Number Of Consecutive Periods Research Articles

A mixed-integer programming-based heuristic for project scheduling with work-content constraints

We consider the project scheduling problem in which each project activity has a prescribed work content that must be completed by a so-called work-content resource and the activities' resource usage may change over time. The resource usage must lie within prescribed bounds and cannot be changed for a minimum number of consecutive periods. The amount of resource units used determines the requirements for further resources. The activities must be scheduled such that the project makespan is minimised. For this problem, we devise a mixed-integer programming-based heuristic that schedules the activities iteratively. To improve the resource usage for multiple activities simultaneously, subsets of activities are rescheduled each time the activities' resource usage appears to be inefficient. Our computational results for a standard test set from the literature show that our heuristic outperforms the state-of-the-art method for medium- and large-sized instances, and that for many small-sized instances, optimal solutions are obtained. [Received 30 September 2016; Revised 26 January 2017; Accepted 26 April 2017]

The dynamic space allocation problem: Applying hybrid GRASP and Tabu search metaheuristics

This work is devoted to the Dynamic Space Allocation Problem, where project duration is divided into a number of consecutive periods, each of them associated with a number of activities. The resources required by the activities have to be available in the corresponding workspaces and those sitting idle during a period have to be stored. This problem contains the Quadratic Assignment Problem (QAP) as a particular case, which puts it in the NP-hard class. In this context, the difficulty of identifying optimal solutions, even for instances of medium size, justifies the use of heuristic techniques. This work proposes a construction and a hybrid algorithm (HGT) based on the GRASP and Tabu search metaheuristics. Comparisons are presented for values obtained by HGT, pure GRASP versions, Tabu search and literature results. Computational results show the proposed methods to be competitive in relation to instances in the literature and to existing techniques.

The Long and Short of It: Why Are Stocks with Shorter Runs Preferred?

This article examines how consumers process graphical financial information to estimate risk. We propose that consumers sample the local maxima and minima of a graph to infer the variation around a trend line, which is used to estimate risk. The local maxima and minima are more extreme the higher the run length of the stocks (the consecutive number of upward or downward movements of a price series with identical mean, variance, skewness, and kurtosis). Three experiments show that this leads to stocks with higher run lengths being perceived as riskier: the run-length effect. Importantly, the run-length effect is greater for investors who are more educated, are employed full time, trade more frequently, have had longer experience trading, and trade a wider range of financial instruments. Implications for the communication of financial products, public policy, and consumer welfare are discussed, as are theoretical implications for the processing of visual and financial information and behavioral finance.

The Long and Short of It: Why are Stocks with Shorter Runs Preferred?

How good are people at interpreting numerical information presented in graphical form? Are they better at doing so when the stakes are high? There is evidence for pessimism on both counts. This paper takes an information processing view of the manner in which people process a large amount of numerical information. We propose that people sample points in a numerical series chosen due to their salience. To the extent the choice of sample points does not accurately represent the entire population of data from which they are chosen this process systematically distorts perceptions of the statistical properties of the series. This paper examines a specific bias in the presentation of graphical numerical data: the run length of a stock series. Run length is the number of consecutive periods over which the stock price moves up or down. The increasing use of graphical data in financial decisionmaking implies that visual biases in data interpretation are of growing economic importance. A primary and robust effect across three experimental studies is that stocks with longer run lengths are perceived as riskier than stocks with shorter runs, leading to a preference for the latter, despite controlling for the first four moments of the stock return paths. The effect of run length on preference for stocks appears to be driven by perceptions of risk rather than perceptions of return and are exacerbated when the stakes of the decision maker are higher. Results are robust to sample characteristics such as gender and financial experience. They are also robust to contextual differences in presentation format. Results are explained in terms of series with higher run lengths being associated with higher local maxima and minima, with these points in the series being more likely to be sampled due to their higher salience. Theoretical implications for the processing of numerical information, graphical information, and financial information are discussed.

Part III THE ACCERETION AND RESORPTION OF CALCIUM IN THE SKELETON

SummaryA method is described for the determination of digestive juices Ca, based on the continuous ingestion of Ca45 with stable Ca in the food. The true absorption of Ca can next be estimated.In the adult rat the digestive juices Ca was found to be in the range of 6.4 to 27.6 mg daily. The variability was considerable. When a number of consecutive periods were averaged in four vitamin D free rats, the variability was about ±15 per cent of the mean value of 11.2 mg Ca daily.Variations in serum Ca concentrations influence the digestive juices Ca as expected. When ionized Ca was calculated, a straight line relation was found between the ionized Ca and the amount of digestive juices Ca.Variations in the amount of food eaten resulted in proportional variations in the digestive juices Ca in rats supplied with vitamin D. In vitamin D free rats, variations in voluntary food consumption resulted in corresponding changes in the secretion of Ca with the digestive juices, not, however, to the same extent as in the rats supplemented with vitamin D.The method was found to be applicable with small errors only when the speed of Ca absorption was low, Serious errors may readily occur when the rate of Ca absorption is high or when high Ca diets are used.Some experiments in which the isotope was administered in a single dose by stomach tube revealed the serious weakness of such a procedure in contrast to the continuous feeding administration.Long‐term balance experiments were carried out to study the accumulation of Sr90 in rats with a constant level of Sr90 in their diet. Four groups were taken into experiment at different ages on a diet with 0.25 per cent Ca. A fifth group received a high Ca diet (0.71 per cent). The rats were kept in the experiment for 50 to 103 days.In the youngest group of rats the net absorption of Ca was nearly complete. The rats on the 0.71 per cent Ca diet did not absorb more Ca than rats of comparable age on the 0.25 per cent diet. The Ca absorption decreased with increasing age of the rats, as expected.Sr90 in faeces increased in the course of the experiments; the initial figures for faecal excretion in each experiment were definitely correlated to the efficiency of Ca absorption. An increase in the level of Ca in the diet resulted in a proportional depression of Sr90 absorption.The Observed Ratio (absorption) was calculated from the figures for net absorption of Ca and Sr90. Corrections have also been made for the secretion of Ca and Sr90 with the digestive juices. The O.R. (absorption) was found to be very high in the youngest rats, which is explained by the very high utilization of dietary Ca in the rats on the 0.25 per cent Ca diets.The urinary level of Ca was low in all the experiments. Sr90 in the urine remained within ten per cent of the intake in practically dl observations. There was a correlation between Sr90 absorbed and the urinary excretion. Within a given experiment, the Sr90 level in the urine became constant from the very early periods.The ratio of Sr90 in serum became constant after about eight days in young rats on continuous ingestion of Sr90.The Sr90/Ca ratio in the body was calculated at the end of each metabolic period. The resulting curves show a peak after approximately 33 days on the Sr90 diet. Next, some decrease followed, due to absorptive and urinary discrimination. The highest ratios for Sr90/Ca (body/diet) were found in the youngest rats, corresponding to the highest rates of absorption and the smallest body pool of Ca. The ratio of Sr90/Ca in the body was reduced in proportion to the increase of Ca in the diet.Following discontinuation of Sr90 ingestion, the faecal excretion was about twice as high as the urinary elimination.The figures for Ca and Ca45 retention were used in a calculation of the rate of bone accretion and resorption. The plasma Ca specific activity was constant in the periods used. The calculation rested on the presumption that the specific activity of Ca in accreted bone equals the specific activity of Ca in the plasma. In the first approximation zero specific activity of resorbed Ca was somewhat erroneously assumed. However a calculation with the aid of a set of figures for the specific activity of resorbed Ca results in: a) that accretion and resorption show a parallel increase, and b) gives a fairly good estimate of the probable size of the two variables under various experimental conditions. Experiments with vitamin D indicate that the vitamin acts primarily by increasing Ca absorption and bone accretion.