Academic literature on the topic 'Resource allocations problems'

Les problèmes d'allocation des ressources sont définis comme les situations concernant les décisions sur la distribution d’un budget limité afin d’optimiser un objectif. Beaucoup d'entre eux impliquent des interactions entre des décideurs compétitifs ; ils peuvent être bien capturés par des modèles de théorie des jeux. Dans cette thèse, nous choisissons d'étudier les jeux d'allocation de ressources. Nous nous concentrons principalement sur le jeu de Colonel Blotto (CB). Dans le jeu CB, deux joueurs compétitifs, chacun ayant un budget fixe, distribuent simultanément leurs ressources vers n champs de bataille. Chaque joueur évalue chaque champ de bataille avec une certaine valeur. Dans chaque champ de bataille, le joueur qui a l'allocation la plus élevée gagne la valeur correspondante tandis que l'autre obtient zéro. Le gain de chaque joueur est à ses gains cumulés sur tous les champs de bataille. Tout d'abord, nous modélisons plusieurs variantes et extensions du jeu CB comme jeux d'informations complètes à un coup. Notre première contribution est une classe d'équilibres approximatifs dans ces jeux et nous prouvons que l'erreur d'approximation est bien contrôlée. Deuxièmement, nous modélisons les jeux d'allocation de ressources avec des structures combinatoires comme des problèmes d'apprentissage en ligne pour étudier des situations impliquant des jeux séquentiels et des informations incomplètes. Nous établissons une connexion entre ces jeux et les problèmes de chemin le plus court en ligne (OSP). Notre deuxième contribution est un ensemble de nouveaux algorithmes d’OSP sous plusieurs paramètres de feedback qui améliorent des garanties de regret et du temps d'exécution<br>Resource allocation problems are broadly defined as situations involving decisions on distributing a limited budget of resources in order to optimize an objective. In particular, many of them involve interactions between competitive decision-makers which can be well captured by game-theoretic models. In this thesis, we choose to investigate resource allocation games. We primarily focus on the Colonel Blotto game (CB game). In the CB game, two competitive players, each having a fixed budget of resources, simultaneously distribute their resources toward n battlefields. Each player evaluates each battlefield with a certain value. In each battlefield, the player who has the higher allocation wins and gains the corresponding value while the other loses and gains zero. Each player's payoff is her aggregate gains from all the battlefields. First, we model several prominent variants of the CB game and their extensions as one-shot complete-information games and analyze players' strategic behaviors. Our first main contribution is a class of approximate (Nash) equilibria in these games for which we prove that the approximation error can be well-controlled. Second, we model resource allocation games with combinatorial structures as online learning problems to study situations involving sequential plays and incomplete information. We make a connection between these games and online shortest path problems (OSP). Our second main contribution is a set of novel regret-minimization algorithms for generic instances of OSP under several restricted feedback settings that provide significant improvements in regret guarantees and running time in comparison with existing solutions

En problemes d'assignació de recursos, normalment s'han de tenir en compte les incerteses que poden provocar canvis en les dades inicials. Aquests canvis dificulten l'aplicabilitat de les planificacions que s'hagin fet inicialment.<br/>Aquesta tesi se centra en l'elaboració de tècniques que consideren la incertesa alhora de cercar solucions robustes, és a dir solucions que puguin continuar essent vàlides encara que hi hagi canvis en l'entorn. Particularment, introduïm el concepte de robustesa basat en reparabilitat, on una solució robusta és una que pot ser reparada fàcilment en cas que hi hagi incidències. La nostra aproximació es basa en lògica proposicional, codificant el problema en una fórmula de satisfactibilitat Booleana, i aplicant tècniques de reformulació per a la generació de solucions robustes. També presentem un mecanisme per a incorporar flexibilitat a les solucions robustes, de manera que es pugui establir fàcilment el grau desitjat entre robustesa i optimalitat de les solucions.<br>Resource allocation problems usually include uncertainties that can produce changes in the data of the problem. These changes may cause difficulties in the applicability of the solutions.<br/>This thesis is focused in the elaboration of techniques that take into account such uncertainties while searching for robust solutions, i.e. solutions that can remain valid even if there are changes in the environment. Particularly, we introduce the concept of robustness based on reparability, where a robust solution is one that can be easily repaired when unexpected events occur. Our approach is based in propositional logic, encoding the problem to a Boolean formula, and applying reformulation techniques in order to generate robust solutions. Additionally, we present a mechanism to incorporate flexibility to the robust solutions, so that one can easily set the desired degree between optimality and robustness.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990.<br>Includes bibliographical references (leaves 213-214).<br>by Patrick Ahamad Hosein.<br>Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2009.<br>Includes bibliographical references (p. 159-162).<br>In this thesis, we study resource allocation problems that arise in the context of stochastic sequential decision making problems. The practical utility of optimal algorithms for these problems is limited due to their high computational and storage requirements. Also, an increasing number of applications require a decentralized solution. We develop techniques for approximately solving certain class of resource allocation problems that arise in the context of stochastic sequential decision making problems that are computationally efficient with a focus on decentralized algorithms where appropriate. The first resource allocation problem that we study is a stochastic sequential decision making problem with multiple decision makers (agents) with two main features 1) Partial observability Each agent may not have complete information regarding the system 2) Limited Communication - Each agent may not be able to communicate with all other agents at all times. We formulate a Markov Decision Process (MDP) for this problem. The features of partial observability and limited communication impose additional computational constraints on the exact solution of the MDP. We propose a scheme for approximating the optimal Q function and the optimal value function associated with this MDP as a linear combination of preselected basis functions. We show that the proposed approximation scheme leads to decentralization of the agents' decisions thereby enabling their implementation under limited communication. We propose a linear program, ALP, for selecting the parameters for combining the basis functions. We establish bounds relating the approximation error due to the choice of the parameters selected by the ALP with the best possible error given the choice of basis functions.<br>(cont.) Motivated by the need for a decentralized solution to the ALP, which is equivalent to a resource allocation problem with separable, concave objective function, we analyze a general class of resource allocation problems with separable concave objective functions. We propose a distributed algorithm for this class of problems when the objective function is differentiable and establish its convergence and convergence rate properties. We develop a smoothing scheme for non-differentiable objective functions and extend the algorithm for this case. Finally, we build on these results to extend the decentralized algorithm to accommodate non-negativity constraints on the resources. Numerical investigations on the performance of the developed algorithm show that our algorithm is competitive with its centralized counterpart. The second resource allocation problem that we study is the problem of optimally accepting or rejecting arriving orders in a Make-To-Order (MTO) manufacturing firm. We model the production facility of the MTO manufacturing firm as a queue and view the time of the production facility as a resource that needs to be optimally allotted between current and future orders. We formulate the Order Acceptance Problem under two arrival processes - Poisson process (OAP-P), and Bernoulli Process (OAP-B) and formulate both problems as MDPs. We provide insights into the structure of the optimal order acceptance policy for OAP-B under the assumption of First Come First Served (FCFS) scheduling of accepted orders.<br>(cont.) We investigate a class of randomized order acceptance policies for OAP-B called static policies that are practically relevant due to their ease of implementation and develop a procedure for computing the policy gradient for any static policy. Using these results for OAP-B, we propose 4 heuristics for OAP-P. We numerically investigate the performance of the proposed heuristics and compare their performance with other heuristics reported in literature. One of our proposed heuristics, FCFS-ValueFunction outperforms other heuristics under a variety of conditions while also being easy to implement.<br>by Hariharan Lakshmanan.<br>Ph.D.

Resource allocation in control and communication systems constitutes the distribution of (finite) system resources in a way that achieves maximum system functionality and or cost effectiveness. Specific resource allocation problems in subband coding, Discrete Multi-tone modulation based systems and autonomous multi-agent control are addressed in this thesis. In subband coding, the number of bits used (out of a target bit budget) to code a sub- band signal are allocated in a way that minimizes the coding distortion. In Discrete Multi-tone modulation based systems, high bit rate streams are split into several parallel lower rate streams. These individual data streams are transmitted over different subchannels. Given a target bit rate, the goal of resource allocation is to distribute the bits among the different subchannels such that the total transmitted power is minimized. The last problem is achieving stable control of a fleet of autonomous agents by utilizing the available communication resources (such as transmitted Power and bandwidth) as effectively as possible. We present an efficient bit loading algorithm that applies to both subband coding and single-user multicarrier communication system. The goal is to effect an optimal distribution of B bits among N subchannels (subbands) to achieve a minimum transmitted power (distortion error variance) for multicarrier (subband coding) systems. All the algorithms in literature, except a few (which provides a suboptimal solution), have run times that increase with B. By contrast, we provide an algorithm that solves the aforementioned problems exactly and with a complexity (given by O(N log(N)),) which is dependent only on N. Bit loading in multi-user multicarrier systems not only involves the distribution of bit rates across the subchannels but also the assignment of these subchannels to different users. The motivation for studying suboptimal bit allocation is underscored by implicit and explicit claims made in some of the papers which present suboptimal bit loading algorithms, without a formal proof, that the underlying problem is NP-hard. Consequently, for no other reason than the sake of completeness, we present a proof for NP-hardness of the multiuser multicarrier bit loading problem, thereby formally justifying the search for suboptimal solutions. There has been a growing interest in the area of cooperative control of networks of mobile autonomous agents. Applications for such a set up include organization of large sensor networks, air traffic control, achieving and maintaining formations of unmanned vehicles operating under- water, air traffic control etc. As in Abel et al, our goal is to devise control laws that, require minimal information exchange between the agents and minimal knowledge on the part of each agent of the overall formation objective, are fault tolerant, scalable, and easily reconfigurable in the face of the loss or arrival of an agent, and the loss of a communication link. A major drawback of the control law proposed in Abel et al is that it assumes all agents can exchange information at will. This is fine if agents acquire each others state information through straightforward sensing. If however, state information is exchanged through broadcast commu- nication, this assumption is highly unrealistic. By modifying the control law presented in Abel et al, we devise a scheme that allows for a sharing of the resource, which is the communication channel, but also achieves the desired formation stably. Accordingly we modify the control law presented in [23] to be compatible with networks constrained by MAC protocols.

Cette thèse s’intéresse aux problèmes d’ordonnancement à une machine où les durées opératoires des tâches peuvent dépendre de différents paramètres. Dans les problèmes d’ordonnancement traditionnels, les durées opératoires sont souvent supposées constantes. Cette hypothèse n’est pas toujours valable dans certains problèmes réels d'ordonnancement en production ou en service. La durée opératoire d'une tâche peut en effet varier selon la quantité de ressources consommables allouées, la performance des opérateurs et l’état des ressources matérielles utilisées, etc. L’ordonnancement optimal peut donc être différent. Nous nous intéressons à quatre problèmes d’ordonnancement avec différentes configurations des facteurs suivants : changement de productivité par la maintenance, quantité de ressources consommables utilisées, effet d’apprentissage, technologie de groupe, temps de réglage et fenêtres horaires dues. Le changement de productivité par la maintenance, qui reflète l'état des machines, est un facteur clé de cette thèse. Il est présent dans tous les problèmes étudié, sauf pour le premier. Cette thèse considère globalement les nouvelles caractéristiques telles que les ressources consommables, les ressources humaines et les machines bien qu'elle soit organisée sous l'angle des ressources consommables et l'effet d'apprentissage. Pour chaque problème considéré, nous construisons d’abord un modèle mathématique. Après l’analyse du modèle construit, nous proposons un algorithme exact de résolution. Enfin la complexité de l’algorithme est étudiée<br>This thesis addresses scheduling problems with consumable resource allocation and learning effect. In traditional deterministic scheduling problems, job processing times are assumed to be constant. However, this assumption is not always appropriate in many real life production and service operations since practical issues, including limited consumable resources, human characteristics (learning effect), usually affect job processing times, which change the whole scheduling process and lead to new characteristics to decision-making and scheduling results. It is therefore necessary and reasonable to study scheduling problems with these features. Based on the above two issues, this thesis mainly concerns four scheduling problems including group technology, rate-modifying activity (RMA), past-sequence-dependent setup times, and due-windows. It is worth to note that RMA which reflects the situations of ma-chines is also a key factor considered. It is involved in all studied problems except the first one. This thesis is also a work considering comprehensively new characteristics of consumable resources, human, and machines although we just organize this thesis from the viewpoint of consumable resource allocation and learning effect. For each problem, we propose a scheduling model, design an exact algorithm, and analyze the complexity

In a data streaming system, each component consumes one or several streams of data on the fly and produces one or several streams of data for other components. The entire Internet can be viewed as a giant data streaming system. Other examples include real-time exploratory data mining and high performance transaction processing. In this thesis we study several measurement and resource allocation optimization problems of data streaming systems. Measuring quantities associated with one or several data streams is often challenging because the sheer volume of data makes it impractical to store the streams in memory or ship them across the network. A data streaming algorithm processes a long stream of data in one pass using a small working memory (called a sketch). Estimation queries can then be answered from one or more such sketches. An important task is to analyze the performance guarantee of such algorithms. In this thesis we describe a tail bound problem that often occurs and present a technique for solving it using majorization and convex ordering theories. We present two algorithms that utilize our technique. The first is to store a large array of counters in DRAM while achieving the update speed of SRAM. The second is to detect global icebergs across distributed data streams. Resource allocation decisions are important for the performance of a data streaming system. The processing graph of a data streaming system forms a fork and join network. The underlying data processing tasks consists of a rich set of semantics that include synchronous and asynchronous data fork and data join. The different types of semantics and processing requirements introduce complex interdependence between various data streams within the network. We study the distributed resource allocation problem in such systems with the goal of achieving the maximum total utility of output streams. For networks with only synchronous fork and join semantics, we present several decentralized iterative algorithms using primal and dual based optimization techniques. For general networks with both synchronous and asynchronous fork and join semantics, we present a novel modeling framework to formulate the resource allocation problem, and present a shadow-queue based decentralized iterative algorithm to solve the resource allocation problem. We show that all the algorithms guarantee optimality and demonstrate through simulation that they can adapt quickly to dynamically changing environments.

With the increasing effect of disasters and long term issues on human well-being and economy over the recent years, effective management of humanitarian supply chains has become more important. This thesis work focuses on three problems in humanitarian supply chains where uncertainty is inherent, namely (i) post-disaster debris clearance with uncertain debris amounts, (ii) allocation of a health/humanitarian commodity in a developing country setting with multiple demand types, and (iii) distribution of specialized nutritious foods by a large scale humanitarian organization. In each of the three parts, the problem is formally defined, and a novel optimal solution approach incorporating the inherent uncertainty in the environment and updates is proposed. In cases where optimal models cannot be solved within reasonable time, novel heuristics are developed. Through structural analysis and computational experiments based on real data, the proposed approaches are compared to those that ignore the uncertainty in the environment and/or updates of information as new data becomes available. Using computational experiments, the proposed approaches are compared to those that are applied in practice, and the aspects of the system where performance improvements are more significant are analyzed.