A Sample-path Optimization Approach for Optimal Resource Allocation in Stochastic Projects

A Sample-path Optimization Approach for Optimal Resource Allocation in Stochastic Projects
Author:
Publisher:
Total Pages:
Release: 2003
Genre:
ISBN:

The purpose of this research has been to develop an optimization method that can be utilized to determine optimal resource allocations for projects in an uncertain (stochastic) environment. The project under consideration is modeled as a stochastic activity network (SAN) where the workload requirements for each activity are assumed to be random with some specified distribution. Our concern is the time/cost tradeoff problem where the project manager can affect the duration of each activity in the project by allocating more or less of a scarce resource to the competing activities (at some cost). The objective is therefore to minimize the total expected cost of the project by assigning the resource to the various activities while simultaneously respecting precedence relationships among the activities and constraints on the total resource available. In particular we would like to analyze stochastic projects of reasonable size (>100 activities) and provide an optimization tool that achieves results in sufficiently small amount of time to make its application practical for realistic project management scenarios.

Optimal Resource Allocation

Optimal Resource Allocation
Author: Igor A. Ushakov
Publisher: John Wiley & Sons
Total Pages: 165
Release: 2013-05-17
Genre: Mathematics
ISBN: 1118400704

A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATION Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems. Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features: An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology Numerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protection The applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problems Practical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithms Optimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.

Resource Allocation with Observable and Unobservable Environments

Resource Allocation with Observable and Unobservable Environments
Author: Santiago Duran
Publisher:
Total Pages: 115
Release: 2020
Genre:
ISBN:

This thesis studies resource allocation problems in large-scale stochastic networks. We work on problems where the availability of resources is subject to time fluctuations, a situation that one may encounter, for example, in load balancing systems or in wireless downlink scheduling systems. The time fluctuations are modelled considering two types of processes, controllable processes, whose evolution depends on the action of the decision maker, and environment processes, whose evolution is exogenous. The stochastic evolution of the controllable process depends on the the current state of the environment. Depending on whether the decision maker observes the state of the environment, we say that the environment is observable or unobservable. The mathematical formulation used is the Markov Decision Processes (MDPs).The thesis follows three main research axes. In the first problem we study the optimal control of a Multi-armed restless bandit problem (MARBP) with an unobservable environment. The objective is to characterise the optimal policy for the controllable process in spite of the fact that the environment cannot be observed. We consider the large-scale asymptotic regime in which the number of bandits and the speed of the environment both tend to infinity. In our main result we establish that a set of priority policies is asymptotically optimal. We show that, in particular, this set includes Whittle index policy of a system whose parameters are averaged over the stationary behaviour of the environment. In the second problem, we consider an MARBP with an observable environment. The objective is to leverage information on the environment to derive an optimal policy for the controllable process. Assuming that the technical condition of indexability holds, we develop an algorithm to compute Whittle's index. We then apply this result to the particular case of a queue with abandonments. We prove indexability, and we provide closed-form expressions of Whittle's index. In the third problem we consider a model of a large-scale storage system, where there are files distributed across a set of nodes. Each node breaks down following a law that depends on the load it handles. Whenever a node breaks down, all the files it had are reallocated to other nodes. We study the evolution of the load of a single node in the mean-field regime, when the number of nodes and files grow large. We prove the existence of the process in the mean-field regime. We further show the convergence in distribution of the load in steady state as the average number of files per node tends to infinity.

Algorithms - ESA '97

Algorithms - ESA '97
Author: Rainer Burkard
Publisher: Springer Science & Business Media
Total Pages: 538
Release: 1997-08-27
Genre: Computers
ISBN: 9783540633976

This book constitutes the refereed proceedings of the 5th Annual International European Symposium on Algorithms, ESA'97, held in Graz, Austria, September 1997. The 38 revised full papers presented were selected from 112 submitted papers. The papers address a broad spectrum of theoretical and applicational aspects in algorithms theory and design. Among the topics covered are approximation algorithms, graph and network algorithms, combinatorial optimization, computational biology, computational mathematics, data compression, distributed computing, evolutionary algorithms, neural computing, online algorithms, parallel computing, pattern matching, and others.

Stochastic Resource Allocation Strategies With Uncertain Information In Sensor Networks

Stochastic Resource Allocation Strategies With Uncertain Information In Sensor Networks
Author: Nan Hu
Publisher:
Total Pages:
Release: 2016
Genre:
ISBN:

Support for intelligent and autonomous resource management is one of the key factors to the success of modern sensor network systems. The limited resources, such as exhaustible battery life, moderate processing ability and finite bandwidth, restrict the systems ability to simultaneously accommodate all missions that are submitted by users. In order to achieve the optimal profit in such dynamic conditions, the value of each mission, quantified by its demand on resources and achievable profit, need to be properly evaluated in different situations.In practice, uncertainties may exist in the entire execution of a mission, thus should not be ignored. For a single mission, uncertainty, such as unreliable wireless medium and variable quality of sensor outputs, both demands and profits of the mission may not be deterministic and may be hard to predict precisely. Moreover,throughout the process of execution, each mission may experience multiple states, the transitions between which may be affected by different conditions. Even if the current state of a mission is identified, because multiple potential transitions may occur each leading to different consequences, the subsequent state cannot be confirmed until the transition actually occurs. In systems with multiple missions, each with uncertainties, a more complicated circumstance arises, in which the strategy for resource allocation among missions needs to be modified adaptively and dynamically based on both the present status and potential evolution of all missions.In our research, we take into account several levels of uncertainties that may be faced when allocating limited resources in dynamic environments as described above, where the concepts of missions that require resources may be matched to those as in certain network applications. Our algorithms calculate resource allocation solutions to corresponding scenarios and always aim to achieve high profit, as well as other performance improvements (e.g., resource utilization rate, mission preemption rate, etc.).Given a fixed set of missions, we consider both demands and profits as random variables, whose values follow certain distributions and may change over time. Since the profit is not constant, rather than achieving a specific maximized profit, our objective is to select the optimal set of missions so as to maximize a certain percentile of their combined profit, while constraining the probability of resource capacity violation within an acceptable threshold. Note that, in this scenario, the selection of missions is final and will not change after the decision has been made. Therefore, this static solution only fits in the applications with long-term running missions.For the scenarios with both long-term and short-term missions, to increase the total achieved profit, instead of selecting a fixed mission set, we propose a dynamic strategy which tunes mission selections adaptively to the changing environments. We take a surveillance application as an example, where missions are targetingspecific sets of events, and both demands and profits of a mission depend on which event is actually occurring. To some extent resources should be focused on those high-valued events with a high probability of occurring; on the other hand, resources should also be distributed to gain an understanding of the overall condition of the environment. We develop Self-Adaptive Resource Allocation algorithm (SARA) to model mission execution as Markov processes, in which the states are decided by the combination of occurring events. In this case, resources need to be allocated before the events actually occur, otherwise, the mission will miss the event due to lack of support. Therefore, a prediction as to which events are about to occur is necessary, and when the prediction fails, in exchange of the loss of profit, the mistakenly allocated resources collect information to assist prediction in the future.When the transitions between mission states can be controlled by taking certain maneuvers at the proper time, the probability of the cases when missions transit to lower profit states may be decreased. As a consequence, sometimes a loss of profit may be avoided. We model this problem as a Semi-Markov Decision Process, andpropose Action-Drive Operation Model With Evaluation of Risk and Executability (ADOM-ERE) to calculate optimal maneuvers. One challenge is that the state transitions can be affected not only by states and actions, but also by external risks and competition for resources. On one hand, external risks (e.g., a DoS attack) may change the existing transition probabilities between states; on the other hand, taking actions to avoid lower profit states may require special constrained resources.As a result, sometimes lower profit missions may not choose its optimal action because of resource exhaustion. ADOM-ERE considers all of states, actions, risks and competition when searching for the optimal allocation solution, and is available for both scenarios in which resources for actions are managed either centralized or managed in a distributed way.Numerical simulation are performed for all algorithms, and the results are compared with several competitive works to show that our solutions are better in terms of higher profit achieved in corresponding settings.