bluuebunny/crossref_metadata_2025_split huggingface dataset:
Jackson Networks (Open and Closed)
Authors: Daduna Hans 
Published: February 2011

AbstractWe describe the classical exponential networks of Jackson and Gordon and Newell and their successor networks and extensions in network theory. The characterizing feature of these networks is the product form steady‐state distribution for the joint queue length process, which we evaluate in detail.We characterize passage time behavior for customers traversing the networks or parts of it. This relies on finding the distributions, which characterizes the situation when such a passage commences.We sketch typical algorithmic methods to efficiently compute performance indices for the networks in steady state.Finally, we describe some networks with additional features that broaden the range of applicability of the networks.
The Knowledge Gradient for Optimal Learning
Authors: Powell Warren B. 
Published: February 2011

AbstractOptimal learning addresses the problem of how to collect information so that it benefits future decisions. For off‐line problems, we have to make a series of measurements or observations before choosing a final design or set of parameters; for on‐line problems, we learn from rewards we are receiving, and we want to strike a balance between rewards earned now and better decisions in the future. This article reviews these problems, describes optimal and heuristic policies, and shows how to compare competing policies. Then, the presentation focuses on the concept of the knowledge gradient, which guides information collection by maximizing the marginal value of information. We show how this idea can be applied to both on‐line and off‐line problems, as well as a broad range of other applications which have not previously yielded to formal techniques.
Lagrangian Optimization for LP
Authors: Desai Jitamitra 
Published: February 2011

Abstract

In this article, we present a methodological framework for solving large‐scale
linear programming
(LP) problems via a Lagrangian optimization approach. Beginning with a formulation of the Lagrangian dual problem, we relate this approach to standard LP theory in two steps: first, we demonstrate that the optimal objective function value obtained by solving the Lagrangian dual is optimal to the original linear program; and second, we include theorems and propositions that characterize the mathematical properties of the Lagrangian dual and establish the equivalence of this approach to classical LP duality. Recognizing that the Lagrangian dual formulation is a nondifferentiable optimization problem, a subgradient algorithm is prescribed for solving this problem, and computational results for an illustrative example are presented. A brief extension of this approach for solving integer programs can also be found in this article.
Lifting Techniques For Mixed Integer Programming
Authors: Richard Jean‐Philippe P. 
Published: February 2011

Abstract
This article provides a review of lifting techniques for the generation of cutting planes in mixed integer programming. After motivating the notion of lifting graphically, four key steps in the derivation of lifted inequalities are described: (i) variables fixing, (ii) derivation of seed inequalities, (iii) (re‐)computation of lifting functions, and (iv) derivation of lifting coefficients. Practical considerations that are relevant to each of these steps are discussed and is emphasized the importance of superadditivity in designing efficient lifting procedures. This concluded with a description of the strength of lifted cuts. Throughout, concepts on a simple example are illustrated.
Limit Theorems for Renewal Processes
Authors: Liu Nan 
Published: February 2011

Abstract
This article describes the key renewal theorem and the Blackwell's renewal theorem. These two limit theorems for renewal processes are equivalent but of different forms. They are particularly useful for characterizing the asymptotic behavior of a probabilistic quantity of interest in a renewal process. We present two classical applications of these limit theorems: the limiting distributions of recurrence times in a renewal process and the asymptotic expansion of a renewal function. Further readings on the theoretical development of these limit theorems and their applications in different areas are also provided.
Linear Programming and Two‐Person Zero‐Sum Games
Authors: Zafra Pablo 
Published: February 2011

AbstractThe equivalence between linear programming (LP) and two‐person zero‐sum games (also commonly referred to asmatrix games) was established when the minimax theorem in game theory proved to be equivalent to the duality concept in LP. The equivalence is discussed as follows: Given a general matrix game, the associated primal‐dual LP problems will be formulated, and, conversely, given an LP problem with a minimization objective function, a skew‐symmetric payoff matrix of the equivalent symmetric game will be constructed. In either case, once the solutions to the equivalent problem are found, it is a simple task to retrieve the solutions to the original problem. Examples are provided to illustrate the transformation procedures, and different types of constraints for the given LP problem are also considered (normal, standard and mixed).
Constraint Programming Links with Math Programming
Authors: Milano Michela 
Published: February 2011

AbstractAlthough operations research (OR) and constraint programming (CP) have different roots, the links between the two communities have grown stronger in recent years. For solving combinatorial optimization problems, the techniques of CP and OR will become so interdependent that the two research communities could eventually merge. In this article, we first describe CP basic concepts, and then we show different ways of integrating CP and mathematical programming (MP). This article presents a CP perspective: MP is seen as a support to the CP decision process, even if existing approaches from the OR literatures consider a cooperation of CP and MP on an equal basis, but they are out of the scope of this article.
L
ittle's Law and Related Results
Authors: Wolff Ronald W. 
Published: February 2011

Abstract

For queues, and similar systems, Little's Law, often written
L
= λ
w
, states that the time average of the number of customers in system is the product of the arrival rate and the customer average of their waiting times. We treat
sample‐path
and
stationary
versions of this result and extensions, including
H
= λ
G
, and a distributional Little's Law. We illustrate how these results are applied and treat the connection between these results and a rate conservation law.
LP
Duality and
KKT
Conditions for
LP
Authors: Clausen Jens 
Published: February 2011

Abstract

Duality is one of the most central concepts in connection with Linear Programming (LP), both from a theoretical and an algorithmic point of view. LP problems always appear in pairs with a primal problem and a corresponding dual problem—a fact which is intimately related to the concept of relaxation and to the necessary and sufficient optimality conditions known as
Karush‐Kuhn‐Tucker (KKT)‐conditions
for nonlinear programs (NLPs).

This article first introduces the concept of LP duality and discusses various ways of presenting duality. The fundamental theorems of Weak and Strong Duality are stated and proven. The Complementary Slackness Conditions for optimality of a set of primal and dual solutions to a set of dual LPs are then introduced, and finally it is demonstrated that these conditions are the Karush‐Kuhn‐Tucker (KKT) conditions known from NLP restated in a linear setting.
Linear Programming Projection Algorithms
Authors: Evtushenko Yury , Golikov Alexander 
Published: February 2011

Abstract
Fast linear programming projection methods for solving primal and dual linear programming problems are described. These methods find the projection of given points on the solution sets of primal or dual LP problems by reducing LP to a single maximization of an auxiliary function, which is solved by globally convergent finitely terminating generalized Newton method. Some results of uniprocessor and multiprocessor computations are presented.
Managing Perishable Inventory
Authors: Baron Opher 
Published: February 2011

AbstractThis article provides an introduction to the management of perishable items. We first highlight some key differences between inventory models for nonperishable items and models for perishable ones. Next, several models for inventory management of perishable items are discussed. An important observation from this discussion is the need for finding effective heuristics for the optimal control of inventory for perishables. Therefore, we demonstrate the development of one such heuristic. The article ends with a list of future research directions on the management of inventory of perishables.
Managing A Portfolio of Risks
Authors: Keisler Jeffrey M. , Linkov Igor I. 
Published: February 2011

AbstractManagers and stakeholders concerned about all sorts of entities often face a complex mixture of threats originating from multiple sources. Traditional management approaches that deal with multiple decisions, such as project portfolio management and risk assessment, are focused on single sources of risk or they integrate risks using simplified assumptions (e.g., simple addition). Current challenges—including emergency response to natural disasters, homeland security threats, emerging materials, and correlated events—and an uncertain future with respect to societal concerns—for example, climate change, economic development, and social/religious instabilities—require integrated application of these methods. This article describes a range of risk approaches that enable a flexible approach to risk portfolio management. Decision quality serves as an integrating framework for applying a mix of analytic methods to facilitate successful risk portfolio management. Methods including portfolio decision analysis and risk management, as well as other tools from risk analysis, utility theory, and modern portfolio theory from finance, help to address complexities of current risk portfolio management challenges.
Markov and Hidden Markov Models
Authors: Soyer Refik 
Published: February 2011

AbstractIn this article we give an overview of Markov models that are used for describing dynamics of operating environments in reliability analysis. We present both continuous‐ and discrete‐time Markov chains as well as diffusion processes. We also consider Markov modulated stochastic processes that are known ashidden Markov modelsand discuss their properties. More specifically, we give an overview of Markov modulated Poisson and Markov modulated Bernoulli processes.
Maximum Flow Algorithms
Authors: Sargut Zeynep , Ahuja Ravindra K. 
Published: February 2011

AbstractIn this article, we will explain the maximum flow problem and the solution algorithms classified under augmenting path, blocking flow, preflow‐push, and other algorithms. For the first three classes, we first present the generic version of the algorithm and then present some elaborate versions in the literature. We also give other approaches and the more efficient algorithms for unit capacity, bipartite, and planar networks. Although the binary blocking flow algorithm has the best theoretical worst‐case running time, the preflow‐push type algorithms are shown to be the most efficient algorithms in practice.
Methods For Large‐Scale Unconstrained Optimization
Authors: Fasano Giovanni 
Published: February 2011

AbstractIn this article, we review methods for the solution of unconstrained optimization problems, where the number of unknowns is large. We first describe the basics of unconstrained optimization, then we consider the iterative methods that are commonly used within large‐scale optimization. The techniques described here explicitly use information on the objective function and some of its derivatives. Extensions to effective quasi‐Newton methods for partially separable optimization are detailed.
Minimum Prediction Error Models and Causal Relations between Multiple Time Series
Authors: Zhang Jicong , Xanthopoulos Petros , Chien Jui‐Hong , Tomaino Vera , Pardalos Panos M. 
Published: February 2011

AbstractPrediction is widely used in economics, finance, weather forecasting, earthquake monitoring, and other social and scientific fields. Though difficult, it is important to know what will happen in the future. Least square error (LSE) model and minimum mean square (MMSE) model are the fundamental models of a large group of minimum prediction error models in deterministic and stochastic senses respectively. The key in the minimum prediction error model is the principle of orthogonality to reach global optimum. Further, the MMSE model can be considered a special case of ARMA/ARIMA models. Besides LSE and MMSE, the causal relations between two, three, and multiple variables are reviewed and explored, and the principle of orthogonality is again part of the intrinsic mathematics. Finally, other prediction methods such as the Box–Jenkins prediction are discussed briefly.
Mixing Sets
Authors: Wolsey Laurence A. 
Published: February 2011

AbstractA mixing set is a simple mixed integer set that has a rich structure and has turned out to provide very effective relaxations for a variety of lot‐sizing problems. Here we describe some applications, some of the basic results on valid inequalities and extended formulations. We then present several of the generalizations that have been studied, and indicate the major results obtained for these general mixing sets.
Modeling and Forecasting by Manifold Learning
Authors: Ni Xuelei (Sherry) 
Published: February 2011

AbstractForecasting can benefit from recently emerged manifold learning algorithms. We describe the connection between manifold learning and forecasting. Moreover, we study the properties of different manifold learning methods and their reconstruction. These will be the technical core of the forecasting. Because manifold‐based forecasting is model‐free and totally nonlinear, it is promising in dealing with complex data.
Structured Optimal Policies forMarkov Decision Processes: Lattice Programming Techniques
Authors: Dragut Andreea 
Published: February 2011

AbstractThe structure (monotonicity, convexity, multimodularity, directional convexity and K‐convexity) of optimal policies is used to reduce the exponential growth with respect to the size of a sequential decision process and to compare different control systems.Monotonicity can be derived using Tattice programming techniques, sample path analysis or discrete events dynamic programming.We cover the discrete and continuous‐time MDP and POMDP models with Borel, countable‐and finite‐state and action spaces, as well nonstationary ones.Applications include admission/control of (networks of) queues, maintenance, inventory, production and innovation.
Multiechelon Multiproduct Inventory Management
Authors: Parker Rodney P. 
Published: February 2011

Abstract
This article summarizes the inventory management literature within the context of multiechelon systems. The optimal inventory policies for the single‐installation under discrete‐time and continuous‐time are described, followed by the optimal inventory policies for the serial multiechelon system, with the interpretation of the associated induced penalty cost functions. The assembly system's optimal policy translation to an “equivalent” serial system is demonstrated and discussed. Although the optimal inventory policies of distribution systems are generally not known, the performance of various simple heuristics are then discussed.
Multistage (Stochastic) Games
Authors: Krishnamurthy Nagarajan , Parthasarathy Thiruvenkatachari 
Published: February 2011

AbstractWe define two‐person zero‐sum and nonzero‐sum stochastic games with finite state space and finite action space. We discuss the case of β‐discounted payoffs as well as that of undiscounted or limiting time average payoffs. We look at certain classes of stochastic games that possess the orderfield property, that is, given rational inputs, such games have a rational solution. To solve such classes exactly, there is hope for finding finite arithmetic‐step algorithms. We discuss algorithms for some such classes. We also briefly discuss determinacy of stochastic games with countable state space and Borel payoffs. Furthermore, we outline some applications of stochastic games as well as some recent work.
Network‐Based Data Mining: Operations Research Techniques and Applications
Authors: Boginski Vladimir 
Published: February 2011

Abstract
We discuss concepts and applications arising in the area of network‐based techniques in data mining. The approach of representing real‐world data sets as large‐scale graphs has become widely used during recent years. The purpose of this article is to briefly review the graph‐theoretic and network optimization concepts that are important in the context of data mining and discuss the interpretation of these concepts in data mining problems from the operations research perspective.
Software For Nonlinearly Constrained Optimization
Authors: Leyffer Sven , Mahajan Ashutosh 
Published: February 2011

Abstract
We categorize and survey software packages for solving constrained nonlinear optimization problems, including interior‐point methods, sequential linear/quadratic programming methods, and augmented Lagrangian methods. In each case, we highlight the main methodological components and provide a brief summary of interfaces and availability.
Operations Research in Data Mining
Authors: Wang Shouyi , Chaovalitwongse Wanpracha Art , Seref Onur 
Published: February 2011

AbstractData mining (DM) and operations research (OR) are two largely independent paradigms of science. DM involves data driven methods that are aimed at extracting meaningful patterns from data instances, whereas OR employs mathematical models and analytical techniques to achieve optimal solutions for complex decision‐making problems. DM and OR are also two overlapping disciplines. There is a growing interest in applying OR techniques to determine the optimal underlying fitting data structures in DM problems. This article provides a description of the basic concepts and methodologies of influential DM techniques, and discusses how OR can be applied to these techniques.
F
ritz–
J
ohn and
KKT
Optimality Conditions for Constrained Optimization
Authors: Andreas April 
Published: February 2011

Abstract
Optimality conditions for Fritz–John and Karush Kuhn Tucker (KKT) points provide one strategy for solving nonlinear optimization problems. In fact, KKT conditions are necessary, if not sufficient, for proving optimality. In this article, we introduce Fritz–John and KKT optimality conditions for constrained optimization. We begin by reviewing some essential definitions for completing the logic, including Gordon's and Farkas' Lemmas. We derive the Fritz–John conditions and show when these conditions are necessary to show optimality. We then derive the necessary and sufficient KKT conditions for optimality. The article concludes with two simple numerical examples illustrating Fritz–John and KKT theory.
Penalty and Barrier Methods
Authors: Nash Stephen G. 
Published: February 2011

Abstract
Penalty and barrier methods solve a constrained optimization problem via a sequence of unconstrained problems. Under appropriate assumptions, the solutions of the unconstrained problems are guaranteed to converge to the solution of the original constrained problem. However, to obtain an accurate solution, the unconstrained problems will typically become ever more ill‐conditioned, and special algorithmic techniques are needed to ensure good performance. Penalty and barrier methods were important during the 1960s, but lost favor because of the difficulties associated with ill‐conditioning (even though remedies were known at that time). However, interest in barrier methods revived in the 1980s in connection with the development of interior‐point methods for linear programming. Penalty and barrier methods are useful methods in their own right, but they also form the theoretical and practical underpinning to other important and widely used methods. They can be grouped together under the label of penalization methods. Penalty methods impose a penalty for violating a constraint, and barrier methods impose a penalty for approaching the boundary of an inequality constraint.
Percolation Theory
Authors: Wierman John 
Published: February 2011

AbstractPercolation theory is a collection of mathematical models for phenomena such as fluid flow and clustering behavior in random media. This article emphasizes three major aspects of the theory: (i) The percolation threshold is a critical point at which the properties of the model exhibit a substantial change. The threshold depends on the detailed structure of the lattice graph used to model the medium, and various approaches for finding exact values, bounds, and estimates of percolation threshold of different lattices are discussed. (ii) The behavior of a model at and near the percolation threshold is believed to be independent of the detailed structure of the graph, described by power laws, which depend only on the dimension in the case of lattice graphs. (iii) The variety of extensions and generalizations of the classical percolation models allow a wide range of phenomena to be modeled. A selection of different percolation models are mentioned to illustrate the possible range of applications.
Performance Bounds in Queueing Networks
Authors: Veatch Michael H. 
Published: February 2011

Abstract
Optimal controls for many multiclass queueing networks are complex and intractable to compute. This paper surveys computable performance bounds. The primary focus is sequencing and scheduling control in open networks to minimize the long run average number of customers, or a weighted average over different customer classes. Lower bounds are given for any policy and, in some cases, upper bounds for a class of policies. Closed networks are considered briefly. Many of these bounds require only solving a linear program. Some pathwise bounds are also discussed.
Phase‐Type (PH) Distributions
Authors: Pérez‐Ocón Rafael 
Published: February 2011

AbstractThe phase‐type (PH) distributions were introduced by Neuts (1981). They are playing an important role in modeling random phenomena due to their interesting properties, and it has a widespread use in applied probability. A continuous PH distribution is the distribution of the absorption time in a Markov chain in continuous time with a finite‐state space and one absorbent state. The cumulative distribution function (CDF) has exponential form, and it is deduced from the underlying Markov process. The class of PH distributions has important closure properties which make it very versatile in applications; it is closed for finite convolution, finite mixture, formation of coherent systems, and order statistics. On the other hand, it has interesting properties of approximation. This class is dense, in the sense of distributions, in the class of distribution functions defined on the positive real half line, so it is possible to approach general distributions by elements of this class. The use of PH distributions in stochastic modeling leads to results that can be presented in algorithmic form and the results are susceptible to computational implementation. The PH distributions together with the Markovian arrival processes are the basic elements in what is known as matrix‐analytic methods.
Power Indices
Authors: Freixas Josep 
Published: February 2011

Abstract
This paper deals with simple games, that is a voting situation in which a single alternative, such as a bill or amendment, is pitted against the status quo. In these systems, each voter responds with a vote “yea” or “nay.” A simple game is simply a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. After studying a little the mathematical structure of simple games, we proceed to introduce power, which is a central concept in political sciences. We revise some well‐known power indices as well as some existent background known in the literature.