Inventory control systems rely on accurate and robust forecasts of future demand to support decisions such as setting of safety stocks. The combination of multiple forecasts is shown to be effective ...not only in reducing forecast errors, but also in being less sensitive to limitations of a single model. Research on forecast combination has primarily focused on improving accuracy, largely ignoring the overall shape and distribution of forecast errors. Nonetheless, these are essential for managing the level of aversion to risk and uncertainty for companies. This study examines the forecast error distributions of base and combination forecasts and their implications for inventory performance. It explores whether forecast combinations transform the forecast error distribution towards desired properties for safety stock calculations, typically based on the assumption of normally distributed errors and unbiased forecasts. In addition, it considers the similarity between in- and out-of-sample characteristics of such errors and the impact of different lead times. The effects of established combination methods are explored empirically using a representative set of forecasting methods and a dataset of 229 weekly demand series from a leading household and personal care UK manufacturer. Findings suggest that forecast combinations make the in- and out-of-sample behaviour more consistent, requiring less safety stock on average than base forecasts. Furthermore we find that using in-sample empirical error distributions of combined forecasts approximates well the out-of-sample ones, in contrast to base forecasts.
Research into time series forecasting for call center management suggests that a forecast based on the simple Seasonal Moving Average (SMA) method outperforms more sophisticated approaches at long ...horizons where capacity planning decisions are made. However in the short to medium term where decisions concerning the scheduling of agents are required, the SMA method is usually outperformed. This study is the first systematic evaluation of the SMA method across averages of different lengths using call arrival data sampled at different frequencies from 5min to 1h. A hybrid method which combines the strengths of the SMA method and nonlinear data-driven artificial neural networks (ANNs) is proposed to improve short-term accuracy without deteriorating long-term performance. Results of forecasting the intraday call arrivals to banks in the US, UK and Israel indicate that the proposed method outperforms standard benchmarks, and leads to improvements in forecasting accuracy across all horizons.
•Different combination operators are evaluated for neural network ensembles.•The proposed mode operator is insensitive to outliers and asymmetric distributions.•The mode is found to provide the most ...accurate forecasts, followed by the median.•The commonly used mean operator ranks last requiring very large ensembles.
The combination of forecasts resulting from an ensemble of neural networks has been shown to outperform the use of a single “best” network model. This is supported by an extensive body of literature, which shows that combining generally leads to improvements in forecasting accuracy and robustness, and that using the mean operator often outperforms more complex methods of combining forecasts. This paper proposes a mode ensemble operator based on kernel density estimation, which unlike the mean operator is insensitive to outliers and deviations from normality, and unlike the median operator does not require symmetric distributions. The three operators are compared empirically and the proposed mode ensemble operator is found to produce the most accurate forecasts, followed by the median, while the mean has relatively poor performance. The findings suggest that the mode operator should be considered as an alternative to the mean and median operators in forecasting applications. Experiments indicate that mode ensembles are useful in automating neural network models across a large number of time series, overcoming issues of uncertainty associated with data sampling, the stochasticity of neural network training, and the distribution of the forecasts.
Inaccurate forecasts can be costly for company operations, in terms of stock-outs and lost sales, or over-stocking, while not meeting service level targets. The forecasting literature, often disjoint ...from the needs of the forecast users, has focused on providing optimal models in terms of likelihood and various accuracy metrics. However, there is evidence that this does not always lead to better inventory performance, as often the translation between forecast errors and inventory results is not linear. In this study, we consider an approach to parametrising forecasting models by directly considering appropriate inventory metrics and the current inventory policy. We propose a way to combine the competing multiple inventory objectives, i.e. meeting demand, while eliminating excessive stock, and use the resulting cost function to identify inventory optimal parameters for forecasting models. We evaluate the proposed parametrisation against established alternatives and demonstrate its performance on real data. Furthermore, we explore the connection between forecast accuracy and inventory performance and discuss the extent to which the former is an appropriate proxy of the latter.
•The forecasting literature prescribes model parameters that minimise fitting errors.•There is evidence that this does not always lead to the best inventory performance.•We propose to parametrise forecasting models directly on inventory metrics.•This is achieved using a simulation optimisation approach, matching the case at hand.•This outperforms benchmarks in terms of forecast bias and inventory performance.
Tutoring technologies for supporting learning from errors via negative feedback are highly developed and have proven their worth in empirical evaluations. However, observations of empirical tutoring ...dialogs highlight the importance of positive feedback in the practice of expert tutoring. We hypothesize that positive feedback works by reducing student uncertainty about tentative but correct problem solving steps. Positive feedback should communicate three pieces of explanatory information: (a) those features of the situation that made the action the correct one, both in general terms and with reference to the specifics of the problem state; (b) the description of the action at a conceptual level and (c) the important aspect of the change in the problem state brought about by the action. We describe how a positive feedback capability was implemented in a mature, constraint-based tutoring system, SQL-Tutor, which teaches by helping students learn from their errors. Empirical evaluation shows that students who were interacting with the augmented version of SQL-Tutor learned at twice the speed as the students who interacted with the standard, error feedback only, version. We compare our approach with some alternative techniques to provide positive feedback in intelligent tutoring systems.
► We discuss the role of positive feedback in intelligent tutoring systems. ► We present an implementation of positive feedback in a constraint-based tutor. ► We compared the system with negative feedback to one with both types of feedback. ► The results show that providing positive feedback cuts the time to mastery in half.
Recent advances have demonstrated the benefits of temporal aggregation for demand forecasting, including increased accuracy, improved stock control and reduced modelling uncertainty. With temporal ...aggregation a series is transformed, strengthening or attenuating different elements and thereby enabling better identification of the time series structure. Two different schools of thought have emerged. The first focuses on identifying a single optimal temporal aggregation level at which a forecasting model maximises its accuracy. In contrast, the second approach fits multiple models at multiple levels, each capable of capturing different features of the data. Both approaches have their merits, but so far they have been investigated in isolation. We compare and contrast them from a theoretical and an empirical perspective, discussing the merits of each, comparing the realised accuracy gains under different experimental setups, as well as the implications for business practice. We provide suggestions when to use each for maximising demand forecasting gains.
•Forecasting with temporal aggregation has been shown to improve forecast accuracy.•Two schools of thought exist: using single optimal or multiple aggregation levels.•We contrast the two approaches and demonstrate the merits of each.•Select a single optimal aggregation level suffers from requiring model certainty.•Using multiple levels is robust to model uncertainty but suboptimal by construction.
Recently, combination algorithms from machine learning classification have been extended to time series regression, most notably seven variants of the popular AdaBoost algorithm. Despite their ...theoretical promise their empirical accuracy in forecasting has not yet been assessed, either against each other or against any established approaches of forecast combination, model selection, or statistical benchmark algorithms. Also, none of the algorithms have been assessed on a representative set of empirical data, using only few synthetic time series. We remedy this omission by conducting a rigorous empirical evaluation using a representative set of 111 industry time series and a valid and reliable experimental design. We develop a full-factorial design over derived Boosting meta-parameters, creating 42 novel Boosting variants, and create a further 47 novel Boosting variants using research insights from forecast combination. Experiments show that only few Boosting meta-parameters increase accuracy, while meta-parameters derived from forecast combination research outperform others.
Since the seminal work by Bates and Granger (1969), the practice of combining two or more models, rather than selecting the single best, has consistently been shown to lead to improvements in ...accuracy. In forecasting, model combination aims to find an optimal weighting given a set of precalculated forecasts. In contrast, machine learning includes methods which simultaneously optimise individual models and the weights used to combine them. Bagging and boosting combine the results of complementary and diverse models generated by actively perturbing, reweighting and resampling training data. Despite large gains in predictive accuracy in classification, limited research assesses their efficacy on time series data. This thesis provides a critical review of, the combination literature, and is the first literature survey of boosting for time series forecasting. The lack of rigorous empirical evidence on forecast accuracy of Bagging and boosting is identified as a major gap. To address this, a rigorous evaluation of Bagging and boosting adhering to recommendations of the forecasting literature is performed using robust error measures on a large set of real time series, exhibiting a representative set of features and dataset properties. Additionally there is a narrow focus on marginal extensions of boosting, and limited evidence of any gains in accuracy. A novel framework is proposed to explore the impact of varying boosting meta-parameters, and to evaluate the empirical accuracy of the resulting 96 boosting variants. The choice of base model and combination size are found to have the largest impact on forecast accuracy. Findings show that boosting overfits to noisy data, however no existing study investigates this crucial issue. New noise robust boosting methods are developed and evaluated for time series forecast models. They are found to significantly improve accuracy above current boosting approaches and Bagging, while neural network model averaging is found to perform best.
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