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.

Continuous electroencephalography in the medical intensive care unit.

OBJECTIVES: To examine predictors and the prognostic value of electrographic seizures (ESZs) and periodic epileptiform discharges (PEDs) in medical intensive care unit (MICU) patients without a primary acute neurologic condition. DESIGN: Retrospective study. SETTING: MICU in a university hospital. PATIENTS: A total of 201 consecutive patients admitted to the MICU between July 2004 and January 2007 without known acute neurologic injury and who underwent continuous electroencephalography monitoring (cEEG) for investigation of possible seizures or changes in mental status. INTERVENTION: None. MEASUREMENTS AND MAIN RESULTS: Median time from intensive care unit (ICU) admission to cEEG was 1 day (interquartile range 1-4). The majority of patients (60%) had sepsis as the primary admission diagnosis and 48% were comatose at the time of cEEG. Ten percent (n = 21) of patients had ESZs, 17% (n = 34) had PEDs, 5% (n = 10) had both, and 22% (n = 45) had either ESZs or PEDs. Seizures during cEEG were purely electrographic (no detectable clinical correlate) in the majority (67%) of patients. Patients with sepsis had a higher rate of ESZs or PEDs than those without sepsis (32% vs. 9%, p < 0.001). On multivariable analysis, sepsis at ICU admission was the only significant predictor of ESZs or PEDs (odds ratio 4.6, 95% confidence interval 1.9-12.7, p = 0.002). After controlling for age, coma, and organ dysfunction, the presence of ESZs or PEDs was associated with death or severe disability at hospital discharge (89% with ESZs or PEDs, vs. 39% if not; odds ratio 19.1, 95% confidence interval 6.3-74.6, p < 0.001). CONCLUSION: In this retrospective study of MICU patients monitored with cEEG, ESZs and PEDs were frequent, predominantly in patients with sepsis. Seizures were mainly nonconvulsive. Both seizures and periodic discharges were associated with poor outcome. Prospective studies are warranted to determine more precisely the frequency and clinical impact of nonconvulsive seizures and periodic discharges, particularly in septic patients.

Modeling the forensic two-trace problem with Bayesian networks

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this problem.

IUP Science Unit collective Bargainging Agreement, July 2007

This Agreement made and entered i into this 1 1st day of July 2007, at Des Moines, Iowa, pursuant to the provisions of Chapter 20 of the Iowa Code, by and between the State of Iowa (hereinafter referred to as the Employer) and UE Local 893/Iowa United Professionals, and its appropriate affiliated locals, as representatives of employees employed by the State of Iowa, as set forth specifically in Appendix A (hereinafter referred to as the Union).

Competition, innovation and growth with limited commitment

We study how barriers to business start-up affect the investment in knowledge capital when contracts are not enforceable. Barriers to business start-up lower the competition for knowledge capital and, in absence of commitment, reduce the incentive to accumulate knowledge. As a result, countries with large barriers experience lower income and growth. Our results are consistent with cross-country evidence showing that the cost of business start-up is negatively correlated with the level and growth of income.

Strategies for an integrated distribution problem

The problems arising in the logistics of commercial distribution are complexand involve several players and decision levels. One important decision isrelated with the design of the routes to distribute the products, in anefficient and inexpensive way.This article explores three different distribution strategies: the firststrategy corresponds to the classical vehicle routing problem; the second isa master route strategy with daily adaptations and the third is a strategythat takes into account the cross-functional planning through amulti-objective model with two objectives. All strategies are analyzed ina multi-period scenario. A metaheuristic based on the Iteratetd Local Search,is used to solve the models related with each strategy. A computationalexperiment is performed to evaluate the three strategies with respect to thetwo objectives. The cross functional planning strategy leads to solutions thatput in practice the coordination between functional areas and better meetbusiness objectives.

On a problem of Alfréd Rényi

Alfréd Rényi, in a paper of 1962, A new approach to the theory ofEngel's series, proposed a problem related to the growth of theelements of an Engel's series. In this paper, we reformulate andsolve Rényi's problem for both, Engel's series and Pierceexpansions.