bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamic Models for Robust Optimization
Authors: Düzgün Ruken , Thiele Aurélie
Published: February 2011

This article discusses recent developments in robust optimization, with a focus on dynamic models. Traditional techniques such as stochastic programming and dynamic programming face dimensionality issues as the size of the problem increases; furthermore, probability distributions are often difficult to accurately estimate. After robust optimization emerged as a tractable modeling framework in static optimization, researchers investigated its applicability to dynamic decision making under uncertainty. We provide an overview and discussion of their findings.
Learning with Dynamic Programming
Authors: Frazier Peter I.
Published: February 2011

We consider the role of dynamic programming in sequential learning problems. These problems require deciding which information to collect in order to best support later actions. Such problems are ubiquitous, appearing in simulation, global optimization, revenue management, and many other areas. Dynamic programming offers a coherent framework for understanding and solving Bayesian formulations of these problems. We present the dynamic programming formulation applied to a canonical problem, Bernoulli ranking and selection. We then review other sequential learning problems from the literature and the role of dynamic programming in their analysis.
Edgeworth Market Games: Price‐Taking and Efficiency
Authors: Chowdhury Prabal Roy
Published: February 2011

This article surveys the Edgeworth market game literature, which formalizes multiagent trading as a game. The key issues are two fold, whether, as the economy becomes large, (i) price‐taking emerges, and (ii) whether efficiency is obtained. The focus here is on production economies under partial equilibrium, where the two questions converge to a single one, that is if the equilibrium approximates the competitive one in the limit. We however also discuss related approaches to market games, in particular (i) the cooperative approach, (ii) the trading post literature, and (iii) Cournot competition under general equilibrium.
Multivariate Elicitation: Association, Copulae, and Graphical Models
Authors: Daneshkhah Alireza , Bedford Tim
Published: February 2011

In practical elicitation problems, we very often wish to elicit from the expert her knowledge about more than one uncertain quantity. When these are considered independent, the uncertainty about them is characterized simply by their marginal distributions; so it is sufficient to elicit the expert's knowledge about the quantities separately. When the independence assumption between the uncertain quantities of interest is not reasonable or has to be explored, the elicitation process becomes more complex. This is where we need to elicit information about the association between the variables in some way. Unfortunately, despite the growing literature about elicitation, this is an area where there is very little guidance to be found. In this article, we present some methods proposed in the literature to specify a multivariate distribution. We focus on the methods that use copulae and vines to construct a joint probability distribution. They enable us to build a multivariate distribution based on the elicited marginal distributions and their dependencies.
Ellipsoidal Algorithms
Authors: Takahashi Ricardo H. C.
Published: February 2011

This article reviews the ellipsoidal algorithms (EAs), starting from its working principles, and then presenting the basic EA and some deep cut variations in a constructive manner. The classes of problems for which the EAs are guaranteed to converge to the exact solutions (linear problems, convex problems, and quasi‐convex problems) are stated in first place. The general principle ofcutting‐plane branch‐and‐cutoperation, that is valid for such classes of problems, is presented. The basic EA is stated, as an instance of such principles, and the convergence properties of this version of EA are discussed. The basic EA is then reformulated, with the inclusion of thedeep cuts, which accelerate the convergence. Specific forms of deep cuts that can be applied to linear‐ and convex problems are presented. Some further implementation issues in EAs are briefly discussed, and some references are indicated.
Feasible Direction Method
Authors: Du Ding‐Zhu , Wu Weili , Pardalos Panos M. , Sohaee Nassim
Published: February 2011

The feasible direction method is an important class of algorithms for solving constrained nonlinear optimization problems. In this article, we survey various historical issues about them, including their global convergence and extension to nonlinear constrained optimization.
Forecasting NonStationary Processes
Authors: Chien Jui‐Hong , Xanthopoulos Petros , Pardalos Panos M. , Tomaino Vera
Published: February 2011

Preprocessing and forecasting nonstationary time series has always been a difficult task. Depending on the methods and tools used, we extract different features from a process, and these features provide us with some routes for forecasting the evolution of a process. Forecasting has extensively and successfully been done for stationary processes. However, nonstationarity smears many convenient properties of stationarity. For forecasting, the conceptual gap between stationary and nonstationary processes must be bridged. Besides, more robust methods which are not easily influenced by the evolution of nonstationary characteristics should be used. In this article, we first familiarize the readers with the concept of local stationarity as the bridge between stationarity and nonstationarity, and then present both parametric and nonparametric methods for nonstationary process preprocessing. Finally, prediction algorithms based on parametric and nonparametric concepts are introduced.
Formulating GoodMILPModels
Authors: Hooker John N.
Published: February 2011

Writing good models is essential to harnessing MILP solution technology. Due to an underlying theorem that characterizes MILP representability, MILP modeling involves identifying two types of structures in a problem: knapsack constraints and choices between discrete alternatives. This article illustrates the modeling process with a series of examples. They include capital budgeting, freight transport, set packing/covering/partitioning, airline crew rostering, facility location, fixed charges, lot sizing, and package delivery. Piecewise linear modeling, logical conditions, symmetry, special ordered sets, indicator constraints, and semicontinuous variables are also discussed.
Geometric Programming
Authors: Rajgopal Jayant
Published: February 2011

Geometric programming (GP) constitutes a special class of nonlinear optimization problems involving objective and constraint functions that are stated in the form of generalized polynomials. While the field is only about 50 years old, it has been studied extensively. This article reviews the important theoretical and computational aspects of GP and also discusses extensions to the original form that have been developed over the years.
Gomory Cuts
Authors: Fukasawa Ricardo
Published: February 2011

Gomory cuts have played an important role in integer and mixed‐integer programming for over 50 years. This article reviews these much studied cuts, surveying some of the research that has been done over the years as well as looks into new research directions that have appeared in the last few years.
Heuristics in Mixed Integer Programming
Authors: Fischetti Matteo , Lodi Andrea
Published: February 2011

MILP heuristics aim at finding a feasible (and hopefully good) solution of the problem above, which is an NP‐hard problem by itself. We present the main ideas underlying some of the heuristics proposed in the literature. In particular, in this article we focus on those algorithms developed with the aim of being tightly integrated within MILP solvers.
Improving Public Health In Developing Countries Through Operations Research
Authors: Yadav Prashant
Published: February 2011

Across the developing world, thousands of people many of them children die each day from malaria, tuberculosis, HIV/AIDS, and other infectious diseases. Many of these conditions are preventable and treatable through well known public health interventions. Operations research (OR) can be a key tool to allocate the scarce resources to cost‐effective interventions that can alleviate the health status in developing countries. This article provides an introduction to the application of OR to public health problems in developing countries for OR/MS practitioners, advanced undergraduate students in OR/MS and graduate researchers initiating work in this field. It explains commonly used public health metrics such as quality‐adjusted life year (QALY), disability‐adjusted life year (DALY), and Gini coefficient. Simple models to understand disease transmission along with a few illustrative applications of OR to solve public health problems are presented.
Integrated Supply Chain Design Models
Authors: Mak Ho‐Yin , Shen Zuo‐Jun Max
Published: February 2011

Traditional facility location models tend to focus on the trade‐off between some measure of budget, often measured by fixed location costs, and some measure of convenience to customers, usually measured by the distance between customers and the respective nearest facilities. This simple setup, although proven to be effective in many other applications, fails to cover potential effects of tactical and operational issues on the strategic design decisions in supply chain settings. For example, inventory sharing and delivery vehicle consolidation lead to economies of scale in the operations of the facilities and thus affect the optimal distribution network configuration. Recently, researchers began to study integrated supply chain design models that take into account important tactical and operational issues when making strategic decisions on facility location and network design. In this article, we review some recent work that belongs to this new research stream. We discuss various modeling issues and the potential benefits of using integrated models over using traditional location models.
Introduction to Diffusion Processes
Authors: Ghosh Arka P.
Published: February 2011

In this section we describe a class of stochastic processes called the diffusion processes. These are continuous‐time, continuous state‐space processes and their sample paths are continuous everywhere but differentiable nowhere. Since diffusions are defined through stochastic differential equations, we give a brief introduction to stochastic differential equations (which include a discussion on stochastic integration as well). Diffusion processes are defined in terms of these differential equations. Finally we conclude the section with some specific example of diffusion processes.
Dynamic Programming: Introductory Concepts
Authors: Sniedovich Moshe
Published: February 2011

Dynamic programming (DP) is a general purpose problem solving methodology based on problem decomposition. The idea is to decompose a “difficult” problem into a family of “related problems”—which are often, but not always, “easier” subproblems of the “difficult” problem. Its plan of attack is then to embed the “difficult” problem of interest—the target problem—in a family of modified problems, and to use a functional equation to relate the solutions to these modified problems to one another. The solution obtained for this functional equation yields the solution to the modified problems as well as to the target problem. This approach has an extremely wide scope of application, but in operations research, DP is used primarily as a framework for the modeling, analysis, and, solution of optimization problems. The evolution of DP has entrenched the convention that DP treats problems as sequential decision problems. This fact is reflected in the DP terminology, notably in the central roles that the concepts “state” and “state transition” play in the theory. The subtle modeling issues associated with this approach have earned DP its reputation (perhaps notoriety) of being an “art.” Although DP's scope of operation is extremely wide‐ranging, in practice its use is often hampered by the curse of dimensionality. This difficulty has spawned the development of a host of methods and techniques aimed at dealing with the computational aspects of DP. This ongoing effort provides challenges and opportunities, especially in the development of general‐purpose DP software.
Large Deviations in Queueing Systems
Authors: Ganesh Ayalvadi J.
Published: February 2011

Large deviations theory deals with fluctuations of random variables from their mean values on larger scales than the central limit scaling. When applied to queueing systems, it provides an elegant unified framework for estimating the probability distributions of queue sizes and waiting times or, more precisely, their tail decay rates. This article provides a brief introduction to large deviation theory as well as its application to some simple queueing models.
Introduction to Large‐Scale Linear Programming and Applications
Authors: Stoyan Stephen J. , Dessouky Maged M. , Wang Xiaoqing
Published: February 2011

Linear programming (LP) has been used as an effective tool to solve a number of applications in manufacturing, transportation, military, health care, and finance. In a number of these applications, the problem size in terms of the number of variables and constraints can become rather large in order to accurately represent the system. For this reason, a number of specialized procedures such as column generation and cutting‐plane methods have been developed to effectively solve these large‐scale linear programs. In other cases, the problem may have a special structure, where decomposition methods can also be used. This article provides an overview of these specialized solution procedures. We conclude the article with an example of a large‐scale linear program developed to balance routes for street sweepers in Southern California.
Level‐Dependent Quasi‐Birth‐and‐Death Processes
Authors: Kharoufeh Jeffrey P.
Published: February 2011

This article defines and describes the level‐dependent quasi‐birth‐and‐death (LDQBD) process, a generalization of the homogeneous (or level‐independent) quasi‐birth‐and‐death (QBD) process. Like its level‐independent counterpart, the LDQBD process is a bivariate Markov process whose transition probability matrix (or infinitesimal generator matrix) exhibits a block tridiagonal structure. However, unlike the level‐independent QBD, its transitions are explicitly dependent on the level. This article defines discrete‐ and continuous‐time versions of the LDQBD process, discusses necessary and sufficient conditions for positive recurrence, and describes the limiting distribution for each case. Algorithmic approaches, extensions of the basic models, and suggestions for further reading are also provided.
Level‐Independent Quasi‐Birth‐and‐Death Processes
Authors: Latouche Guy
Published: February 2011

The definition and basic properties of quasi‐birth‐and‐death processes are presented, both in continuous and discrete time. The main resolution algorithms are given, and various extensions are discussed.
Lift‐and‐Project Inequalities
Authors: Louveaux Quentin
Published: February 2011

The lift‐and‐project technique is a systematic way to generate valid inequalities for a mixed binary program. The technique is interesting both on the theoretical and on the practical point of view. On the theoretical side it allows one to construct the inequality description of the convex hull of all mixed‐{0, 1} solutions of a binary mixed‐integer program (MIP) innrepeated applications of the technique, wherenis the number of binary variables. On the practical side, a variant of the method allows one to derive some cutting planes from the simplex tableau rather efficiently.
Markov Chains of theM/G/1‐Type
Authors: Bini Dario Andrea , Meini Beatrice
Published: February 2011

This article reports the main properties of M/G/1‐type Markov chains together with the classical and the most advanced algorithms for their analysis.
Markovian Arrival Processes
Authors: Chakravarthy Srinivas R.
Published: February 2011

Marked point processes (MPP's) play an important role in stochastic modeling. A special class of MPP's is the Markovian Arrival Process (MAP). In this section we will review the concepts, including the history of MAP both in continuous time and in discrete time.
Disjunctive Inequalities: Applications And Extensions
Authors: Belotti Pietro , Liberti Leo , Lodi Andrea , Nannicini Giacomo , Tramontani Andrea
Published: February 2011

We survey some applications and extensions of disjunctive programming with special emphasis on recent developments. Specifically, after recalling the basic ingredients of disjunctive inequalities we report on recent results in the context of mixed integer linear programming. We then consider the application of disjunctive constraints both as modeling tool and cutting planes in mixed integer nonlinear programming. Finally, we discuss the application of disjunctions as branching conditions in enumerative algorithms, as opposed to the cutting approach.
Multivariate Input Modeling
Authors: Biller Bahar
Published: February 2011

As large‐scale discrete‐event stochastic simulation becomes a tool that is used routinely for the design and analysis of service and manufacturing systems, it is critical to develop multivariate input models that are flexible enough to capture the joint distributional properties of multivariate input processes. In this document, we review the recent advances in multivariate input modeling with focus on developing fast sampling algorithms for driving large‐scale discrete‐event stochastic simulations.
Nash Equilibrium (Pure and Mixed)
Authors: Jones Michael A.
Published: February 2011

This article defines and examines the Nash equilibrium solution concept for noncooperative strategic form games. Examples of canonical (2 × 2) bimatrix form games are used to demonstrate that a noncooperative strategic form game may have a unique pure or mixed strategy Nash equilibrium (Prisoners' Dilemma and Matching Pennies, respectively), may have both pure and mixed strategy Nash equilibria (Battle of the Sexes), or an infinite number of Nash equilibria. Nash's application of the Kakutani fixed point theorem to prove the existence of equilibria is discussed and applied to specific games. Motivated by the possible multiplicity of Nash equilibria in noncooperative strategic form games, the number of equilibria, the construction of games with a unique, prespecified equilibrium, and the calculation of equilibria are considered. The article concludes with a short description of the attempts to refine the Nash equilibrium concept, including perfect and proper equilibria, as well as evolutionary stability.
Network Reliability Performance Metrics
Authors: Antonio Salvatore D.
Published: February 2011

The need to define and use network reliability performance metrics arises from the need to compare different measurement results and to measure network behaviour with a reproducible, unambiguous methodology which is independent from transmission technology and implementation aspects. This introductory article aims at presenting the most important network performance and reliability metrics, and methods for measuring them as defined by the standardization bodies such as the IETF (Internet Engineering Task Force) and ITU‐T.
Newsvendor Models
Authors: Petruzzi Nicholas C. , Dada Maqbool
Published: February 2011

The newsvendor model has a rich and expansive history in operations research and management science. In its essential formulation, the newsvendor model characterizes the following optimization problem: a firm facing random demand for a product that becomes obsolete at the end of a single period must decide how many units of the product to stock in order to maximize expected profit for the period. The celebrated solution to this problem prescribes a supply quantity that equates the expected cost of overstocking to the expected (opportunity) cost of understocking. This classic model, with its intuitively appealing optimal solution, serves as the launch pad for such vast and important literature as stochastic inventory theory, supply chain coordination, and the operations/marketing interface.
N
ewton‐Type Methods
Authors: Murray Walter
Published: February 2011

Newton's method is one of the most famous numerical methods. Its origins, as the name suggests, lies in part with Newton, but the form familiar to us today is due to Simpson of “Simpson's Rule” fame. Originally proposed to find the roots of polynomials it was Simpson who proposed using it for general nonlinear equations and for its use in optimization by finding a root of the gradient. Here, we discuss Newton's method for both of these problems with the focus on the somewhat harder optimization problem. A disadvantage of Newton's method, in its original form, is that it has only local convergence unless the class of functions is severely restricted. Much of the discussion here will be about the many ways in which Newton's method may be modified to achieve global convergence. A key aim of all these methods is that once the iterates come sufficiently close to a solution, the method takes Newton steps.
Nonstationary Input Processes
Authors: Kuhl Michael E.
Published: February 2011

Nonstationary input processes are utilized in simulation to model time‐varying patterns of events. The focus of this article is on modeling and simulating nonstationary arrival processes. In particular, we discuss nonparametric, parametric, and semiparmetric methods for modeling and simulating nonhomogeneous Poisson processes. In addition, we present methods for modeling and simulating nonstationary non‐Poisson arrival processes.
Nurse Scheduling Models
Authors: Bard Jonathan F.
Published: February 2011

The continued interest in nurse scheduling is fueled by both, academic and economic concerns. Most of the issues surrounding the construction of midterm or monthly schedules are present throughout the service industry, so models and methods developed for managing nurses readily carry over to other areas. From a practical point of view, the cost of the nursing staff represents over 50% of the cost of running a health‐care facility so improved scheduling can have a measurable impact on profitability. The goal of this article is to review the parameters that planners must consider when formulating schedules to meet daily staffing requirements in the face of labor agreements, skill requirements, hospital policies, and changing governmental regulations. At the midterm level, models must take into account individual preferences, seniority, the distribution of gaps in coverage, and skill substitution. On a daily basis, critical resources must be tracked and schedules updated to meet changes in demand. Short‐term issues come into play just prior to the beginning of each shift where last‐minute call outs, emergencies, and other unanticipated disruptions imply a need for online control. To find solutions to these problems, various analytic methods have been proposed but few have actually found their way into practice. The article concentrates on the more effective techniques with an eye toward implementation.
Operational Research Society of Turkey
Authors: Bilgiç Taner , Güllü Refik
Published: February 2011

We briefly give an account of how ORST was founded and its impact on the education and practice of operational research in Turkey.
Managing Corporate Mobile Voice Expenses: Plan Choice, Pooling Optimization, and Chargeback
Authors: Chiu Samuel S.
Published: February 2011

Mobility communication management spans the spectrum of user choice, device procurement/inventory/replacement, IT security, corporate policy compliance, expense optimization, and billing. Today, there are many vendors providing a subset or a full spectrum of such mobility communication management services to corporate customers, a service collectively (perhaps not quite accurately) known as TEM, telecom expense management. The focus of this article is on mobile voice expense optimization. A mobile voice subscription plan can generally be characterized by three parameters: a monthly fixed charge, a peak minute allowance, and an overage rate when usage exceeds a plan's minute allowance. An (stand‐alone) individual user has to decide which plan to choose: too large a base plan will result in unused wasted minutes, while too small a plan will incur expensive overage charges. Similar to family plans, a corporation has different pooling options. A pooling plan allows subscribers in the same pool to share a common pool of minutes. An overage results when the collective usage exceeds the common pool of minutes. We examine the mathematics behind pooling and how to create the best pooling arrangement minimizing mobile voice expenses. The contribution of this paper first lies in the formulation of the problem, making it tractable. This formulation allows an efficient and effective solution to such a complex combinatory pooling optimization problem, using a column generation technique. We provide case studies to illustrate the potential (and actual savings) for the stand‐alone plan choice decision as well as the collective pooling optimization; typically resulting in 20–30% of annual savings, which translate into tens of millions of dollars for large corporations. A very important, often a stumbling block to implement a pooling solution, aspect of pooling is
chargeback
—how to allocate monthly pooled expenses to individual accounts (which often belong to different units in an organization). We share with you a simple and equitable chargeback scheme, which is well received and readily implemented by corporate clients. An actual case study will be presented as well as some concluding remarks.
Option Pricing: Theory and Numerical Methods
Authors: Babich Volodymyr , Kamrad Bardia
Published: February 2011

The goal of this article is to introduce readers to the fundamental ideas underlying theory and practice of financial derivatives pricing. We begin by defining financial derivatives. Our discussion is focused on stock options, although the same ideas apply to other derivatives. We present commonly used models for the evolution of stock prices: binomial and trinomial trees; and geometric Brownian motion. We discuss shortcomings of these models and suggest alternatives. Using the binomial model for the stock price evolution, we illustrate the main idea of asset pricing theory—no‐arbitrage pricing—and derive the price of a stock option. This formula creates an opportunity to discuss another important idea in asset pricing—risk‐neutral valuation. We introduce the Black–Scholes and Merton model and present the celebrated Black–Scholes and Merton PDE and option pricing formulas. Although some derivatives afford closed form expressions (e.g., Black–Scholes and Merton formulas) for their prices, the vast majority of derivatives must be priced numerically. We discuss advantages and disadvantages of three main numerical methods: lattice models, Monte Carlo simulation, and finite difference methods. The article is concluded with a brief overview the literature that will help readers to continue learning about this fascinating topic.
OR

Models in Freight Railroad Industry
Authors: Nemani Ashish K. , Ahuja Ravindra K.
Published: February 2011

The transportation sector, especially the rail mode, is a very rich source of optimization problems and has been a primary focus of operations researchers. A plethora of articles dedicated to each transportation mode (rail, road, air, and water) can be found in the literature. Ironically, the industries are still using rules of thumb instead of mathematical models for most of the planning and scheduling processes. There are two main reasons for
not
using the operations research (OR) models: (i) the highly complex nature of the problems, and (ii) the huge gap between the academic (theoretical) and industrial (practical) approaches. With the steep growth in computational capabilities, we have started developing innovative algorithms by shifting the focus from finding
optimal‐but‐impractical
solutions to finding
good‐and‐implementable
solutions. We are developing state‐of‐the‐art ideas combining exact approaches such as network flows and mixed integer programming, with heuristics and meta‐heuristics such as the tabu search and the very large‐scale neighborhood (VLSN) search. In this article, we provide an overview of the railroad planning and scheduling problems at the strategic, tactical, and operational levels. We describe the best algorithms successfully implemented at US railroads, which have the potential of saving hundreds of millions of dollars annually.
Foundations of Constrained Optimization
Authors: Leyffer Sven , Mahajan Ashutosh
Published: February 2011

This article presents the foundations of nonlinearly constrained optimization, or nonlinear programming. We emphasize general methods and highlight their key components, such as the approximate subproblem and global convergence mechanism. We summarize convergence results.
Single‐Dimensional Search Methods
Authors: Chong Edwin K. P. , Żak Stanislaw H.
Published: February 2011

This article considers the problem of minimizing a real‐valued function defined on the real line (i.e., a single‐dimensional problem). This function is referred to as the
objective function
. The approach is to use an iterative search algorithm, also called a line‐search method. Single‐dimensional search methods are of interest for the following reasons. First, they are special cases of search methods used in multivariable problems. Second, they are used as part of general multivariable algorithms. An iterative algorithm starts with an initial candidate solution and generate a sequence of
iterates
. The iterative algorithm may use only values of the objective function, or perhaps also its first derivative and even its second derivative. This article presents several algorithms: the golden section and Fibonacci methods (which use only objective function values), the bisection and secant methods (which use only derivative values), and Newton's method (which uses both first and second derivatives).
Parallel Configurations
Authors: Agustin Marcus
Published: February 2011

This article will consider the reliability of a system in parallel. The focal point is to establish the system reliability of a parallel system for the case when component lifetime is a random variable that follows some distribution.
Parametric
LP
Analysis
Authors: Holder Allen
Published: February 2011

Parametric linear programming is the study of how optimal properties depend on data parametrizations. The study is nearly as old as the field of linear programming itself, and it highlights how a problem depends on its data. We present a modern perspective on the classical analysis of the objective value's response to parametrizations in the right‐hand side and/or the cost vector. We also mention a few applications and provide citations for further study.
Partially ObservableMDPs(POMDPS): Introduction and Examples
Authors: Yaylali Emine , Ivy Julie S.
Published: February 2011

A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process where the states of the model are not completely observable by the decision maker. Noisy observations provide a belief regarding the underlying state, while the decision maker has some control over the progression of the model through the selection of actions. In this article, we introduce POMDPs and discuss the relationship between Markov models and POMDPs. A general POMDP formulation and a wide range of POMDP applications from the literature are also presented.
Progressive Adaptive User Selection Environment (PAUSE) Auction Procedure
Authors: Steinberg Richard
Published: February 2011

PAUSE is a combinatorial auction procedure that permits all combinatorial bids, is computationally manageable for the auctioneer, and is transparent to the bidders. Further, it mitigates the threshold problem and can allow for multiple winners.
Perfect Bayesian Equilibrium and Sequential Equilibrium
Authors: Okada Akira
Published: February 2011

Two equilibrium concepts for an extensive‐form game are reviewed: a (weak) perfect Bayesian equilibrium and a sequential equilibrium. These equilibrium concepts are defined in terms of a pair comprising a behavioral strategy profile and a system of beliefs so that they satisfy sequential rationality and consistency. A (weak) perfect Bayesian equilibrium requires a weak consistency that the Bayes rule should be applied whenever possible. A sequential equilibrium requires a stronger consistency that uses the trembling‐hand approach for a perfect equilibrium.
Mathematical Models for Perishable Inventory Control
Authors: Nahmias Steven
Published: February 2011

This article is intended to provide the reader with the fundamentals underlying the theory of managing perishable inventories. The emphasis is on the mathematical models for perishable inventory control, rather than on the application of these models. Perishable inventories constitute a huge portion of the world economy. These include virtually all foodstuffs and pharmaceuticals and many others. If we view obsolescence as a type of perishability, then most electronic items would be included in this list as well. We hope this article provides the reader with a basic understanding of the issues and mathematics underlying these models, and the tools to pursue further reading on his or her own.
Poisson Process and its Generalizations
Authors: Ramaswami Vaidyanathan
Published: February 2011

This article provides an overview of the Poisson process and many of its widely used generalizations.
Polynomial Time Primal Integer Programming via Graver Bases
Authors: Onn Shmuel
Published: February 2011

We describe recent developments in primal methods for integer programming which lead to the polynomial time solution of new broad classes of integer programming problems with linear and various nonlinear objective functions.
Probability Weighting Functions
Authors: Al‐Nowaihi Ali , Dhami Sanjit
Published: February 2011

Expected utility (EU) theory is unable to accommodate the observed nonlinear weighting of probabilities. We outline three stylized facts on nonlinear weighting that a theory of risk must ideally address. These are that people overweight small probabilities and underweight large ones (S1), do not choose stochastically dominated options when such dominance is obvious (S2), and ignore very small probabilities and code extremely large probabilities as one (S3). We then show that the concept of a probability weighting function (PWF) is crucial in addressing S1–S3. A PWF is not, however, in itself, a theory of risk. PWFs need to be embedded within some theory of risk in order to have significant predictive content. The two main alternative theories that are relevant in this regard arerank‐dependent utility(RDU) andcumulative prospect (CP) theory. RDU and CP explain S1, S2 but not S3. We outline the recent proposal of al‐Nowaihi and Dhami forcomposite prospect (CPP) theorythat uses thecomposite Prelec probability weighting function(CPF). CPF is axiomatically founded, is flexible, and, is parsimonious. CPP can explain all three stylized facts S1, S2, and S3.
Push and Pull Production Systems
Authors: Benton W.C.
Published: February 2011

The terms push and pull are used to describe alternative systems for executing the production process in manufacturing organizations. A “push” system is based on forecasted demand that is completed and sent to the next work station or in the case of the final work station is pushed to finished goods inventory. On the other hand, in a “pull” system, the movement of work is based on the requirements of the following work station. Each succeeding workstation pulls (demands) output from the previous workstation as needed. The next work station determines when and how much output is requested. The output from the final workstation is pulled by customer demand or the master production schedule.

The choice between the push and pull systems is based on firm's production–inventory relationship. Firms that have highly repetitive production processes and well‐defined work flows of standardized items require the pull system based on the need for tighter control of inventory and output at the work stations. On the other hand, production processes with long lead times, accurate demand forecasts, a large number of products produced on common production processes, and a diverse customer base tend to use the push systems.
Quantum Game Theory
Authors: Landsburg Steven E.
Published: February 2011

Quantum game theory is the study of strategic behavior by agents with access to quantum technology. This technology can be employed either as part of a randomization device or as part of a communication device. We survey models of each sort, emphasizing analogies with classical game theory and classical notions of equilibrium.
Quasi‐Newton Methods
Authors: Yuan Ya‐Xiang
Published: February 2011

Quasi‐Newton methods are a class of important methods for solving unconstrained optimization and for solving nonlinear equations. In this article, a review on quasi‐Newton methods for unconstrained optimization is given. Well‐known quasi‐Newton update formulae are given and theoretical properties of the updates are presented. Convergence results and open questions about quasi‐Newton methods are also given.
Queueing Disciplines
Authors: Harchol‐Balter Mor
Published: February 2011

This article introduces queueing disciplines, also known asscheduling policies, and describes their effect on the performance of computer systems, call centers, and other systems where queueing is involved.
Regenerative Processes
Authors: Vlasiou Maria
Published: February 2011

We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d. cycles. Although we focus on the classical definition, we present a more general definition that allows for some form of dependence between two adjacent cycles, and mention two further extensions of the second definition. We mention the connection of regenerative processes to the single‐server queue, to multiserver queues, and more generally to Harris ergodic Markov chains and processes. In the main theorem, we pay some attention to the conditions under which a limiting distribution exists and provide references that should serve as a starting point for the interested reader.
Rendezvous Search Games
Authors: Alpern Steve
Published: February 2011

Rendezvous search studies the problem faced by a number of people (or animals or robots) who are trying to find each other after becoming separated (perhaps by a storm) or on reaching a large meeting area independently. Formally, it is a common‐interest game where two (or more) unit speed players seek to minimize the time taken to meet. The game begins with a known (sometimes, an unknown) joint distribution of the players in a known search regionQ, which is dark (so the players cannot see each other until they are sufficiently close). Although originally proposed by the author in 1976, these problems did not receive much attention until the 1990s. However, much progress has been made in the last 20 years. These games can be viewed as search game extensions of the spatial coordination problems posed by Schelling in 1960. But where Schelling was concerned with “focal points,” the rendezvous theory typically avoids these by assuming symmetrical search regions.
Renewal Function and Renewal‐Type Equations
Authors: Liu Liqiang
Published: February 2011

Renewal functions, renewal arguments, and renewal‐type equations play important roles in renewal theory. This article introduces main conceptual knowledge on these topics.
Renewal Processes With Costs and Rewards
Authors: Vlasiou Maria
Published: February 2011

We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the Elementary Renewal Theorem and avoids the technicalities in the proof that is presented in most textbooks. Moreover, we mention briefly the extension of the theory to partial rewards, where it is assumed that rewards are accrued not only at renewal epochs but also during the renewal cycle. For this case, we present a counterexample which indicates that the standard conditions for the renewal reward theorem are not sufficient; additional regularity assumptions are necessary. We present a few examples to indicate the usefulness of this theory, where we prove the inspection paradox and Little's law through the renewal reward theorem.
Repairable Systems: Renewal and NonRenewal
Authors: Rigdon Steven E.
Published: February 2011

Repairable systems are systems that can be restored to an operating condition by some repair operation. Models for repairable system are inherently different from models for nonrepairable systems. For nonrepairable systems, it is reasonable to assume that the lifetimes are independent and identically distributed. Models for the reliability of repairable systems must account for the occurrence of events in time. Often, these event times or interevent times are not independent and not identically distributed. This article presents models for repairable systems that account for these factors.
Risk Averse Models
Authors: Shapiro Alexander
Published: February 2011

This article deals with risk averse stochastic optimization. Various approaches to controlling the risk are discussed in the framework of the portfolio selection problem. An axiomatic approach to constructing coherent risk measures is outlined and it is shown how it can be applied to two‐stage stochastic programming problems. Finally, possible extensions to risk averse multistage stochastic programming are mentioned.
Robust External Risk Measures
Authors: Kou Steven , Peng Xianhua , Heyde Christopher C.
Published: February 2011

Choosing a proper external risk measure is of great regulatory importance, as exemplified in the Basel II Accord and its recent revision, which use Value‐at‐Risk (VaR) with scenario analysis as the external risk measure for setting capital requirement. The main motivation of this article is to investigate how to choose a good external risk measure. While many risk measures may be suitable for internal risk management, we argue that risk measures used for external regulation should have robustness with respect to model misspecification (e.g., by incorporating scenario analysis) and small changes in the data (e.g., by using robust statistics). We propose new data‐based risk measures called natural risk statistics that are characterized by a new set of axioms based on comonotonicity from decision theory. Natural risk statistics include VaR with scenario analysis, in particular Basel II risk measures, as special cases; therefore, we provide a theoretical framework to understand and extend the Basel II accord, if needed.
Saddlepoints and
von
N
eumann Minimax Theorem
Authors: Hezarkhani Behzad
Published: February 2011

This section introduces the basic properties of two‐person zero‐sum (TPZS) games and presents their general solution concepts.
Stochastic Gradient Methods For Simulation Optimization
Authors: Fu Michael C.
Published: February 2011

This article presents an overview of the two most well‐known techniques for estimating gradients from stochastic simulation: perturbation analysis and the likelihood ratio (or score function) method. The primary motivation is to derive efficient estimators for use in simulation optimization algorithms. Simple examples are used to illustrate the approaches, practical guidelines are provided for implementation, and applications in queueing, inventory, and finance are discussed.
Sampling Methods
Authors: Shapiro Alexander
Published: February 2011

This article deals with Monte Carlo sampling–based approaches to solving two‐stage stochastic programming and chance‐constrained problems. Sample size estimates, required to solve a considered problem with a given accuracy, are discussed from theoretical and practical points of view. Difficulties with extending these techniques to multistage programming are pointed out.
Scenario Generation
Authors: Römisch Werner
Published: February 2011

Stability‐based methods for scenario generation in stochastic programming are reviewed. In particular, we briefly discuss Monte Carlo sampling, Quasi–Monte Carlo methods, quadrature rules based on sparse grids, and optimal quantization. In addition, we provide some convergence results based on recent developments in multivariate integration. The method of optimal scenario reduction and techniques for scenario trees generation are also reviewed.
Semi‐
M
arkov Processes
Authors: Serin Yasemin
Published: February 2011

A semi‐Markov process is a generalization of continuous‐time Markov chain, so that the sojourn times come from general distributions. In this article, after some basic definitions, some results related to the transient and limiting properties of the semi‐Markov processes are given. Some results are demonstrated with examples.
Sensitivity Analysis and Dynamic Programming
Authors: Tan Chin Hon , Hartman Joseph C.
Published: February 2011

The validity of any dynamic programming solution depends on the accuracy of the model and the data for a given instance. However, the parameters of the model are often uncertain and estimated in practice. In this paper, we discuss various concepts of sensitivity analysis and survey the work on sensitivity analysis in the dynamic programming literature. In addition, we highlight the relationship between dynamic programming and linear programming and how the approaches and results from the latter can be applied to dynamic programs. A list of promising areas of future research is provided.
Sensitivity Analysis in Linear Programming
Authors: Filippi Carlo
Published: February 2011

Sensitivity analysis in linear programming studies the stability of optimal solutions and the optimal objective value with respect to perturbations in the input data. This analysis is often relevant in practical applications. We discuss the main approaches to sensitivity analysis, including ordinary sensitivity, the 100% rule, and the tolerance approach, giving special attention to degeneracy issues. We focus on the effects of perturbations in the right‐hand side and objective vectors.
Series Systems
Authors: Park Minjae , Pham Hoang
Published: February 2011

This paper presents a cost analysis of series systems based on the altered quasi‐renewal process with random parameter and a mixed quasi‐renewal process considering replacements and repairs. A numerical example is discussed to demonstrate the applicability of the proposed cost models.
The Shapley Value and Related Solution Concepts
Authors: Vlach Milan
Published: February 2011

The Shapley value not only belongs to the most important solution concepts of cooperative game theory but it is also an easily tractable mathematical object with a remarkably wide range of applications. After necessary preliminaries, we introduce basic properties and characterizations of the Shapley value for cooperative games with transferable utility. Then we deal with some of its extensions appearing frequently in the literature. In particular, we present the Aumann–Drèze and Owen generalizations to games with a coalition structure, and the Myerson extension to games with a graph structure. We conclude with the probabilistic values and a brief discussion of application to cost allocation problems.