Probabilistic forecasting of heterogeneous consumer transaction-sales time series

We present new Bayesian methodology for consumer sales forecasting. With a focus on multi-step ahead forecasting of daily sales of many supermarket items, we adapt dynamic count mixture models to forecast individual customer transactions, and introduce novel dynamic binary cascade models for predicting counts of items per transaction. These transactions-sales models can incorporate time-varying trend, seasonal, price, promotion, random effects and other outlet-specific predictors for individual items. Sequential Bayesian analysis involves fast, parallel filtering on sets of decoupled items and is adaptable across items that may exhibit widely varying characteristics. A multi-scale approach enables information sharing across items with related patterns over time to improve prediction while maintaining scalability to many items. A motivating case study in many-item, multi-period, multi-step ahead supermarket sales forecasting provides examples that demonstrate improved forecast accuracy in multiple metrics, and illustrates the benefits of full probabilistic models for forecast accuracy evaluation and comparison. Keywords: Bayesian forecasting; decouple/recouple; dynamic binary cascade; forecast calibration; intermittent demand; multi-scale forecasting; predicting rare events; sales per transaction; supermarket sales forecastingComment: 23 pages, 5 figures, 1 tabl

Multiplicative State-Space Models for Intermittent Time Series

Intermittent demand forecasting is an important supply chain task, which is commonly done using methods based on exponential smoothing. These methods however do not have underlying statistical models, which limits their generalisation. In this paper we propose a general state-space model that takes intermittence of data into account, extending the taxonomy of exponential smoothing models. We show that this model has a connection with conventional non-intermittent state space models and underlies Croston’s and Teunter-Syntetos-Babai (TSB) forecasting methods. We discuss properties of the proposed models and show how a selection can be made between them in the proposed framework. We then conduct experiments on simulated data and on two real life datasets, demonstrating advantages of the proposed approach

Stochastic demand forecast and inventory management of a seasonal product a supply chain system

Estimation of seasonal demand prior to an active demand season is essential in supply chain management. The business cycle of the seasonal demand is divided into two stages: stage-1, the slow-demand period, and stage-2, the peak-demand period. The focus here is to determine an appropriate demand forecast for the peak-demand period. In the first set of forecasting model, a standard gamma and an inverse gamma prior distribution are used to forecast demand. The parameters of the prior model are estimated and updated based on current observation using Bayesian technique. The forecasts are derived for both complete and incomplete datasets. The second set of forecast is derived by ARIMA method using Box-Jenkins approaches. A Bayesian ARIMA is proposed to forecast demand from incomplete dataset. A partial dataset of a seasonal product, collected from the US census bureau, is used in the models. Missing values in the dataset often arise in various situations. The models are extended to forecast demand from an incomplete dataset by the assumption that the original dataset contains missing values. The forecast by a multiplicative exponential smoothing model is used to compare all the forecast. The performances are tested by several error measures such as relative errors, mean absolute deviation, and tracking signals. A newsvendor inventory model with emergency procurement options and a periodic review model are studied to determine the procurement quantity and inventory costs. The inventory cost of each demand forecast relative to the cost of actual demand is used as the basis to choose an appropriate forecast for the dataset. This study improves the quality of demand forecasts and determines the best forecast. The result reveals that forecasting models using Bayesian ARIMA model and Bayesian probability models perform better. The flexibility in the Bayesian approaches allows wider variability in the model parameters helps to improve demand forecasts. These models are particularly useful when past demand information is incomplete or limited to few periods. Furthermore, it was found that improvements in demand forecasting can provide better cost reductions than relying on inventory models

Reliable Prediction Intervals and Bayesian Estimation for Demand Rates of Slow-Moving Inventory

Application of multisource feedback (MSF) increased dramatically and became widespread globally in the past two decades, but there was little conceptual work regarding self-other agreement and few empirical studies investigated self-other agreement in other cultural settings. This study developed a new conceptual framework of self-other agreement and used three samples to illustrate how national culture affected self-other agreement. These three samples included 428 participants from China, 818 participants from the US, and 871 participants from globally dispersed teams (GDTs). An EQS procedure and a polynomial regression procedure were used to examine whether the covariance matrices were equal across samples and whether the relationships between self-other agreement and performance would be different across cultures, respectively. The results indicated MSF could be applied to China and GDTs, but the pattern of relationships between self-other agreement and performance was different across samples, suggesting that the results found in the U.S. sample were the exception rather than rule. Demographics also affected self-other agreement disparately across perspectives and cultures, indicating self-concept was susceptible to cultural influences. The proposed framework only received partial support but showed great promise to guide future studies. This study contributed to the literature by: (a) developing a new framework of self-other agreement that could be used to study various contextual factors; (b) examining the relationship between self-other agreement and performance in three vastly different samples; (c) providing some important insights about consensus between raters and self-other agreement; (d) offering some practical guidelines regarding how to apply MSF to other cultures more effectively

The boomerang returns? Accounting for the impact of uncertainties on the dynamics of remanufacturing systems

Recent years have witnessed companies abandon traditional open-loop supply chain structures in favour of closed-loop variants, in a bid to mitigate environmental impacts and exploit economic opportunities. Central to the closed-loop paradigm is remanufacturing: the restoration of used products to useful life. While this operational model has huge potential to extend product life-cycles, the collection and recovery processes diminish the effectiveness of existing control mechanisms for open-loop systems. We systematically review the literature in the field of closed-loop supply chain dynamics, which explores the time-varying interactions of material and information flows in the different elements of remanufacturing supply chains. We supplement this with further reviews of what we call the three ‘pillars’ of such systems, i.e. forecasting, collection, and inventory and production control. This provides us with an interdisciplinary lens to investigate how a ‘boomerang’ effect (i.e. sale, consumption, and return processes) impacts on the behaviour of the closed-loop system and to understand how it can be controlled. To facilitate this, we contrast closed-loop supply chain dynamics research to the well-developed research in each pillar; explore how different disciplines have accommodated the supply, process, demand, and control uncertainties; and provide insights for future research on the dynamics of remanufacturing systems