Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

The return of the wage Phillips curve

The standard New Keynesian model with staggered wage settingis shown to imply a simple dynamic relation between wage inflationand unemployment. Under some assumptions, that relation takes aform similar to that found in empirical wage equations-starting fromPhillips' (1958) original work-and may thus be viewed as providingsome theoretical foundations to the latter. The structural wage equation derived here is shown to account reasonably well for the comovement of wage inflation and the unemployment rate in the U.S. economy, even under the strong assumption of a constant natural rate ofunemployment.

Social security, retirement, and the single-mindedness of the electorate

We propose a positive theory that is consistent with two important featuresof social security programs around the world: (1) they redistributeincome from young to old and (2) they induce retirement. We construct avoting model that includes a political campaign or debate prior to theelection. The model incorporates single-mindedness of the groups that donot work: while the workers divide their political capital between their age concerns and occupational concerns , the retired concentrate alltheir political capital to support their age group. In our model, theelderly end up getting transfers from the government (paid by the young)and distortionary labor income taxes induce the retirement of the elderly.In addition, our model predicts that occupational groups that work morewill tend to have more political power. The opposite is true fornon-occupational groups (such as the elderly). We provide some evidencethat supports these additional predictions.

Monetary unions and the transaction cost savings of a single currency

This paper studies the transaction cost savings of moving froma multi-currency exchange system to a single currency one. Theanalysis concentrates exclusively on the transaction andprecautionary demand for money and abstracts from any othermotives to hold currency. A continuous-time, stochastic Baumol-like model similar to that in Frenkel and Jovanovic (1980) isgeneralized to include several currencies and calibrated to fitEuropean data. The analysis implies an upper bound for thesavings associated with reductions of transaction costs derivedfrom the European Monetary Union of approximately 0.6\% of theCommunity GDP. Additionally, the magnitudes of the brokeragefee and the volatility of transactions, whose estimation hastraditionally been difficult to address empirically, areapproximated for Europe.

The gain-loss asymmetry and single-self preferences

Kahneman and Tversky asserted a fundamental asymmetry between gains and losses, namely a reflection effect which occurs when an individual prefers a sure gain of $ pz to anuncertain gain of $ z with probability p, while preferring an uncertain loss of $z with probability p to a certain loss of $ pz.We focus on this class of choices (actuarially fair), and explore the extent to which thereflection effect, understood as occurring at a range of wealth levels, is compatible with single-self preferences.We decompose the reflection effect into two components, a probability switch effect,which is compatible with single-self preferences, and a translation effect, which is not. To argue the first point, we analyze two classes of single-self, nonexpected utility preferences, which we label homothetic and weakly homothetic. In both cases, we characterize the switch effect as well as the dependence of risk attitudes on wealth.We also discuss two types of utility functions of a form reminiscent of expected utility but with distorted probabilities. Type I always distorts the probability of the worst outcome downwards, yielding attraction to small risks for all probabilities. Type II distorts low probabilities upwards, and high probabilities downwards, implying risk aversion when the probability of the worst outcome is low. By combining homothetic or weak homothetic preferences with Type I or Type II distortion functions, we present four explicit examples: All four display a switch effect and, hence, a form of reflection effect consistent a single self preferences.

Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case

We address the performance optimization problem in a single-stationmulticlass queueing network with changeover times by means of theachievable region approach. This approach seeks to obtainperformance bounds and scheduling policies from the solution of amathematical program over a relaxation of the system's performanceregion. Relaxed formulations (including linear, convex, nonconvexand positive semidefinite constraints) of this region are developedby formulating equilibrium relations satisfied by the system, withthe help of Palm calculus. Our contributions include: (1) newconstraints formulating equilibrium relations on server dynamics;(2) a flow conservation interpretation of the constraintspreviously derived by the potential function method; (3) newpositive semidefinite constraints; (4) new work decomposition lawsfor single-station multiclass queueing networks, which yield newconvex constraints; (5) a unified buffer occupancy method ofperformance analysis obtained from the constraints; (6) heuristicscheduling policies from the solution of the relaxations.

Portfolio choice beyond the traditional approach

This paper surveys asset allocation methods that extend the traditional approach. An important feature of the the traditional approach is that measures the risk and return tradeoff in terms of mean and variance of final wealth. However, there are also other important features that are not always made explicit in terms of investor s wealth, information, and horizon: The investor makes a single portfolio choice based only on the mean and variance of her final financial wealth and she knows the relevant parameters in that computation. First, the paper describes traditional portfolio choice based on four basic assumptions, while the rest of the sections extend those assumptions. Each section will describe the corresponding equilibrium implications in terms of portfolio advice and asset pricing.

The determinants of the prevalence of single mothers: A cross-country analysis

This paper examines the effect of public assistance, labor market and marriage marketconditions on the prevalence of single mother families across countries and over time. Amultinomial logit derived from a random utility approach is estimated using individualleveldata for 14 countries. I find evidence that increases in the level of public support are significantly and positively associated with a higher incidence of both never marriedand divorced mothers. The results also suggest that single mothers are more prevalentwhen female wages are lower. Higher male earnings and employment opportunities in awoman s marriage market appear to lead to fewer never married mothers, but more divorced mothers. Higher child support or alimony payments are associated with a higher prevalence of divorced mothers.

Single mothers and incentives to work: The French experience

This paper analyzes the effect of the 1998 reform of the French single parents allowanceon the labor supply of single mothers with very young children. The reform aimed atencouraging participation by allowing eligible single parents to accumulate benefits andlabor earnings for a limited period of time. Using data from the French EmploymentSurvey, the analysis shows that single mothers affected by the reform had experienced asignificant increase in their employment rate four years after the reform wasimplemented. During the same period, the employment rate of married mothers withyoung children did not experience a significant change, suggesting that at least part ofthe increase was a consequence of the reform. These results provide some evidence thatbenefit schedules that provide financial incentives to work can have significant effectsin getting single moms back to work, even in the presence of very young children.

Life-time redistribution effects of the Spanish public pension system

The paper analyses the inter and intragenerational redistribution effects ofthe public pensions system in Spain. This is achieved by first comparing the expected present value of life-time income transfers (PVT) and internalrates of return (IRR) of different population cohorts. Secondly, we study the intragenerational aspects of the Spanish public pensions by calculating PVTs the IRRs for workers of different categories, grouped by earnings, gender and marital status.The results obtained show the nature of the important intergenerational effects of the Social Security System in Spain. The oldest 1935 cohort clearlybenefits in relation to the youngest 1965 cohort. This is basically due to thegap between current wages and the contribution bases established in the 60s and 70s in Spain during the early stages of the Social Security System, and to the worsening shortfall in Social Security funding, combined with the longer of life expectancy.In addition, intragenerational effects exist by income levels. For contributors who pay between the minimum and the maximum allowable contribution bases, net transfers and rates of return are higher in actuarial terms for high incomecontributors. The social security `dealï is again more profitable for highincome individuals since they contribute at the maximum basis, with respect tolow income contributors at the minimum basis. This is due to the late entry and a higher survival rate for high income contributors.The system tends to favour women, given that they generally live longer than men and this factor is only partially offset by their lower wages. Married males, given the fact that they have longer life expectancy and leave a pension to their spouse, obtain higher present net transfers too than do single contributors.We close the paper with some comments on the slight impact and moderate effects of proposals for Social Security reform and on how these may change the previously observed redistribution effects.

New findings regarding return autocorrelation anomalies and the importance of non-trading periods

In this paper, differences in return autocorrelation across weekdays havebeen investigated. Our research provides strong evidence of the importanceon non-trading periods, not only weekends and holidays but also overnightclosings, to explain return autocorrelation anomalies. While stock returnsare highly autocorrelated, specially on Mondays, when daily returns arecomputed on a open-to-close basis, they do not exhibit any significantlevel of autocorrelation. Our results are compatible with theinformation processing hypotheses as an explanation of the weekendeffect.

Earth's Changing Land

Entre el 14 i el 18 de març de 1998 es va celebrar a Barcelona la conferència Earth’s Changing Land sota la tutela dels programes internacionals Global Change in Terrestrial Ecosystems (GCTE) i Land Use and Land Cover Change (LUCC). L’objectiu principal de la trobada era presentar les darreres aportacions científiques sobre els efectes presents i previsibles del canvi global sobre els ecosistemes terrestres i la societat. Al mateix temps, es volia afavorir l’establiment de ponts de diàleg entre els professionals implicats en el canvi global

Morfogènesi de pilars de terra (earth Pillars, hoodoos). Exemples de la Riera de Gaià (Vallès Occidental, Barcelona) i del Bernal de Yátor (Las Alpujarras, Granada)

The origin and the primary features of the erosive earth pillar-like formations that develop in the Riera de Gaià (Barcelona) and in the Bernal de Yátor (Granada) are described. They are dynamic formations typical of areas subjected to strong water erosion

Aprovechamiento educativo y turístico de formas erosivas tipo pilares de tierra (earth pillars, hoodoos) : ejemplos de la riera de Gaià (Vallès occidental, Barcelona) y del Bernal de Yátor (la Alpujarra, Granada)

Se describen los principales rasgos geomorfológicos de las formas erosivas de tipo pilares de tierra que se desarrollan en la Riera de Gaià (Barcelona) y en el Bernal de Yátor (Granada) Se trata de formas dinámicas, propias de zonas sometidas a una fuerte erosión hídrica, con un elevado interés científico, estético y didáctico

Optimum Redundant Array Configurations for Earth Observation Aperture Synthesis Microwave Radiometers

Two-dimensional aperture synthesis radiometry is the technologyselected for ESA's SMOS mission to provide high resolution L-bandradiometric imagery. The array topology is a Y-shaped structure. Theposition and number of redundant elements to minimise instrumentdegradation in case of element failure(s) are studied.