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.

When to carry eccentric products? Optimal retail assortment under consumer returns

To understand whether retailers should consider consumer returns when merchandising, we study howthe optimal assortment of a price-taking retailer is influenced by its return policy. The retailer selects itsassortment from an exogenous set of horizontally differentiated products. Consumers make purchase andkeep/return decisions in nested multinomial logit fashion. Our main finding is that the optimal assortmenthas a counterintuitive structure for relatively strict return policies: It is optimal to offer a mix of the mostpopular and most eccentric products when the refund amount is sufficiently low, which can be viewed asa form of risk sharing between the retailer and consumers. In contrast, if the refund is sufficiently high, orwhen returns are disallowed, optimal assortment is composed of only the most popular products (a commonfinding in the literature). We provide preliminary empirical evidence for one of the key drivers of our results:more eccentric products have higher probability of return conditional on purchase. In light of our analyticalfindings and managerial insights, we conclude that retailers should take their return policies into accountwhen merchandising.

Competing engines of growth: Innovation and standardization

We study a dynamic general equilibrium model where innovation takes theform of the introduction of new goods whose production requires skilled workers.Innovation is followed by a costly process of standardization, whereby these newgoods are adapted to be produced using unskilled labor. Our framework highlightsa number of novel results. First, standardization is both an engine of growth anda potential barrier to it. As a result, growth is an inverse U-shaped function ofthe standardization rate (and of competition). Second, we characterize the growthand welfare maximizing speed of standardization. We show how optimal protection of intellectual property rights affecting the cost of standardization vary withthe skill-endowment, the elasticity of substitution between goods and other parameters. Third, we show that, depending on how competition between innovatingand standardizing firms is modelled and on parameter values, a new type of multiplicity of equilibria may arise. Finally, we study the implications of our model forthe skill-premium and we illustrate novel reasons for linking North-South trade tointellectual property rights protection.

Shared knowledge

Agents use their knowledge on the history of the economy in orderto choose what is the optimal action to take at any given moment of time,but each individual observes history with some noise. This paper showsthat the amount of information available on the past evolution of theeconomy is an endogenous variable, and that this leads to overconcentrationof the investment, which can be interpreted as underinvestment in research.It presents a model in which agents have to invest at each period in one of$K$ sectors, each of them paying an exogenous return that follows a welldefined stochastic path. At any moment of time each agent receives an unbiasednoisy signal on the payoff of each sector. The signals differ across agents,but all of them have the same variance, which depends on the aggregate investmentin that particular sector (so that if almost everybody invests in it theperceptions of everybody will be very accurate, but if almost nobody doesthe perceptions of everybody will be very noisy). The degree of hetereogeneityacross agents is then an endogenous variable, evolving across time determining,and being determined by, the amount of information disclosed.As long as both the level of social interaction and the underlying precisionof the observations are relatively large agents behave in a very preciseway. This behavior is unmodified for a huge range of informational parameters,and it is characterized by an excessive concentration of the investment ina few sectors. Additionally the model shows that generalized improvements in thequality of the information that each agent gets may lead to a worse outcomefor all the agents due to the overconcentration of the investment that thisproduces.

Sitobion graminis Takahashi, 1950 (Hemiptera, Aphididae): first record in Brazil, biological and morphometric parameters

The species Sitobion graminis Takahashi, 1950 (Hemiptera, Aphididae) was first detected in Brazil in 1998, in Curitiba, Paraná state, associated with the grass species Erianthus sp., Calamagrotis sp. and Paspalum urvilei. Both the field-collected and laboratory-reared specimens presented a noticeable intrapopulational variation in body and appendix length and in dorso-abdominal sclerotization. This species has been recorded in Malaysia, New Guinea, India, Philippines and Africa, where it colonizes several species of Poaceae. S. graminis differs from other Sitobion species from Brazil associated with grasses, as it presents black cauda and siphunculi and exhibits a constriction in the base of the last rostral segment. Biological data were obtained in the laboratory by rearing newborn nymphs on the inflorescence of the host plants. They passed through four nymphal instars. The mean duration of the nymphal stage was of 11.4 days, with a mortality ratio of 36.5%. The mean pre-larviposition period was of 1.8 days; mean longevity of the females was 25.2 days; and mean fecundity was 18.7 nymphs/female, ranging from 2 to 41 nymphs/female.

The optimum quantity of money: Theory and evidence

In this paper we propose a simple and general model for computing the Ramsey optimal inflation tax, which includes several models from the previous literature as special cases. We show that it cannot be claimed that the Friedman rule is always optimal (or always non--optimal) on theoretical grounds. The Friedman rule is optimal or not, depending on conditions related to the shape of various relevant functions. One contribution of this paper is to relate these conditions to {\it measurable} variables such as the interest rate or the consumption elasticity of money demand. We find that it tends to be optimal to tax money when there are economies of scale in the demand for money (the scale elasticity is smaller than one) and/or when money is required for the payment of consumption or wage taxes. We find that it tends to be optimal to tax money more heavily when the interest elasticity of money demand is small. We present empirical evidence on the parameters that determine the optimal inflation tax. Calibrating the model to a variety of empirical studies yields a optimal nominal interest rate of less than 1\%/year, although that finding is sensitive to the calibration.

On optimal location with treshold requirements

The optimal location of services is one of the most important factors that affects service quality in terms of consumer access. On theother hand, services in general need to have a minimum catchment area so as to be efficient. In this paper a model is presented that locates the maximum number of services that can coexist in a given region without having losses, taking into account that they need a minimum catchment area to exist. The objective is to minimize average distance to the population. The formulation presented belongs to the class of discrete P--median--like models. A tabu heuristic method is presented to solve the problem. Finally, the model is applied to the location of pharmacies in a rural region of Spain.

Optimal regulation of a fully insured deposit banking system

We analyze risk sensitive incentive compatible deposit insurancein the presence of private information when the market value of depositinsurance can be determined using Merton's (1997) formula. We show that,under the assumption that transferring funds from taxpayers to financialinstitutions has a social cost, the optimal regulation combines differentlevels of capital requirements combined with decreasing premia on depositinsurance. On the other hand, it is never efficient to require the banksto hold riskless assets, so that narrow banking is not efficient. Finally,chartering banks is necessary in order to decrease the cost of asymmetricinformation.

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Aspects thérapeutiques de la vitamine D: quels taux cibler avec quels traitements [Therapeutic goal of vitamin D: optimal serum level and dose requirements].

Therapeutic goal of vitamin D: optimal serum level and dose requirements Results of randomized controlled trials and meta-analyses investigating the effect of vitamin D supplementation on falls and fractures are inconsistent. The optimal serum level 25(OH) vitamin D for musculoskeletal and global health is > or = 30 ng/ml (75 nmol/l) for some experts and 20 ng/ml (50 nmol/l) for some others. A daily dose of vitamin D is better than high intermittent doses to reach this goal. High dose once-yearly vitamin D therapy may increase the incidence of fractures and falls. High serum level of vitamin D is probably harmful for the musculoskeletal system and health at large. The optimal benefits for musculoskeletal health are obtained with an 800 UI daily dose and a serum level of near 30 ng/ml (75 nmol/l).

Value of sTREM-1, procalcitonin and CRP as laboratory parameters for postmortem diagnosis of sepsis.

OBJECTIVES: Triggering receptor expressed on myeloid cells-1 (TREM-1) was reported to be up-regulated in various inflammatory diseases as well as in bacterial sepsis. Increased cell-surface TREM-1 expression was also shown to result in marked plasma elevation of the soluble form of this molecule (sTREM-1) in patients with bacterial infections. In this study, we investigated sTREM-1, procalcitonin and C-reactive protein in postmortem serum in a series of sepsis-related fatalities and control individuals who underwent medico-legal investigations. sTREM-1 was also measured in pericardial fluid and urine. METHODS: Two study groups were prospectively formed, a sepsis-related fatalities group and a control group. The sepsis-related fatalities group consisted of sixteen forensic autopsy cases. Eight of these had a documented clinical diagnosis of sepsis in vivo. The control group consisted of sixteen forensic autopsy cases with various causes of death. RESULTS: Postmortem serum sTREM-1 concentrations were higher in the sepsis group with a mean value of 173.6 pg/ml in septic cases and 79.2 pg/ml in control individuals. The cutoff value of 90 pg/ml provided the best sensitivity and specificity. Pericardial fluid sTREM-1 values were higher in the septic group, with a mean value of 296.7 pg/ml in septic cases and 100.9 pg/ml in control individuals. The cutoff value of 135 pg/ml provided the best sensitivity and specificity. Mean urine sTREM-1 concentration was 102.9 pg/ml in septic cases and 89.3 pg/ml in control individuals. CONCLUSIONS: Postmortem serum sTREM-1, individually considered, did not provide better sensitivity and specificity than procalcitonin in detecting sepsis. However, simultaneous assessment of procalcitonin and sTREM-1 in postmortem serum can be of help in clarifying contradictory postmortem findings. sTREM-1 determination in pericardial fluid can be an alternative to postmortem serum in those situations in which biochemical analyses are required and blood collected during autopsy proves insufficient.