Discrete-time spare ordering policy with randomized lead times and discounting

The paper considers a generalized discrete‐time order‐replacement model for a single unit system, which is subject to random failure when in operation. Two types of discrete randomized lead times are considered for a spare unit; one is for regular (preventive) order and another is for expedited (emergency) order. The model is formulated based on the discounted cost criterion. The underlying two‐dimensional optimization problem is reduced to a simple one‐dimensional one and then the optimal ordering policy for the spare unit is characterized under two extreme conditions: (i) unlimited inventory time and (ii) zero inventory time for the spare unit. A numerical example is used to determine the optimal spare‐ordering policy numerically and to examine the sensitivity of the model parameters.     

Delay discounting of real and hypothetical rewards.

The degree to which real and hypothetical rewards were discounted across delays ranging from 6 hr to 1 year was explored in a within-subjects design. An adjusting-amounts procedure was used to estimate the subjective value of real and hypothetical rewards at each delay. A hyperbolic discounting function provided a significantly better fit to individual participants' preferences than did an exponential function. No significant effect of reward type on degree of hyperbolic discounting or area under the discounting curves was detected. These findings offer some support for the validity of using hypothetical rewards to estimate discounting rates in substance-abusing and other populations, but caution is suggested because this support is gleaned from a failure to detect an effect of reward type. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

一种新的证据复合折扣合成方法

D-S证据理论是一种重要的决策级信息融合方法,但传统的Dempster证据合成规则会导致一些与直觉相悖的结果.针对该问题,在经典的Shafer折扣方法基础上,提出了一种综合可靠性和重要性因素的复合折扣因子计算方法.该方法首先借助证据包含度合理地定义了证据可靠性度量;然后综合证据清晰度、证据一致性和证据积累程度等因素,建立了证据重要性模型;最后两者通过乘法算子共同构成复合折扣因子.实验结果表明,文章方法的证据处理过程与生物学研究中人的信息积累过程一致,能够解决证据合成中的悖论问题,合成证据可靠有效.     

The short of it: Abbreviating the temporal discounting procedure.

A typical temporal discounting procedure determines the present, subjective value (indifference point) of a delayed outcome at 5 to 8 different delays to that outcome. These indifference points are used to determine a single index of discounting called a discounting rate. One concern that remains in the collection of this data is the high number of trials or choices, resulting in participant fatigue or other factors that may affect the validity of the data. In this report, we propose an abbreviated alternative to the more comprehensive and time-consuming discounting procedure. Specifically, we propose that fewer indifference points can be used to determine statistically equivalent discount rates with no loss in data sensitivity. We reanalyzed temporal discounting data obtained with 7 indifference points, and estimated discount rates from all combinations of 2, 3, and 4 of the 7 indifference points. Results indicate that valid and sensitive discounting indices can be obtained with fewer indifference points, and the most appropriate sets of indifference points are highlighted. The proposed abbreviated procedure is likely to be particularly useful when time constraints or participant fatigue is a concern as well as in repeated-measures contexts. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Now or later? Striatum and insula activation to immediate versus delayed rewards.

Neuroimaging studies on delay discounting tasks that use reward delays ranging from minutes to days have implicated the insula and striatum in the processing of intertemporal decisions. This study aimed at assessing whether these brain regions would also be involved in decision-making when subjects have to wait through the delays within the range of seconds. Using functional MRI in 13 healthy volunteers, we repeatedly presented monetary options with delays that differed within the range of multiple seconds. Using a region-of-interest approach, we found significant activation in the bilateral anterior insula and striatum when subjects chose either the immediate (smaller) or delayed (larger) option. In particular, insular activation was observed after the response and the delay, when the outcome of the immediate or the delayed choice was shown. Significantly greater activation was observed in the ventroanterior striatum while subjects chose the immediate, as opposed to the delayed, options and also after receiving the outcome of waiting through the longer delay option. The evidence presented here indicates that both the ventral striatum and the insula are involved in the processing of choosing delay options as well as the consequences of choices with delays in the seconds' range. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Temporal horizons in decision making.

The perception of duration is crucial when we make choices between immediate and delayed rewards. Immediate rewards are valued more than the same rewards if they are delayed. Preferences for earlier rewards become even stronger when the reward can be received within a subjectively proximate time frame. A “rational” decision to wait for a delayed reward may be overruled by an “impulsive” choice when the option for the closer reward falls within this proximate time range. Based on findings on circadian and circannual physiological rhythms, we suggest that there are 2 time units that are both biologically and culturally determined and have an impact on human experience and behavior: the day and the year. We highlight results of a neuroimaging study showing that rewards with delays up to 1 year are discounted differently than reward delays longer than 1 year. This duration-dependent discounting is associated with specific brain activation in the striatum. We present various conceptualizations of subjective time incorporated in parametric models of intertemporal decisions that may lead to a better understanding of human choice behavior. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Novel models of intertemporal valuation: Past and future outcomes.

Temporal discounting refers to the reduction in the present subjective value of an outcome as a function of the temporal distance to that outcome. Though a number of mathematical models have been proposed to describe this time/value relationship, this search has largely excluded insights from the literature on memory decay. This study examines the utility of memory decay models by comparing the fits of 4 of these models to fits from established temporal discounting models using past and future temporal discounting data. These results (a) suggest that a single model describes valuation of both future and past outcomes; (b) indicate the exponential-power model, from memory decay literature, is statistically superior in fitting discounting data from both past and future outcomes; and (c) support the advancing perspective of the psychological interconnectedness of the future and past. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Temporal discounting of rewards in patients with bipolar disorder and schizophrenia.

Patients with bipolar disorder (BD) and schizophrenia (SZ) often show decision-making deficits in everyday circumstances. A failure to appropriately weigh immediate versus future consequences of choices may contribute to these deficits. We used the delay discounting task in individuals with BD or SZ to investigate their temporal decision making. Twenty-two individuals with BD, 21 individuals with SZ, and 30 healthy individuals completed the delay discounting task along with neuropsychological measures of working memory and cognitive function. Both BD and SZ groups discounted delayed rewards more steeply than did the healthy group even after controlling for current substance use, age, gender, and employment. Hierarchical multiple regression analyses showed that discounting rate was associated with both diagnostic group and working memory or intelligence scores. In each group, working memory or intelligence scores negatively correlated with discounting rate. The results suggest that (a) both BD and SZ groups value smaller, immediate rewards more than larger, delayed rewards compared with the healthy group and (b) working memory or intelligence is related to temporal decision making in individuals with BD or SZ as well as in healthy individuals. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Discounting future green: Money versus the environment.

In 3 studies, participants made choices between hypothetical financial, environmental, and health gains and losses that took effect either immediately or with a delay of 1 or 10 years. In all 3 domains, choices indicated that gains were discounted more than losses. There were no significant differences in the discounting of monetary and environmental outcomes, but health gains were discounted more and health losses were discounted less than gains or losses in the other 2 domains. Correlations between implicit discount rates for these different choices suggest that discount rates are influenced more by the valence of outcomes (gains vs. losses) than by domain (money, environment, or health). Overall, results indicate that when controlling as many factors as possible, at short to medium delays, environmental outcomes are discounted in a similar way to financial outcomes, which is good news for researchers and policy makers alike. (PsycINFO Database Record (c) 2010 APA, all rights reserved)