Managing Supply Chain Demand Variability: The Bullwhip Effect


Mr. Saroj Kumar Dash
Skyline Institute of Engineering and technology
Greater Noida

1. Introduction

In a typical supply chain, there is a flow of funds, goods and information. All kinds of interactions are important for the well being of supply chain since there are different parties and their interests involved. Every stage in the chain tries to increase its pie of profit via its operations with downstream and upstream. Moreover, interests of the parties generally conflict with each other. For instance manufacturers' objective of making large production batches conflicts with the inventory reduction objective of the warehouses and distribution centers [1]. However, the parties that compose the chain have different advantages against each other. Manufacturer has the advantage of supplying the products demanded and lower levels have the advantage of reaching demand information, retailer having the most precise demand information of the end customer since it faces the customer. Coordination is dependent on the arrangements between the links in the chain. The problem is whether the owner of the information shares it with the others or not. Precise information is very crucial since all the decisions related with orders and production is tied to it. Accurate information will help to make better forecasts, enable lead-time reductions and give way to higher service levels. So, manufacturers will face lower variances and they will be capacity wise more transparent to retailers. Maybe retailers might be given more initiative such as revenue sharing in order to cooperate for information issue.

This proposal basically deals with the information flow and a problem related with it. Bullwhip effect (or alternatively whiplash effect) is the distortion in demand information in a supply chain. There is a common situation that retail orders to manufacturer do not coincide with the actual retail sales. The following figure taken from Lee et al. [2] illustrates this situation clearly.

There are several reasons behind this problem such as demand signal processing, rationing game, order batching and price variations [2]. Moreover, as lead times increase, variability also increases. Retailers order from upstream according to the demand realizations occurred; they see realizations as signals of future demand. If forecast of the future demand is done accurately, life will be easier for all the parties in the chain. Furthermore, retailers want economies of scale in pricing so that they batch their orders rather than frequent orders in small amounts; they prefer fewer orders in larger amounts. Rationing is the situation, where demand of retailers outstrips the supply and manufacturer rations the products according to the ordered amounts to the retailers. Price variations lead to an uncertain market and variability in demand and this is reflected to higher levels of the chain in exaggerated amounts.

Since bullwhip effect is an important phenomenon for supply chains, there should be a way to quantify it somehow so that the severity of the problem can be understood. There were previous studies that aim at defining and quantifying the bullwhip effect. This research basically aims to focus on quantifying bullwhip effect in a multi retailer supply chain.

2. Literature Review

There are several studies on bullwhip effect in literature. Lee et al. [2] has a research on bullwhip effect, defining the phenomenon and analyzing the causes of it. There are precautions suggested to hedge against bullwhip problem in this study. In this paper, symptoms of bullwhip effect are listed as excessive inventory, poor product forecasts, insufficient or excessive capacities, poor customer service, uncertain production planning and high costs. This is a basic study in literature that deals with the preliminaries of bullwhip effect.  Moreover, Beer Distribution Game, which was developed at MIT in 1960's, is a successful tool to visualize the bullwhip effect. There are four roles, namely retailer, wholesaler, distributor and manufacturer, which try to satisfy demand in lower levels in the chain. The parties do not know the actual demand figures downstream, but the order amount from one level down. The resulting orders are highly variable specifically in upper levels. Because safety inventory held by one level is supposed to be the actual demand figure for the supplier and all plans are made accordingly. One scenario lets all of the players to see the customer demand. This time, information availability decreases the variability. Consequently, this game illustrates the bullwhip phenomenon very effectively.

Disney and Towill have a study on the effects of vendor-managed inventory on bullwhip effect reduction Simulation models are presented to show manufacturer's ordering decisions. Important results gathered from this study are:

  • With VMI implementation two sources of the bullwhip effect may be completely eliminated, i.e. rationing game or the Houlihan effect, and the order batching effect or the Burbidge effect.
  • VMI is also significantly better at responding to rogue changes in demand due to the promotion effect or to price induced variations.
  • VMI offers a significant opportunity to reduce the bullwhip effect in real-world supply chains.

Lee et al. [4] has a study on value of information sharing in a two level supply chain. The authors are dealing with the benefits of information sharing here. They claim that information sharing could provide significant inventory reduction and cost savings to the manufacturer. Moreover, they show that underlying demand process and the lead times have significant impact on the magnitudes of cost savings and inventory reductions that come along with information sharing. Demand is characterized by AR (1) process in this research. Retailer observes inventory level after demand materializes and places its order; the process is the same with the one that we will be applying in our model with multiple retailers. Backordering is permitted. At manufacturer side, demand is met one way or another. If manufacturer does not have enough resources on hand, it has to meet the demand from an alternative source. Ordering decisions of the parties are analyzed, manufacturer's decision is analyzed with and without information sharing. As a result it is presented that retailer's cost is not affected by information sharing whereas manufacturer's cost is decreased in case where information is shared. Moreover, it is concluded that if demand is highly correlated over time, highly variable or lead-time is long; manufacturer gains large reductions when information is shared among members of the chain.

Cachon [6] has a paper on supply chain demand variability with scheduled ordering policies. There are one-supplier and N retailers that face stochastic demand. The main result of this study is that the supplier's demand variance will generally decline as the retailers' order interval is lengthened or as their batch size is increased. Moreover, there are five variables presented that influence the supplier's demand variance. Two of the variables are structural: consumer demand variability and the number of retailers. Remaining three variables are policy parameters, which are the retailers' batch size; the retailers' order interval length, and the alignment of the retailers' order intervals. Furthermore, Cachon and Fisher have a study on supply chain inventory management and value of shared information. They analyzed the value of sharing information in a model with one supplier, N identical retailers, and stationary stochastic consumer demand. They compare a traditional information policy that does not use shared information with a full information policy that does exploit shared information. In a numerical study they find that supply chain costs are 2.2% lower on average with the full information policy than with the traditional information policy, and the maximum difference is 12.1%. In full information gathering policy, supplier reaches the inventory position data of the retailers. However, this study concludes that cost reductions via full information are not very significant; there can be more reductions via lead-time and batch size related differences.

The inspiring study behind this proposal is the Chen et al.'s "Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times and Information". This study intends to be an extension to that study. The distinguishing feature of the model to be analyzed is the multi retailer environment set here rather than a two-stage chain with one retailer only. An in depth reference will be given to that study since the proposal is an extension. Chen et al. considers a supply chain, a single retailer observes its inventory level and places its order to a single manufacturer. After order is given, retailer fills customer demand for the period. Unmet demands can be backlogged. There is a fixed lead-time, L, between placement of orders and receipt of the orders. They assume order-up-to inventory policy. The forecast method is simple moving average, where p is number of periods to base the forecast on. There are analyses with the scenarios in which excess inventory is returned and not returned. It is found that the way one treats excess inventory has little impact on the increase in variability for different values of p and , which is the correlation parameter for demand process. Moreover, when forecasts are dependent on larger p values, increase in variability is negligible. Also, one of the results is that when lead times increase, variability increases. Correlation coefficient related results are such that if the demands are positively correlated, variability is smaller and when the demands are negatively correlated for even values of p, the variability will be smaller whereas the variability will be higher for odd values of p. Furthermore, in a multistage supply chain, where all demand information is shared by all parties, and the same forecasting technique is used by all, the bullwhip effect will not be completely eliminated. In addition to those results, it is found that for supply chains with centralized demand information, increase in variability at each stage is an additive function of the lead time and the lead time squared, while for supply chains without centralized information increase in variability is a multiplicative. Thus, centralizing demand information can significantly reduce the bullwhip effect. One of the drawbacks of this paper is the lack of complexities related with real supply chains. Ryan has a study on multi retailer case but there are not any other researches on this issue in the literature. The motivation lies in here.

3. Model and Research Questions to be Analyzed  

In this study, we will be following Chen et al. study as a roadmap as mentioned before. In this study there will be one manufacturer and multiple retailers. The number of retailers will be N. All of the retailers will be using the same forecasting technique and order lead times for each one of them will be fixed and equal to L.

In each period t, N retailers observe their inventory level and order qit, where i = 1, 2, , N. After the placement of orders, retailers meet customer demand Dti . Backlogging is allowed. If retailers order at time t, they will receive at t+L.

Customer demand is characterized as:

Dti= + D(t-1)i+ti     for each i= 1,2,,N;  the same in Chen et al. paper.

Demands are i.i.d. with and 2 . Moreover, retailers follow order-up-to policy, where order-up-to point is yt :

Retailers use a simple moving average to estimate and . Variance is dependent on CL,p, a constant function of L, and p. A detailed discussion of C function is given in Ryan (1997) [8]. Manufacturers are assumed to receive orders at the amount of sum of individual orders of N retailers.

The main focus of the research will be quantifying the bullwhip effect in a multi retailer environment. Specifically, we will be searching the answers for the following questions:

  • What will change when there are multiple retailers rather than one retailer and one manufacturer? Can the relations set in Chen's model be extended in linear form for this scenario?
  • What are the effects of demand forecasting and order lead times to bullwhip effect in multi retailer case?
  • Can we treat N retailers as a single retailer and order quantity as the sum of order quantities of N individual retailers?
  • What are the complications related with the forecasting techniques of different retailers? What if they do not use the same method to make forecasts?
  • What is the picture like in multi stage system with multiple retailers?
  • What are the results for multi retailer case when demand between retailers is positively correlated negatively correlated, uncorrelated?

We expect the model to give the same results for the N retailer case with the single retailer case since we treat order quantities and demands as summation of N items to be incorporated in the model as one variable. When ordering of retailers are balanced, not correlated, bullwhip effect is expected to be lower since variations in individual orders offset each other.

Moreover, we expect bullwhip effect not to be completely eliminated by centralizing demand information. That means when the manufacturer also reaches demand information of the retailers.

Furthermore, we expect to have smaller variability when demand forecasts are dependent on longer time periods (p is large). Also, if lead times are long, the variability is expected to be greater. With centralized demand information, we expect increase in variability to be an additive function of lead time and lead time squared whereas in without centralized demand information case this value should be a multiplicative function of lead time and lead time squared.

We again expect to have larger variances in upper levels of the supply chain if we are concerned about a multi stage multi retailer scenario, which is in the very heart of the Bullwhip problem. In a multi stage chain making these analyses with multiple retailers will be realistic and helpful for both academia and practitioners.    

4. Solution Methodology

The main motivation behind this proposal was said to be Chen et al. paper. Since this is aimed to be an extension, same methodologies will be used to quantify bullwhip effect. Lead times and demand forecasting will be the main aspects to be analyzed for a multi retailer case.

The extension of multi retailers will be in the form of quantities ordered by N retailers rather than one retailer. This will be a summation of individual quantities of all the retailers and the demands faced by retailers will again be additive. N retailers will face the demand Dij , which is a random variable. Total demand will be the summation of Dij's. All of the retailers are assumed to use simple moving average forecasting technique. We will be quantifying the bullwhip effect via using Chen's methodology, so that the variance of order quantities will be compared to the demand variability in the form of:

Since lead times are all the same for all retailers and they will be assumed to use same forecasting technique with the same p value, findings presented by Chen et al. should be validated again. 

Bullwhip problem is an important one among the problems related with supply chain. Costs associated with the demand variability are high and bitter for the parties especially that are in the upper levels of the chain. There is an urgent need for solution methodologies in this area. Therefore, researches on this area are critical and may be life saving.


1. Simchi-Levi D., Kaminsky P., Simchi-Levi E. (2003) Designing and Managing the Supply Chain, Concepts, Strategies and Case Studies (p.3). New York: McGraw Hill.

2. Lee H.L., Padmanabhan V., Whang S. (1997) Information Distortion in a Supply Chain: The Bullwhip Effect. Management Science Vol.43, No.4 (pp.546-558).

3. Disney S.M. and Towill D.R. (2203) Vendor-managed inventory and bullwhip reduction in a two-level supply chain. International Journal of Operations and Production Management
, Vol. 23 Issue 6 (pp.625-651)

4. Lee H.L., So K.C., Tang C.S. (2000) The Value of Information Sharing in a Two-Level Supply Chain. Management Science Vol.46, No.5 (pp.226-243)

5. Chen F., Drezner Z., Ryan J.K., Simchi-Levi D. (2000) Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times and Information. Management Science Vol.46, No.3 (pp.436-443)

6. Cachon G. (1999) Managing Supply Chain Demand Variability with Scheduled Ordering Policies. Management Science Vol.45, Issue 6 (pp.843-856)

7. Cachon G. and Fisher M. (2000) Supply Chain Inventory Management and the Value of Shared Information. Management Science Vol.46, Issue 8 (pp.1032-1048)

8. Ryan, J. K. (1997) Analysis of inventory models with limited demand information. Ph.D. Dissertation, Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL.

Managing Supply Chain Demand Variability : The Bullwhip Effect

Mr. Saroj Kumar Dash
Skyline Institute of Engineering and technology
Greater Noida

Source: E-mail February 27, 2006


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