract information regarding the solution structure of a stochastic problem out of the solutions of particular combinations of scenarios. We subsequently propose the Learn&Optimize matheuristic, which makes use of the learning methods in inferring a set of promising design variables, in conjunction with a state-ofthe- art MIP solver to address a reduced problem. In the second article, we introduce a Reduced-Cost-Based Restriction and Refinement Matheuristic. We study on how to efficiently design learning mechanisms based on dual information as a means of guiding variable fixing in the context of stochastic network design. The present work investigates how the reduced cost associated with non-basic variables in deterministic solutions can be leveraged to guide variable selection within stochastic formulations. We specifically propose several strategies to extract reduced cost information so as to effectively identify an appropriate set of fixed variables within a restricted model. We then propose a matheuristic approach using problem reduction techniques iteratively (i.e., defining and exploring restricted region of global solutions, as guided by applicable dual information). Finally, in the third article, our main goal is to design a solution method that is able to manage a large number of scenarios. We rely on the progressive hedging algorithm (PHA) where the scenarios are grouped in subproblems. We propose a two phase integrated learning and progressive hedging (ILPH) approach to deal with a large number of scenarios. Within our proposed approach, the learning mechanisms from the first study of this dissertation have been adapted as an efficient heuristic method to address the multi-scenario subproblems within each iteration of PHA.We introduce a new reference point within each aggregation step of our proposed ILPH by exploiting the information garnered from subproblems, and using this information to update the penalties. Consequently, the ILPH is governed and guided by the local information provided by the learning procedure, resulting in an integrated approach capable of handling very large and complex instances. In all of the three mentioned articles, we show, by means of extensive experimental campaigns, the interest of the proposed approaches in terms of computation time and solution quality, especially in dealing with very difficult instances with a large number of scenarios