Jeroen Dejonckheere

Measuring and avoiding the bullwhip effect: A control theoretic approach

An important contributory factor to the bullwhip effect (i.e. the variance amplification of order quantities observed in supply chains) is the replenishment rule used by supply chain members. First the bullwhip effect induced by the use of different forecasting methods in order-up-to replenishment policies is analysed. Variance amplification is quantified and we prove that the bullwhip effect is guaranteed in the order-up-to model irrespective of the forecasting method used. Thus, when production is inflexible and significant costs are incurred by frequently switching production quantities up and down, order-up-to policies may no longer be desirable or even achievable. In the second part of the paper a general decision rule is introduced that avoids variance amplification and succeeds in generating smooth ordering patterns, even when demand has to be forecasted. The methodology is based on control systems engineering and allows important insights to be gained about the dynamic behaviour of replenishment rules.

The impact of information enrichment on the Bullwhip effect in supply chains: A control engineering perspective

This paper examines the beneficial impact of information sharing in multi-echelon supply chains. We compare a traditional supply chain, in which only the first stage in the chain observes end consumer demand and upstream stages have to base their forecasts on incoming orders, with an information enriched supply chain where customer demand data (e.g. EPOS data) is shared throughout the chain. Two types of replenishment rules are analysed: order-up-to (OUT) policies and smoothing policies (policies used to reduce or dampen variability in the demand). For the class of OUT policies, we will show that information sharing helps to reduce the bullwhipeffect (variance amplification of ordering quantities in supply chains) significantly, especially at higher levels in the chain. However, the bullwhip problem is not completely eliminated and it still increases as one moves up the chain. For the smoothing policies, we show that information sharing is necessary to reduce order variance at higher levels of the chain. The methodology is based on control systems engineering and allows us to gain valuable insights into the dynamic behaviour of supply chain replenishment rules. We also introduce acontrolengineering based measure to quantify the variance amplification (bullwhip) or variance reduction.

Transfer function analysis of forecasting induced bullwhip in supply chains

The present paper analyses the bullwhip problem generated by exponential smoothing algorithms in both “stand alone” passing-on-orders mode, and within inventory controlled feedback systems. Results are predicted from transfer function analysis, and then confirmed by simulation via the Bullwhip Explorer supply chain software. A novel feature of the paper is the introduction of the “matched filter” concept into the exponential smoothing algorithm. This adjusts the value of the smoothing constant depending on whether the Constant, Linear, or Quadratic forecasting model is used. It is shown that matching the filter via noise bandwidth equalises the output variance when the demand is a random signal. Hence some of the unwanted effects of using the Linear and Quadratic forecasting models are attenuated. However, there is little benefit obtained by using sophisticated forecasting methods within inventory controlled feedback systems as their tracking ability is reduced.

The dynamics of aggregate planning

Recent software developments in system modelling via transfer function analysis now enables a much broader understanding of the dynamics of aggregate planning to be gained. In particular it opens up the possibility of exploiting filter theory as a focal point during algorithm design. This is particularly attractive in view of the fact that we have established, via transfer function models, that there is commonality between HMMS and the order-up-to replenishment rules used extensively within both local and global supply chains. Filter theory allows us to relate these dynamics directly to present-day production planning strategy as observed in much industrial practice. It covers the spectrum of production strategies recently identified as preferred industrial practice. These strategies range from ‘level scheduling’ (i.e. lean production) right through to ‘pure chase’ (i.e. agile manufacture) with appropriate simple algorithmic control support via APIOBPCS software.

Explicit filters and supply chain design

Due to the complexity of present day supplychains it is important to select the simplest supplychain scheduling decision support system (DSS) which will determine and place orders satisfactorily. We propose to use a generic design framework, termed the explicitfilter methodology, to achieve this objective. In doing so we compare the explicitfilter approach to the implicitfilter approach utilised in previous OR research the latter focusing on minimising a cost function. Although the eventual results may well be similar with both approaches it is much clearer to the designer, both why and how, an ordering system will reduce the Bullwhip effect via the explicitfilter approach. The “explicitfilter” approach produces a range of DSS designs corresponding to best practice. These may be “mixed and matched” to generate a number of competitive delivery pipelines to suit the specific business scenario.