Measure of bullwhip effect in supply chains with autoregressive demand process

In supply chain management, one of the most critical problems which require a lot of effort to deal with is how to quantify and alleviate the impact of bullwhip effect – the phenomenon in which information on demand is distorted while moving upstream. Although it is well established that demand forecast, lead time, order batching, shortage gaming and price fluctuation are the main sources that lead to the bullwhip effect, the problem of quantifying bullwhip effect still remain unsolved in many situations due to the complex nature of the problem. In this research, a measure of bullwhip effect will be developed for a simple two-stage supply chain that includes only one retailer and one supplier in the environment where the retailer employs base stock policy for their inventory and demand forecast is performed through the first-order autoregressive model, AR(1). The effect of autoregressive coefficient and lead time on this measure will then be investigated.     

Measure of bullwhip effect in supply chains: The case of high order autoregressive demand process

Bullwhip effect – the phenomenon in which variance of demand is amplified when moving upstream – has attracted the attention of many researchers for the last few decades. Although the main sources that cause bullwhip effect have been identified, quantifying the bullwhip effect still remains a challenge. In the past, measuring the bullwhip effect for supply chains with autoregressive demand process has been conducted by some researchers. However, most past researches focused mainly on the simple AR(1) model. In many practical situations, autoregressive models with higher order should be employed because they might better represent the demand process. Up to now, very little effort has been spent on this matter. Therefore, this research is conducted to fill this gap by first dealing with AR(2) demand process and investigating the behavior of the developed measure with respect to autoregressive coefficients and order lead-time. Extension to the general AR(p) demand process is then considered.     

Delayed demand information and dampened bullwhip effect

This paper considers an inventory setting in which the historical data used for demand forecasting is delayed. When the replenishment is controlled via an order-up-to policy, we show that such delays reduce the variability of the order history and dampen the bullwhip effect. We discuss the intuition behind this result.     

Conditions of reverse bullwhip effect in pricing for price-sensitive demand functions

Supply chain mechanisms that exacerbate price variation needs special attention, since price variation is one of the root causes of the bullwhip effect. In this study, we investigate conditions that create an amplification of price variation moving from the upstream suppliers to the downstream customers in a supply chain, which is referred as the “reverse bullwhip effect in pricing” (RBP). Considering initially a single-stage supply chain in which a retailer faces a random and price-sensitive demand, we derive conditions on a general demand function for which the retail price variation is higher than that of the wholesale price. The investigation is extended to a multi-stage supply chain in which the price at each stage is determined by a game theoretical framework. We illustrate the use of the conditions in identifying commonly used demand functions that induce RBP analytically and by means of several numerical examples.     

Controlling the bullwhip effect in a supply chain system with constrained information flows

The bullwhip effect problem is one of the most important issues in supply chain management. Limited information sharing increases the difficulty of reducing the bullwhip effect and leads to inefficient supply chain management. The purpose of this paper is to explore new ways to reduce the bullwhip effect in supply chain systems that face uncertainties with respect to information sharing. We first present a supply chain state transition model, based on which we explore the endogenous mechanism of bullwhip effect, especially those related to impacts from limited information sharing. Then we propose a novel inventory control method and study the corresponding control optimization problem, with the aim of reducing inventory volatility in supply chains. Both quantitative analysis and simulation study are conducted. Simulation results show the effectiveness and flexibility of our proposed method in reducing bullwhip effect and in improving supply chain performance, even under conditions of limited information sharing.     

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.     

A robust optimization approach to reduce the bullwhip effect of supply chains with vendor order placement lead time delays in an uncertain environment

Supply chain management is important for companies and organizations to improve their business and enhance competitiveness in the global marketplace. The bullwhip effect problem of supply chain systems with vendor order placement lead time delays in an uncertain environment is addressed in this paper. Among the numerous causes of bullwhip effect, we focus on uncertainties with respect to demand, production process, supply chain structure, inventory policy implementation and especially vendor order placement lead time delays. Minimizing the negative effect of these uncertainties in inducing bullwhip effect creates a need for developing dynamical inventory policy that increases responsiveness to demand and decreases volatility in inventory replenishment. First, a dynamic model of supply chain with above uncertainties is developed. Then, a novel uncertainty-dependent robust inventory control method using inventory position information is proposed. Additionally, the maximum allowable vendor order placement lead time delay that ensures the stability of supply chains and the suppression of bullwhip effect under the proposed inventory control policy is explored and measured. We find that vendor order placement lead time delays do play important role in supply chain dynamics and contribute to its turbulence and volatility. The effectiveness and flexibility of proposed method is verified through simulation study.     

Robust tests for the bullwhip effect in supply chains with stochastic dynamics

This paper analyzes the bullwhip effect in single-echelon supply chains driven by arbitrary customer demands and operated nondeterministically. The supply chain, with stochastic system parameters, is modeled as a Markovian jump linear system. The paper presents robust analytical conditions to diagnose the bullwhip effect and bound its magnitude. The tests are independent of the customer demand. Examples are given. Ordering policies that pass these tests, and thus avoid the bullwhip effect in random environments for arbitrary customer demands, are shown to exist. The paper also presents possible extensions to multi-echelon chains.     

Bullwhip effect in a supply chain model with multiple delivery delays

We develop a model of differential equations for a supply chain with delivery time delays between every adjacent firms. Based on the supply chain model, we provide a new perspective of the bullwhip effect and show that the bullwhip effect is intrinsic in supply chains in the sense that the equilibrium state of each firm in the supply chain is a cumulative forward product of the ratios of order fulfillment and placement between adjacent firms toward the end customer demand. We also show that it is the multiple time delays instead of the constant end consumer demand that determine the stability of the equilibrium states. However, the consumer demand has impacts on the stability of the equilibrium states of the supply chain when the end retailer’s inventory decisions are linearly related to the end consumer demand.     

The effect of replenishment policies on the bullwhip effect: A transfer function approach

An important phenomenon in supply chain management, known as the bullwhip effect, suggests that demand variability increases as one moves up a supply chain. This paper examines the influence of different replenishment policies on the occurrence of the bullwhip effect. The paper demonstrates that certain replenishment policies can in themselves be inducers of the bullwhip effect, while others inherently lower demand variability. The main causes of increase in variability are projections of future demand expectations, which result in over-exaggerated responses to changes in demand. We suggest that through appropriate selection and use of certain replenishment rules, the bullwhip effect can be avoided, subsequently allowing supply chain management costs to be lowered.     

The bullwhip effect in supply chain networks

This paper analyzes the propagation and amplification of order fluctuations (i.e., the bullwhip effect) in supply chain networks operated with linear and time-invariant inventory management policies. The supply chain network is allowed to include multiple customers (e.g., markets), any network structure, with or without sharing information. The paper characterizes the stream of orders placed by any supplier for any stationary customer demand processes, and gives exact formulas for the variance of the orders placed and the amplification of order fluctuations. The paper also derives robust analytical conditions, based only on inventory management policies, to predict the presence of the bullwhip effect for any network structure, any inventory replenishment policies, and arbitrary customer demand processes. Numerical examples show that the analytical results accurately quantify the bullwhip effect; managerial insights are drawn from the analysis. The methodology presented in this paper generalizes those in previous studies for serial supply chains.     

Application of machine learning techniques for supply chain demand forecasting

Full collaboration in supply chains is an ideal that the participant firms should try to achieve. However, a number of factors hamper real progress in this direction. Therefore, there is a need for forecasting demand by the participants in the absence of full information about other participants’ demand. In this paper we investigate the applicability of advanced machine learning techniques, including neural networks, recurrent neural networks, and support vector machines, to forecasting distorted demand at the end of a supply chain (bullwhip effect). We compare these methods with other, more traditional ones, including naïve forecasting, trend, moving average, and linear regression. We use two data sets for our experiments: one obtained from the simulated supply chain, and another one from actual Canadian Foundries orders. Our findings suggest that while recurrent neural networks and support vector machines show the best performance, their forecasting accuracy was not statistically significantly better than that of the regression model.     

Inventory control of supply chains: Mitigating the bullwhip effect by centralized and decentralized Internal Model Control approaches

In this paper, a two-degrees-of-freedom Internal Model Control structure is incorporated in production inventory control for a supply chain system. This scheme presents an intuitive and simple parametrization of controllers, where inventory target tracking and disturbance (demand) rejection in the inventory level problems are treated separately. Moreover, considering that the lead times are known, this scheme presents a perfect compensation of the delay making the stabilization problem easier to handle. This control structure is formulated for a serial supply chain in two ways (by using a centralized and a decentralized control approach). The behavior of these inventory control strategies is analyzed in the entire supply chain. Analytical tuning rules for bullwhip effect avoidance are developed for both strategies. The results of controller evaluations demonstrate that centralized control approach enhances the behavior with respect to the inventory target tracking, demand rejection and bullwhip effect in the supply chain systems.     

The incremental bullwhip effect of operational deviations in an arborescent supply chain with requirements planning

Lee et al. (1997) advocated the idea of sharing demand and order information among different supply chain entities to mitigate the bullwhip effect. Even with full supply chain visibility afforded by IT systems with requirements planning and with no information distortion, we identify a “core” bullwhip effect inherent to any supply chain because of the underlying demand characteristics and replenishment lead times. In addition, we quantify an incremental bullwhip effect as various operational deviations (inaccurate order placements, batching, lag in sharing demand forecast) contribute incrementally to the variance of the order quantity not only at the node where the deviation is taking place but also at all upstream supply chain nodes. We discuss some managerial implications of our results in the context of a UK manufacturer.     

Modeling and analysis of the causes of bullwhip effect in centralized and decentralized supply chain using response surface method

The “bullwhip” effect is a major cause of supply chain deficiencies. This phenomenon refers to grow the amplification of demand or inventory variability as it moves up the supply chain. Supply chain managers experience this variance amplification in both inventory levels and orders. Other side, dampening variance in orders may have a negative impact on customer service due to the increase in the inventory variance. This paper with simulating a three stage supply chains consisting of a single retailer, single wholesaler and single manufacturer under both centralized and decentralized chains. In this paper, it is intended to analysis the causes of bullwhip effect from two dimensions of order and inventory variance using the response surface methodology. The results show that in both supply chains, rationing factor is considered as the least important cause of bullwhip effect. While the wholesaler’s order batching and the chain’s order batching are considered as the main causes for the bullwhip effect in the decentralized and centralized chains, respectively.     

Contracting with asymmetric demand information in supply chains

We solve a buyback contract design problem for a supplier who is working with a retailer who possesses private information about the demand distribution. We model the retailer’s private information as a space of either discrete or continuous demand states so that only the retailer knows its demand state and the demand for the product is stochastically increasing in the state. We focus on contracts that are viable in practice, where the buyback price being strictly less than the wholesale price, which is itself strictly less than the retail price. We derive the optimal (for the supplier) buyback contract that allows for arbitrary allocation of profits to the retailer (subject to the retailer’s reservation profit requirements) and show that in the limit this contract leads to the first-best solution with the supplier keeping the entire channel’s profit (after the retailer’s reservation profit).     

The effect of information sharing on supply chain stability and the bullwhip effect

This paper analyzes the bullwhip effect in multi-stage supply chains operated with linear and time-invariant inventory management policies and shared supply chain information. Such information includes past order sequences and inventory records at all supplier stages. The paper characterizes the stream of orders placed at any stage of the chain when the customer demand process is known and ergodic, and gives an exact formula for the variance of the orders placed. The paper also derives robust analytical conditions, based only on inventory management policies, to predict the presence of the bullwhip effect and bound its magnitude. These results hold independently of the customer demand. The general framework proposed in this paper allows for any inventory replenishment policies, any ways of sharing and utilizing information, and any customer demand processes. It is also shown as a special case that sharing customer demand information across the chain significantly reduces, but does not completely eliminate, the bullwhip effect.     

Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

Impact of replenishment rules with endogenous lead times on supply chain performance

This text summarizes the PhD thesis of Robert Boute, obtained at the Katholieke Universiteit Leuven (Belgium) under supervision of Marc Lambrecht. This doctoral dissertation in the field of Supply Chain Management demonstrates that significant cost reductions can be obtained for both the retailer and the manufacturer when they align their replenishment policy. Such a collaboration strategy goes far beyond “information sharing”. In this summary, we present the research model, the general outline of the thesis and the methodology used. The PhD thesis, written in English, is available from the author upon request.