Optimality and robustness of combinations of moving averages

A combination of moving averages has been shown previously to be more accurate than simple moving averages, under certain conditions, and to be more robust to non-optimal parameter specification. However, the use of the method depends on specification of three parameters: length of greater moving average, length of shorter moving average, and the weighting given to the former. In this paper, expressions are derived for the optimal values of the three parameters, under the conditions of a steady state model. These expressions reduce a three-parameter search to a single-parameter search. An expression is given for the variance of the sampling error of the optimal combination of moving averages and this is shown to be marginally greater than that for exponentially weighted moving averages (EWMA). Similar expressions for optimal parameters and the resultant variance are derived for equally weighted combinations. The sampling variance of the mean of such combinations is shown to be almost identical to the optimal general combination, thus simplifying the use of combinations further. It is demonstrated that equal weight combinations are more robust than EWMA to noise to signal ratios lower than expected, but less robust to noise to signal ratios higher than expected

The implications of judgemental interventions into an inventory System

Physical inventories constitute a considerable proportion of companies’ investments in today’s competitive environment. The trade-off between customer service levels and inventory investments is addressed in practice by formal quantitative inventory management (stock control) solutions. Given the tremendous number of Stock Keeping Units (SKUs) that contemporary organisations deal with, such solutions need to be fully automated. However, managers very often judgementally adjust the output of statistical software (such as the demand forecasts and/or the replenishment decisions) to reflect qualitative information that they possess. In this research we are concerned with the value being added (or not) when statistical/quantitative output is judgementally adjusted by managers. Our work aims to investigate the effects of incorporating human judgement into such inventory related decisions and it is the first study to do so empirically. First, a set of relevant research questions is developed based on a critical review of the literature. Then, an extended database of approximately 1,800 SKUs from an electronics company is analysed for the purpose of addressing the research questions. In addition to empirical exploratory analysis, a simulation experiment is performed in order to evaluate in a dynamic fashion what are the effects of adjustments on the performance of a stock control system. The results on the simulation experiment reveal that judgementally adjusted replenishment orders may improve inventory performance in terms of reduced inventory investments (costs). However, adjustments do not seem to contribute towards the increase of the cycle service level (CSL) and fill rate. Since there have been no studies addressing similar issues to date, this research should be of considerable value in advancing the current state of knowledge in the area of inventory management. From a practitioner’s perspective, the findings of this research may guide managers in adjusting order-up-to levels for the purpose of achieving better inventory performance. Further, the results may also contribute towards the development of better functionality of inventory support systems (ISS)

Centralised demand information sharing - A Thesis submitted for the degree of Doctor of Philosophy

This thesis explores Centralised Demand Information Sharing (CDIS) in supply chains. CDIS is an information sharing approach where supply chain members forecast based on the downstream member’s demand. The Bullwhip Effect is a demand variance amplification phenomenon: as the demand moves upstream in supply chains, its variability increases. Many papers in the literature show that, if supply chain members forecast using the less variable downstream member’s demand, this amplification can be reduced leading to a reduction in inventory cost. These papers, using strict model assumptions, discuss three demand information sharing approaches: No Information Sharing (NIS), Downstream Demand Inference (DDI) and Demand Information Sharing (DIS). The mathematical analysis in this stream of research is restricted to the Minimum Mean Squared Error (MMSE) forecasting method. A major motivation for this PhD research is to improve the above approaches, and assess those using less restrictive supply chain assumptions. In this research, apart from using the MMSE forecasting method, we also utilise two non-optimal forecasting methods, Simple Moving Averages (SMA) and Single Exponential Smoothing (SES). The reason for their inclusion is the empirical evidence of their high usage, familiarity and satisfaction in practice. We first fill some gaps in the literature by extending results on upstream demand translation for ARMA (p, q) processes to SMA and SES. Then, by using less restrictive assumptions, we show that the DDI approach is not feasible, while the NIS and DIS approaches can be improved. The two new improved approaches are No Information Sharing – Estimation (NIS-Est) and Centralised Demand Information Sharing (CDIS). It is argued in this thesis that if the supply chain strategy is not to share demand information, NIS-Est results in less inventory cost than NIS for an Order Up To policy. On the other hand, if the strategy is to share demand information, the CDIS approach may be used, resulting in lower inventory cost than DIS. These new approaches are then compared to the traditional approaches on theoretically generated data. NIS-Est improves on NIS, while CDIS improves on the DIS approach in terms of the bullwhip ratio, forecast error (as measured by Mean Squared Error), inventory holding and inventory cost. The results of simulation show that the performance of CDIS is the best among all four approaches in terms of these performance metrics. Finally, the empirical validity of the new approaches is assessed on weekly sales data of a European superstore. Empirical findings and theoretical results are consistent regarding the performance of CDIS. Thus, this research concludes that the inventory cost of an upstream member is reduced when their forecasts are based on a Centralised Demand Information Sharing (CDIS) approach

Optimality and robustness of combinations of moving averages

A combination of moving averages has been shown previously to be more accurate than simple moving averages, under certain conditions, and to be more robust to non-optimal parameter specification. However, the use of the method depends on specification of three parameters: length of greater moving average, length of shorter moving average, and the weighting given to the former. In this paper, expressions are derived for the optimal values of the three parameters, under the conditions of a steady state model. These expressions reduce a three-parameter search to a single-parameter search. An expression is given for the variance of the sampling error of the optimal combination of moving averages and this is shown to be marginally greater than that for exponentially weighted moving averages (EWMA). Similar expressions for optimal parameters and the resultant variance are derived for equally weighted combinations. The sampling variance of the mean of such combinations is shown to be almost identical to the optimal general combination, thus simplifying the use of combinations further. It is demonstrated that equal weight combinations are more robust than EWMA to noise to signal ratios lower than expected, but less robust to noise to signal ratios higher than expected