On Certain Greedoid Polyhedra, Partially Indexable Scheduling Problems, and Extended Restless Bandit Allocation Indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid (whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then the problem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Materials and Mix Optimization Procedures for PCC Pavements, March 2006

Severe environmental conditions, coupled with the routine use of deicing chemicals and increasing traffic volume, tend to place extreme demands on portland cement concrete (PCC) pavements. In most instances, engineers have been able to specify and build PCC pavements that met these challenges. However, there have also been reports of premature deterioration that could not be specifically attributed to a single cause. Modern concrete mixtures have evolved to become very complex chemical systems. The complexity can be attributed to both the number of ingredients used in any given mixture and the various types and sources of the ingredients supplied to any given project. Local environmental conditions can also influence the outcome of paving projects. This research project investigated important variables that impact the homogeneity and rheology of concrete mixtures. The project consisted of a field study and a laboratory study. The field study collected information from six different projects in Iowa. The information that was collected during the field study documented cementitious material properties, plastic concrete properties, and hardened concrete properties. The laboratory study was used to develop baseline mixture variability information for the field study. It also investigated plastic concrete properties using various new devices to evaluate rheology and mixing efficiency. In addition, the lab study evaluated a strategy for the optimization of mortar and concrete mixtures containing supplementary cementitious materials. The results of the field studies indicated that the quality management concrete (QMC) mixtures being placed in the state generally exhibited good uniformity and good to excellent workability. Hardened concrete properties (compressive strength and hardened air content) were also satisfactory. The uniformity of the raw cementitious materials that were used on the projects could not be monitored as closely as was desired by the investigators; however, the information that was gathered indicated that the bulk chemical composition of most materials streams was reasonably uniform. Specific minerals phases in the cementitious materials were less uniform than the bulk chemical composition. The results of the laboratory study indicated that ternary mixtures show significant promise for improving the performance of concrete mixtures. The lab study also verified the results from prior projects that have indicated that bassanite is typically the major sulfate phase that is present in Iowa cements. This causes the cements to exhibit premature stiffening problems (false set) in laboratory testing. Fly ash helps to reduce the impact of premature stiffening because it behaves like a low-range water reducer in most instances. The premature stiffening problem can also be alleviated by increasing the water–cement ratio of the mixture and providing a remix cycle for the mixture.

Importância da Programação Linear na Determinação de Informações de Gestão - Caso Moave, Sa

A Investigação Operacional vem demonstrando ser uma valiosa ferramenta de gestão nos dias de hoje em que se vive num mercado cada vez mais competitivo. Através da Programação Linear pode-se reproduzir matematicamente um problema de maximização dos resultados ou minimização dos custos de produção com o propósito de auxiliar os gestores na tomada de decisão. A Programação Linear é um método matemático em que a função objectivo e as restrições assumem características lineares, com diversas aplicações no controlo de gestão, envolvendo normalmente problemas de utilização dos recursos disponíveis sujeitos a limitações impostas pelo processo produtivo ou pelo mercado. O objectivo geral deste trabalho é o de propor um modelo de Programação Linear para a programação ou produção e alocação de recursos necessários. Optimizar uma quantidade física designada função objectivo, tendo em conta um conjunto de condicionalismos endógenas às actividades em gestão. O objectivo crucial é dispor um modelo de apoio à gestão contribuindo assim para afectação eficiente de recursos escassos à disposição da unidade económica. Com o trabalho desenvolvido ficou patente a importância da abordagem quantitativa como recurso imprescindível de apoio ao processo de decisão. The operational research has proven to be a valuable management tool today we live in an increasingly competitive market. Through Linear Programming can be mathematically reproduce a problem of maximizing performance or minimizing production costs in order to assist managers in decision making. The Linear Programming is a mathematical method in which the objective function and constraints are linear features, with several applications in the control of management, usually involving problems of resource use are available subject to limitations imposed by the production process or the market. The overall objective of this work is to propose a Linear Programming model for scheduling or production and allocation of necessary resources. Optimizing a physical quantity called the objective function, given a set of endogenous constraints on management thus contributing to efficient allocation of scarce resources available to the economic unit. With the work has demonstrated the importance of the quantitative approach as essential resource to support the decision process.

Determinants of linear judgment: A meta-analysis of lens model studies

The mathematical representation of Brunswik s lens model has been usedextensively to study human judgment and provides a unique opportunity to conduct ameta-analysis of studies that covers roughly five decades. Specifically, we analyzestatistics of the lens model equation (Tucker, 1964) associated with 259 different taskenvironments obtained from 78 papers. In short, we find on average fairly high levelsof judgmental achievement and note that people can achieve similar levels of cognitiveperformance in both noisy and predictable environments. Although overall performancevaries little between laboratory and field studies, both differ in terms of components ofperformance and types of environments (numbers of cues and redundancy). An analysisof learning studies reveals that the most effective form of feedback is information aboutthe task. We also analyze empirically when bootstrapping is more likely to occur. Weconclude by indicating shortcomings of the kinds of studies conducted to date, limitationsin the lens model methodology, and possibilities for future research.

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

A tractable consideration set structure for network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing from an offerset, have recently become popular in assortment optimization and revenue management. The dynamicprogram for these models is intractable and approximated by a deterministic linear program called theCDLP which has an exponential number of columns. When there are products that are being consideredfor purchase by more than one customer segment, CDLP is difficult to solve since column generationis known to be NP-hard. However, recent research indicates that a formulation based on segments withcuts imposing consistency (SDCP+) is tractable and approximates the CDLP value very closely. In thispaper we investigate the structure of the consideration sets that make the two formulations exactly equal.We show that if the segment consideration sets follow a tree structure, CDLP = SDCP+. We give acounterexample to show that cycles can induce a gap between the CDLP and the SDCP+ relaxation.We derive two classes of valid inequalities called flow and synchronization inequalities to further improve(SDCP+), based on cycles in the consideration set structure. We give a numeric study showing theperformance of these cycle-based cuts.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Fate of linear and supercoiled multinucleosomic templates during transcription.

Electron microscopy was used to monitor the fate of reconstituted nucleosome cores during in vitro transcription of long linear and supercoiled multinucleosomic templates by the prokaryotic T7 RNA polymerase and the eukaryotic RNA polymerase II. Transcription by T7 RNA polymerase disrupted the nucleosomal configuration in the transcribed region, while nucleosomes were preserved upstream of the transcription initiation site and in front of the polymerase. Nucleosome disruption was independent of the topology of the template, linear or supercoiled, and of the presence or absence of nucleosome positioning sequences in the transcribed region. In contrast, the nucleosomal configuration was preserved during transcription from the vitellogenin B1 promoter with RNA polymerase II in a rat liver total nuclear extract. However, the persistence of nucleosomes on the template was not RNA polymerase II-specific, but was dependent on another activity present in the nuclear extract. This was demonstrated by addition of the extract to the T7 RNA polymerase transcription reaction, which resulted in retention of the nucleosomal configuration. This nuclear activity, also found in HeLa cell nuclei, is heat sensitive and could not be substituted by nucleoplasmin, chromatin assembly factor (CAF-I) or a combination thereof. Altogether, these results identify a novel nuclear activity, called herein transcription-dependent chromatin stabilizing activity I or TCSA-I, which may be involved in a nucleosome transfer mechanism during transcription.