Marc Lambrecht

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.

Heuristic Procedures for the Single Operation, Multi-Item Loading Problem

Abstract This paper considers the planning of individual machine groups or work centers producing many different products such as components, subassemblies or assemblies. The deterministic multi-item lot size problem with limited capacity has attracted much attention during the past two decades but no efficient optimization techniques are available up to now. We therefore suggest an efficient heuristic which is an extension of the Eisenhut heuristic. The resulting production programs always adhere to the characteristics of the dominant schedules. Special attention is given to the characterization of these dominant schedules.

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.

An integrated production and inventory model to dampen upstream demand variability in the supply chain

Abstract We consider a two-echelon supply chain: a single retailer holds a finished goods inventory to meet an i.i.d. customer demand, and a single manufacturer produces the retailer’s replenishment orders on a make-to-order basis. In this setting the retailer’s order decision has a direct impact on the manufacturer’s production. It is a well known phenomenon that inventory control policies at the retailer level often propagate customer demand variability towards the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). The manufacturer, however, prefers to smooth production, and thus he prefers a smooth order pattern from the retailer. At first sight a decrease in order variability comes at the cost of an increased variance of the retailer’s inventory levels, inflating the retailer’s safety stock requirements. However, integrating the impact of the retailer’s order decision on the manufacturer’s production leads to new insights. A smooth order pattern generates shorter and less variable (production/replenishment) lead times, introducing a compensating effect on the retailer’s safety stock. We show that by including the impact of the order decision on lead times, the order pattern can be smoothed to a considerable extent without increasing stock levels. This leads to a situation where both parties are better off.

Taming the bullwhip effect whilst watching customer service in a single supply chain echelon

We study a generalised order-up-to policy that has highly desirable properties in terms of order and inventory variance and customer service levels it generates. We quantify exactly the variance amplification in replenishment orders, i.e. the bullwhip effect, and the variance of inventory levels over time, for i.i.d. and the weakly stationary auto regressive (AR), moving average (MA) and auto regressive moving average (ARMA) demand processes. We demonstrate that high customer service as measured by fill-rate, and smooth replenishments need not increase inventory cost substantially. We observe that in some instances of the ARMA demand pattern this comes at the expense of a relatively small increase in safety stock, whilst in other instances inventory levels can actually be reduced.

On replenishment rules, forecasting and the bullwhip effect in supply chains

In this review we focus on supply coordination and use the bullwhip effect as the key example of supply chain inefficiency. We emphasize the managerial relevance of the bullwhip effect and the methodological issues so that both managers and researchers can benefit.

Protective stocks in multi-stage production systems

SUMMARY Uncertainty in MRP systems does exist in several forms, variability in demand from period to period, uncertainty in the supply from stage to stage due to the variability in the yields from each production batch, and uncertainty in the lead times. The goals of the paper are to develop theoretical models for determining optimal decisions in this uncertain environment, to develop a computationally tractable heuristic and to examine how safety stock and safety time can arise. Finally, our methodology is compared with MRP practice.

Extending the shifting bottleneck procedure to real-life applications

Abstract Much research has been devoted to the job shop scheduling problem since its introduction in the late 50s. Despite these efforts, even moderate sized benchmarking problems remained unsolved for many years. Given the complexity of the job shop scheduling problem, there is little hope for solving large real-life problems optimally within reasonable time. We therefore rely on heuristics, of which the shifting bottleneck procedure, developed by Adams et al. (1988), is performing excellently. We examine several extensions of the shifting bottleneck procedure towards real-life applications. We introduce due dates, release dates, assembly structures, split structures, overlapping operations, setup times, transportation times, parallel machines and beginning inventory. This generalized shifting bottleneck procedure is compared with priority dispatching rules on a set of large test problems.

A general approximation for the single product lot sizing model with queueing delays

Abstract The objective of this paper is to derive a general approximation for the single product lot sizing model with queueing delays, explicitly including a non-zero setup time. Most research focuses on bulk (batch) arrival and departure processes. In this paper we assume an individual arrival and departure process allowing the modelling of more realistic demand patterns. A general approximation of the expected lead time and the variance of the lead time is derived. The lead time probability distribution is approximated by means of a lognormal distribution. This allows the manufacturer to quote lead times satisfying a specified customer service level as a function of the lot size. The main result is a convex relationship of the expected lead time and the quoted lead time as a function of the lot size. The results are illustrated by means of numerical examples.