THE BULLWHIP EFFECT

THE BULLWHIP EFFECT

the influence of demand information sharing in a two-level supply chain

Joyce Popping

Masterthesis Operations Research

Supervisor: prof. dr. R.H. Teunter

The bullwhip effect:

the influence of demand information sharing in a two-level supply chain

Joyce Popping, University of Groningen July 4, 2016

Abstract

An important phenomenon observed in supply chains that reduces the efficiency of these chains is called the bullwhip effect. The bullwhip effect refers to the phe- nomenon of demand variability amplification as one moves up the supply chain.

In the literature on the bullwhip effect, the papers of Lee et al. (2000) and Chen

et al. were given a strong academic interest. In these papers it was shown that

the bullwhip effect is reduced by demand information sharing. However, the com-

parison made in these papers is unfair, since the difference between the service in

the two situations is not taken into account. Therefore, in this thesis a comparison

between the bullwhip and service performance is made. This thesis shows that

there is a benefit of demand information sharing, but that it is much smaller than

previously thought.

Contents

1 Introduction 5

2 Literature review 7

3 Model 9

3.1 Model description . . . . 9

3.2 Assumptions . . . . 9

3.3 Notation . . . . 10

3.4 Customer demand . . . . 11

3.5 Retailer . . . . 11

3.5.1 Forecasting technique . . . . 11

3.5.2 Inventory policy . . . . 12

3.6 Manufacturer (DIS) . . . . 12

3.6.1 Forecasting technique . . . . 12

3.6.2 Inventory policy . . . . 12

3.7 Manufacturer (NIS) . . . . 12

3.7.1 Forecasting technique . . . . 13

3.7.2 Inventory policy . . . . 13

3.8 Service level . . . . 13

3.9 Simulation model . . . . 14

4 Results 15 4.1 Experimental design . . . . 15

4.2 Experiment 1: the base case . . . . 15

4.2.1 The bullwhip effect . . . . 16

4.2.2 The service level . . . . 16

4.2.3 Trade-off holding costs vs service . . . . 17

4.3 Experiment 2: variation of the number of consecutive periods T . . . . . 17

4.4 Experiment 3: variation of the number of periods for moving average N . 19 4.5 Experiment 4: variation of the mean demand µ. . . . 21

4.6 Experiment 5: variation of the standard deviation of demand σ. . . . 22

4.7 Experiment 6: variation of the desired service of the retailer z

. . . . 23

4.8 Experiment 7: variation of the lead time `

and `

. . . . . 24

4.9 Experiment 8: variation of the correlation coefficient ρ. . . . 25

5 Conclusion 27

1 Introduction

Creation and sale of goods often involves a number of companies operating as a serial supply chain. Typically, suppliers provide raw material to manufacturers, who on their turn supply finished good to wholesalers. The wholesalers combine many products of manufacturers for sale to retailers. Finally the retailers sell these products to customers.

Beside this physical flow of goods downstream the supply chain, there is an information flow about demand, upstream the chain. Traditionally, only the last stage in the supply chain, the retailer, faces the demand of customers. The demand seen by other stages in the chain consists of orders from downstream companies. For example, the demand faced by a manufacturer consists of orders from wholesalers [Metters, 1997].

The goal of many industries is to improve the efficiency of their supply chains. They can improve the efficiency by matching supply and demand in such a way that they reduce the costs of inventory and stockouts. If they are able to do so, this will lead to great cost savings. But a phenomenon observed in these chains, which counteracts the efficiency, is the bullwhip effect. This effect can create problems such as excessive inventories or shortages and poor customer service due to unavailability of products or long backorders [Lee et al., 2000]. Clearly, companies would like to avoid this phenomenon.

The bullwhip effect, also known as the whip-lash or whip-saw effect refers to the phe- nomenon of demand variability amplification as one moves up the supply chain. The first writing an academic paper about this phenomenon is Forrester [1961]. In his pa- per he discusses its causes and remedies in the context of industrial dynamics. His work inspired many authors to do research on the bullwhip effect. The existence of the bullwhip effect is described in various papers. In direct response to the paper of Forrester, Sterman showed the existence of the bullwhip effect in the ”beer distribution game”. In this game participants simulate a supply chain consisting of a beer retailer, wholesaler, distributor and brewery. The game shows that a small change in customer demand variability can result in large orders and inventories upstream the supply chain [Sterman, 1989]. Besides the existence of the bullwhip effect in this game, the presence of the bullwhip effect was observed in many real industries as well. For example in the Textile Industry [Zymelman, 1965], Hewlet-Packard (HP) [Lee et al., 2004] and Phillip Electronics [de Kok et al., 2005].

Not only the existence of the bullwhip effect was investigated, but the sources of this effect were discussed as well. Lee et al. [2004] proposed four sources of the bullwhip ef- fect in their paper: demand signal processing, rationing game, order batching and price variations. Other causes of the bullwhip effect, such as the lead time, the replenishment rule, behavioral aspects of managers and overestimation were described in, for example, [Chen et al., 2000], [Dejonckheere et al., 2003], [Croson and Donohue, 2006] and [Sucky, 2009].

Since the bullwhip effect can create problems such as excessive inventory and poor cus- tomer service, research on strategies to counter the bullwhip effect has been done as well.

Sharing sales information has been viewed as the major strategy to counter the bullwhip

effect. By letting all companies in the supply chain have complete information on cus-

tomer demand, the bullwhip effect can be reduced. Different successive implementations

of demand information sharing were described. The most celebrated implementation is

Wal-Mart’s Retail Link program. In this program an online summary of customer de-

mand information was provided to suppliers such as Johnson and Johnson and Lever

Brothers [Lee et al., 2000].

Furthermore, the benefits of information sharing were quantified. Bourland et al. [1996], Cachon and Fisher [2000] and Gavirneni et al. [1999] quantified the value of informa- tion sharing between manufacturers and retailers for different cases. In the paper of Bourland et al. the case in which the review periods do not necessarily coincide is considered. They showed that a reduction of inventories due to demand information sharing depends on demand variability, the service level provided by the supplier and the degree to which the order and production cycles are out of phase. Cachon and Fisher compared the value of information sharing to reducing lead times and increasing delivery frequency by reducing shipment batch sizes. They showed that the latter is significantly more valuable than to expand the flow of information. Next, Gavirneni et al. examined the case in which the manufacturer has limited capacity. In these three papers the demand processes is assumed to be independent and identically distributed.

Lee et al. [2000] quantified the benefits of information sharing in a two-level supply chain, consisting of one manufacturer and one retailer where the underlying demand process is autocorrelated. They showed that in this case, the value of information sharing provides benefits to the manufacturer in two ways: a reduction of inventory and expected costs.

Regarding the research on the bullwhip effect, this paper of Lee et al. has received a strong academic interest. A look at the database of Web of Science shows that this paper has been cited 687 times. This paper was the basis of a lot of other papers such as Cui et al. [2013], Wagner [2015] and Yan and Pei [2015].

Lee et al. compared in their paper the bullwhip effect under demand information sharing (DIS) to the situation with no demand information sharing (NIS). They compared the bullwhip, which refers to increasing swings in inventory in response to shifts in customer demand, in these situations by comparing variances of the manufacturer’s orders based on customer demands (DIS), to manufacturer’s orders based on retailer demands (NIS).

In the situation of demand information sharing both, the service of the manufacturer to the retailer and as a result the service of the retailer to the customer are poorer than in the situation of no information sharing. The service is in this case poorer, because the safety stocks are lower than in the case of no demand information sharing (NIS), since they are based on customer demand instead of retailer’s orders. Since the service of the manufacturer to the retailer as well as the service of the retailer to the customer is poorer in the case of demand information sharing (DIS), the comparison of variances as done in the paper of Lee et al. is unfair, as will be shown in this thesis. A comparison based on both, the bullwhip and service performance shows that there is a benefit of sharing demand information as mentioned in [Chen et al., 2000], but that it is much smaller than previously thought.

This thesis is structured as follows. In Chapter 2 the literature is reviewed on the bull-

whip effect. In Chapter 3 the two-stage supply chain model used for the simulations is

described, as well as the assumptions made in this models and the notation used. Fur-

thermore, the customer demand model is described as well as the forecasting technique

and inventory policy used by the retailer and manufacturer. For the manufacturer two

situations are discussed, the situation of demand information sharing and the situation

of no information sharing. In Chapter 4 the results of the simulations are discussed and

Chapter 5 contains a conclusion and ideas for further research.

2 Literature review

In this section the literature is reviewed on the bullwhip effect.

Forrester was the first academic writing about the bullwhip effect. In Industrial Dynam- ics (1961) he described that it was empirically common that the variance of demand to the manufacturer exceeds the variance of customer demand. Furthermore, he discussed that this effect amplifies as one moves up the supply chain. He ascribed this effect to difficulties in the information feedback loop between companies. According to Forrester, the bullwhip effect can be reduced by understanding the system as a whole. Therefore, the system should be modeled with ’system dynamics’ simulation models [Forrester, 1961].

In direct response to the work of Forrester, Sterman showed the existence of the bullwhip effect in an experiment. In the experiment, a role-playing simulation of the industrial production and distribution of beer is played by thousands of people all over the world.

The game, called the ”Beer Distribution Game”, was developed by Forrester together with a group of academics at MIT. In the game, a supply chain consisting of a retailer, wholesaler, distributor and factory is simulated. Sterman used the game to show that a small change in customer demand variability can result in large orders and inventories upstream the supply chain. So, he showed the existence of the bullwhip effect in the

”Beer Distribution Game” [Sterman, 1989].

A few years earlier, Kahn found evidence for the bullwhip effect as well. In his paper, he presented a production and inventory behavior model with nonnegativity constraints on inventories. The model is a two-level supply chain model consisting of a firm and a single customer. In the model, customer demand shows positive serial correlation and the firm has the ability to backlog excess demand. Kahn found that the variance of production will exceed the variance of sales, even if there are no productivity shocks.

Hence, he showed that productivity smoothing in the face of fluctuating demand is not that important to avoid the bullwhip effect [Kahn, 1987].

Where Kahn showed the existence of the bullwhip effect in a two-level supply chain, Baganha and Cohen did this in a multi-stage supply chain. They developed a model to analyze the stabilization effect of inventories in multi-echelon supply chains. With their model they explained the bullwhip effect, but they also presented some cases in which the bullwhip effect is not present. In these cases, inventories have a stabilizing effect.

The stabilizing effect is based on on the interaction of cost, technology and market at- tributes. Furthermore, they found that the inventory control policies utilized at each echelon of the chain affect the stabilization [Baganha and Cohen, 1998].

Metters showed that it is profitable to avoid the bullwhip effect. In his paper he ex- pressed the significance of the bullwhip effect in monetary terms. He found that the importance of the bullwhip effect depends a lot on the specific business environment.

However, his results showed that eliminating the bullwhip effect can improve the prof- itability by 10-30% [Metters, 1997].

But to avoid the bullwhip effect, it is important to know its sources. Therefore, Lee et al. (2004) analyzed four sources of the bullwhip effect: demand signal processing, rationing game, order batching and price variations. They showed that each of these effects is capable of generating rational behaviors that result in the bullwhip effect.

Furthermore, they discussed that sharing sell-through data and information on inven-

tory status with downstream links can help mitigate the bullwhip effect [Lee et al., 2004].

The fact that sharing demand information can help mitigate the bullwhip effect was mentioned before. The paper of Bourland et al. was an opening contribution to the analytic study of sharing demand information. They studied a simple two-level supply chain consisting of a supplier and a single customer. Remarkable in this model, is the assumption that the equal-length production cycles of the levels do not necessarily co- incide. With this model they investigated the possible benefits of demand information sharing for the supplier. The possible benefits for the supplier are a reduction of invento- ries and/or an increase in the service to its customer. Furthermore, they discussed that these benefits are influenced by the demand variability, the service level at the supplier and the degree of which the order and production cycles are out of phase [Bourland et al., 1996].

Cachon and Fisher studied the value of information sharing as well. They investigated the value of information sharing in a model with one supplier, a number of identical retailers and stationary stochastic demand. They compared a traditional information policy in which information is not shared with a full information sharing policy in which the information about customer demand is known in all stages. They found that the supply chain costs in the latter case are lower than in the traditional case, as expected.

Furthermore, they found the remarkable result that simply flowing goods through the supply chain more quickly and evenly produced, results in greater costs savings than information sharing [Cachon and Fisher, 2000].

Where Cachon and Fisher and Bourland et al. examined the benefits of demand infor- mation sharing in the case of independent and identically distributed demand, Lee et al.

(2000) investigated the situation in which the demand is autocorrelated. They studied this situation in a two-level supply chain. Lee et al. quantified the benefits of informa- tion sharing and identified the drivers that have significant impact. They found that the manufacturer obtains larger reductions in average inventory and average cost when the demand is highly correlated over time, or when the lead time is long [Lee et al., 2000].

In the paper of Chen et al. these results were extended to multi-stage supply chains.

They examined that the bullwhip effect is caused by demand forecasting. Furthermore, they showed that demand information sharing can significantly reduce the bullwhip ef- fect. However, the bullwhip effect will exist even when demand information is shared with each stage in the chain. Lee et al. [2000]

The papers of Lee et al. (2000) and Chen et al. were the reason for writing this thesis.

In these papers the bullwhip in the situation of demand information sharing is compared

to the situation of no information sharing, but the comparison is unfair. They did not

take into account, that in the case of demand information sharing, the service to the

customer is lower than in the case of no demand information sharing. In the case of

DIS, the service to the customer is actually lower that in the case of NIS, because in the

first case the safety stocks are higher than in the latter case. In this paper the service

is taken into account. The bullwhip in the situation of DIS and NIS is compared taken

into account the service performance.

3 Model

In this section, first the model is described, then the assumptions made in this model are discussed, as well as the notation used. After that the autocorrelated demand process used in this model is described as well as both, the retailer’s and the manufacturer’s or- dering processes. Furthermore, the way the service is determined and how the simulation model is built is discussed shortly.

3.1 Model description

Consider a two-stage supply chain consisting of a single retailer and a single manufac- turer. The inventory system of both the retailer and the manufacturer is controlled by a periodic review policy. Periodic review means that the inventory is inspected at regular moments in time. A period may be for example, a day, week or month. In this model, one period is equal to one week. For a model where the inventory is controlled by periodic review, the order of events is important. In the model used in this thesis, the order of events in each time period t is,

1. demand occurs;

2. inventories are determined.

3. the order is placed;

4. an order is received;

For the retailer this means that he faces and realizes customer demand at the begin of each time period t. After that, he places an order to the manufacturer to replenish his inventory. He will receive this order at the start of period t+`

, where `

is the lead time from manufacturer to retailer. We assume that any unfilled demands are backlogged.

Backlogging is common in many industries.

The manufacturer receives the retailer’s order and ships the required order to the retailer in each time period t. To replenish his inventory, he places an order Y

to an external supplier. He receives this order at the start of period t + `

, where `

is the lead time from the external supplier to the manufacturer. The manufacturer guarantees supply to the retailer. That means, if he has not enough stock to fill the order, he will obtain the required units from an ”alternative” source. The supplier also guarantees supply to the manufacturer, as is typically assumed in the inventory literature.

In each time period t, the retailer and the manufacturer have to determine how much to order to replenish their inventories. Therefore, they have to forecast customer demand.

There are different techniques to forecast this demand. In this model, a moving average is used, since this one is most widely used in practice. Furthermore, the retailer and the manufacturer have to use a certain inventory policy to replenish their inventory.

Here, an order-up-to policy is chosen. In section 3.3, the order-up-to policy, and the forecasting technique for both the retailer and the manufacturer are discussed in more detail. For the manufacturer, a distinction between the situation of demand information sharing (DIS) and no demand information sharing (NIS) is made.

3.2 Assumptions

Summarizing, the following assumptions are made in the model:

• Assumption 1 : Customer demand is serially correlated.

• Assumption 2 : A periodic review policy is used. In each period the order of events is: demand, determination of inventories, order and delivery.

• Assumption 3 : Excess demand is backlogged at both levels.

• Assumption 4 : Orders are delivered after a fixed lead time.

• Assumption 5 : The manufacturer guarantees supply to the retailer.

• Assumption 6 : A simple moving average is used to forecast demand.

• Assumption 7 : An order-up-to policy is used to replenish the inventory.

3.3 Notation

In the model, the following notation is used:

input

n: number of replications;

T : number of consecutive periods;

N : number of periods for moving average;

µ: mean customer demand;

σ: standard deviation of customer demand;

ρ: correlation coefficient;

`

: lead time from manufacturer to retailer;

`

: lead time from external supplier to manufacturer;

z

: safety stock factor of retailer;

z

: safety stock factor of manufacturer;

customer demand

D

: random variable denoting customer demand in period t;

retailer

F

: forecast of the lead time demand by the retailer in period t;

M SE

: forecast of the MSE of the lead time demand by the retailer in period t;

S

: order-up-to point of the retailer in period t;

Y

: size of the retailer’s order in period t;

IL

: inventory level of the retailer in the case of demand information sharing (DIS) in period t;

manufacturer (DIS)

F

forecast of the lead time demand by the manufacturer in the situation of demand information sharing (DIS) in period t;

M SE

: forecast of the MSE of the lead time demand by the manufacturer in the situation of demand information sharing (DIS) in period t;

S

: order-up-to point of the manufacturer in the situation of demand information sharing (DIS) in period t;

Y

: size of the manufacturer’s order in the situation of demand information sharing (DIS) in period t;

IL

: inventory level of the manufacturer in the case of demand information

sharing (DIS) in period t;

manufacturer (NIS)

F

forecast of the lead time demand by the manufacturer in the situation of NIS in period t

M SE

: forecast of the MSE of the lead time demand by the manufacturer in the situation of NIS in period t;

S

: order-up-to point of the manufacturer in the situation of NIS in period t;

Y

: size of the manufacturer’s order in the case of no information sharing

(NIS) in period t.

IL

: inventory level of the manufacturer in the case of demand information sharing (DIS) in period t;

3.4 Customer demand

The underlying demand process faced by the retailer is a simple autocorrelated AR(1) process. If customer demand in period t is denoted by D

, then

D

= µ + ρD

+ 

, (1)

where µ is a nonnegative constant, ρ is a correlation coefficient with | ρ |< 1 and 

is the error term in period t. The error terms, 

, are independent and identically distributed (i.i.d) from a normal distribution with mean 0 and variance σ

, i.e. 

∼ N (0, σ

).

Assume that σ is significantly smaller than µ, to make sure that the probability of having negative demand is negligible. If ρ = 0 in (1), the model amounts to a constant demand model. In this case, the demand is independent and identical distributed in each period t.

3.5 Retailer

In this subsection, the forecasting technique and the inventory policy of the retailer are considered.

3.5.1 Forecasting technique

The retailer uses a simple moving average to estimate the mean demand and the mean squared error of the demand forecast in period t based on the demand observations from the previous N periods. The mean demand in period t is estimated by

F

= P

i=1

D

N , (2)

and the mean squared error of the demand forecast in period t by

M SE

= P

i=1

(D

− F

)

N . (3)

The estimate of the mean lead time demand in period t is

F

= `

F

. (4)

The mean squared error of the lead time demand forecast in period t is estimated by

M SE

= `

M SE

. (5)

3.5.2 Inventory policy

The retailer follows an order-up-to policy. In each period t, he orders up to the point S

. This order-up-to point is estimated by

S

= F

+ z

q

M SE

, (6)

where F

is an estimate of the mean lead time demand as given in (4), M SE

is an estimate of the mean squared error of the lead time forecast as given in (5) and z

is a constant chosen to meet a desired service level. Hence, the retailer’s order quantity in period t is

Y

= D

+ S

− S

. (7)

3.6 Manufacturer (DIS)

In the case of demand information sharing, the manufacturer has complete information on customer demand, he uses this information to determine his order quantity.

3.6.1 Forecasting technique

Since the manufacturer has complete information on customer demand, he uses the same estimate of the mean demand in period t as the retailer uses, which is

F

= F

= P

i=1

D

N . (8)

An estimate of the mean squared error of the demand forecast in period t is given by

M SE

= P

i=1

(Y

− F

)

N . (9)

An estimate of the mean lead time demand in period t is given by

F

= `

F

. (10) The mean squared error of the mean lead time demand forecast in period t is given by M SE

= `

M SE

. (11) 3.6.2 Inventory policy

If demand information is shared, the manufacturer’s order-up-to point in period t is estimated by

S

= F

+ z

q

M SE

, (12) where F

is given in (10), M SE

in (11) and z

is a constant chosen to meet a desired service level. Hence, the manufacturer’s order quantity in period t is

Y

= Y

+ S

− S

. (13)

3.7 Manufacturer (NIS)

If information about customer demand is not shared with the manufacturer, the manu-

facturer determines his order quantity only based on retailer’s orders. Hence, manufac-

turer’s ”demand” corresponds to retailer’s orders.

3.7.1 Forecasting technique

Using a simple moving average, the mean demand in period t is estimated by

F

= P

i=1

Y

N . (14)

The mean squared error of the demand forecast in period t by

M SE

= P

i=1

(Y

− F

)

N . (15)

The estimate of the mean lead time demand in period t is

F

= `

F

. (16) The mean squared error of the lead time demand forecast in period t is estimated by

M SE

= `

M SE

. (17) 3.7.2 Inventory policy

In case of no information sharing, the order-up-to point of the manufacturer in period t is estimated by

S

= F

+ z

q

M SE

, (18) where F

is given in (16), M SE

in (17) and z

is a constant chosen to meet a desired service level. Hence, the manufacturer’s order quantity in period t is

Y

= Y

+ S

− S

. (19)

3.8 Service level

To determine the service level of the retailer and the manufacturer, the following defi- nition of the service level is used: the service level is the probability of no stockout per order cycle [Axs¨ ater, 2007]. Therefore, the number of stock-outs has to be determined to compute the service level. To determine whether there is a stockout, the inventory level is determined in each period t after customer demand is observed and before an order arrives. The inventory level of the retailer is determined as follows

IL

= IL

− D

, t = 1, . . . , `

+ 1, IL

= IL

+ Y

− D

, t = `

+ 2, . . . , T.

The inventory level of the manufacturer in the case of DIS is

IL

= IL

− Y

, t = 1, . . . , `

+ 1, IL

= IL

+ Y

− Y

, t = `

+ 2, . . . , T, and the inventory level of the manufacturer in the case of NIS

IL

= IL

− Y

, t = 1, . . . , `

+ 1, IL

= IL

Y

− Y

, t = `

+ 2, . . . , T.

There is a stockout if the inventory level is negative in period t. For T consecutive

time periods, the number of stock-outs is counted for the retailer, the manufacturer in

the case of DIS and the manufacturer in the case of NIS. Given these numbers, the service level of the retailer, the manufacturer (DIS) and the manufacturer (NIS) can be determined. For example, the service level of the retailer is

service retailer = 1 − # stock-outs of retailer

T .

The service level of the manufacturer in the case of DIS and the service level of the manufacturer in the case of NIS are determined in a similar way.

3.9 Simulation model

In MATLAB a simulation model is built to simulate the two-stage supply chain consist- ing of a single retailer and manufacturer as described above. In this simulation model a number of replications is performed to reduce the variability in the results, which leads to an increase in their significance. In each replication the inventory system of both the retailer and the manufacturer is simulated for T consecutive time periods. In each time period, a random demand occurs, after that, the inventory level of the retailer is determined, as well as the order-up-to level and the order quantity of the retailer. For the manufacturer, in each time period, an order of the retailer is received and then the inventory level of the manufacturer as well as the order-up-to level and the order quan- tity is determined. For the manufacturer this is done in two cases, the case of demand information sharing (DIS) and no demand information sharing (NIS). After this, the number of times that the inventory level is negative is determined for the retailer, the manufacturer (DIS) and the manufacturer (NIS). Based on these numbers, the service levels of these three are determined as described before. The service level of the re- tailer in the i-th replication is denoted by service

. Similarly, the service level of the manufacturer (DIS) in the i-th replication is service

and the service level of the manufacturer (NIS) in the i-th replication is service

. A number of such replica- tions is performed and the average service level of the retailer, the manufacturer (DIS) and the manufacturer (NIS) is computed. For example, the average service level of the retailer is determined as follows:

average service

= 1 n

n

X

i=1

service

,

where n is the number of replications. The average service level of the manufacturer

in the case of DIS (average service

) and in the case of NIS (average service

) are

determined in a similar way. The average service level of the manufacturer in the case

of DIS and NIS are compared to determine the influence of demand information sharing

on the service level of the manufacturer.

4 Results

In this section the results of the simulations are discussed.

4.1 Experimental design

The simulation model as described in the previous section is used to determine the in- fluence of demand information sharing on the service level of the manufacturer. 10 000 runs are performed in each experiment, since in this case the results are reliable, see Figure 1. In Figure 1 the number of runs performed is plotted against the achieved service level of the retailer when the target service level is equal to 0.95. The service level of the retailer remains the same after 10 000 runs.

Figure 1: The number of runs plotted against the service level of the retailer for a target service level of 0.95.

Below eight experiments are performed. In the first experiment a base case is considered.

After that all parameters in the base case are varied one by one to determine how robust the observations in the base case are in the rest of the experiments.

4.2 Experiment 1: the base case

First the base case is considered. In the base case the number of time periods T is equal to 10 000. The number of time periods used for the moving average is equal to 4, which means that the forecast is based on the demand data from the previous month.

The mean demand for one product is equal to 100, which is equal to the mean demand

used in the paper of Lee et al. [2000]. The standard deviation of the product is 20, this

value should not be to large compared to the mean demand, because otherwise there is

a probability of negative demand. For simplicity, ρ = 0 in the base case which means

that there is no correlation between demand in two consecutive time periods. This

assumption implies that customer demands are independent and identically distributed

in the base case. The lead-time from retailer to manufacturer and from external supplier

order-up-to order size stock on service

level mean variance hand level

retailer 249 100 754 84 0.9489

manufacturer (DIS) 259 100 1740 931 0.9355

manufacturer (NIS) 268 100 2030 1117 0.9472

Table 1: Simulation results for the base case, the target service levels of the retailer and the manufacturer are both 0.95.

to manufacturer is 2. Hence, an order is delivered after two weeks. The safety stock factor of the retailer, z

, is 1.64, which means that the desired service level of the retailer is 95%. The safety factor of the manufacturer is varied in this experiment. To start with, the safety stock factor of the manufacturer in both situations, z

and z

, is set to 1.64 as well. Hence, the desired service level of the manufacturer is the same as the desired service level of the retailer, which is 95%. This means that in 95% of the periods there is no stockout expected. The output of the simulation model for these values is given in Table 1. For normally distributed demand, the average order-up-to level is 200+1.64·20· √

2 = 246.39. Here, the demand is not totally normally distributed, therefore the average order-up-to level of the retailer is somewhat higher. Furthermore, the average order size of the retailer and the manufacturer in both cases is around 100.

4.2.1 The bullwhip effect

In the base case, the bullwhip effect in the situation of no demand information sharing (NIS) is observed as can be seen in Table 1. Note that the variance in customer demands resulting from the simulations is 400. In Table 1, the variance of retailer’s orders and the variance of manufacturer’s orders for both the situation of demand information sharing (DIS) as well as the situation of no demand information sharing (NIS) are shown. The variance in the retailer’s orders is 88.5% higher than the variance in customer demands.

In the situation of NIS, the variance in the manufacturer’s orders is 169.3% higher than the variance in the retailer’s orders. Hence, in the case of NIS, the variance in the orders amplifies as one moves up the supply chain, which is known as the bullwhip effect.

Another observation in this example is that the bullwhip effect can be reduced by de- mand information sharing, but not completely eliminated. Consider Table 1 again, the variance in the manufacturer’s orders in the case of DIS is 130.8% higher than the variance in retailer’s orders. Hence, in the situation of DIS, the bullwhip effect is still observed. However, the bullwhip effect is reduced in this situation, since the variance in the manufacturer’s orders is 16.7% lower than the variance in the manufacturer’s orders in the case of NIS. Hence in this example, sharing demand information reduces the bullwhip by 16.7%. These observations are in line with those of the papers by Lee et al. [2000] and Chen et al. [2000].

4.2.2 The service level

Sharing demand information reduces the bullwhip effect as discussed above, but the

question is what the effect of demand information sharing is on the service level of the

manufacturer compared to the situation of no demand information sharing. In the base

case, the desired service level of the retailer is 0.95. To start with, the desired service

level of the manufacturer was set at 0.95 as well. Performing the simulations for this

case, the average service level of the retailer and the manufacturer in both situations

are determined. These service levels are shown in Table 1. Here, the service level of the

retailer as well as the service level of the manufacturer in the situation of NIS are almost equal to the desired service level of 0.95. However, the service level of the manufacturer in the case of DIS is lower than the desired service level. This service level is equal to 0.9355, which is 1.2% lower than the service level in the case of NIS. Hence, if demand information is shared, the bullwhip effect is reduced by 16.7%, but as a consequence the service level of the manufacturer is reduced by 1.2% as well.

The fact that the service level of the manufacturer becomes worse in the case of DIS compared to the situation of NIS can be explained by the fact that the safety stocks in the latter case need to be higher. In the case of NIS, the safety stocks are based on retailer’s orders, where they are based on customer demands in the case of DIS. There is more variation in retailer’s orders than in customer demands, therefore the order-up-to level in the case of NIS is on average higher. In the base case, the average order-up-to level of the manufacturer in the situation of NIS is indeed higher than in the situation of DIS as seen in Table 1. The average order-up to level is 3.3% higher in the case of no demand information sharing. As a result, the average stock on hand of the manufacturer in the case of NIS is 19.9% higher than in the case of DIS, see Table 1 as well. Since the average stock on hand in the situation of NIS is higher, the probability of a stockout is smaller and therefore the service level of the manufacturer is higher in this case.

For the specific case that the target service level of the retailer and the manufacturer is 0.95, the service level of the manufacturer in the situation of DIS is lower than in the situation of NIS. An interesting question is then, what happens with the service level of the manufacturer in both situations for different target service levels. Figure 2 shows this, here the service level of the manufacturer in the case of DIS and NIS is shown for target service levels between 0.75 and 0.99. These values are considered since these values are relevant in practice. The service level of the manufacturer in the case of NIS is always higher than the service level in the case of DIS. The difference between the service levels in both situations is larger for lower target service levels. This can be explained by the fact that the safety stocks in the case of NIS are already lower, hence the safety stocks in the case of DIS are even lower and therefore the probability of a stock-out is larger.

4.2.3 Trade-off holding costs vs service

In Figure 3 a trade-off between the average holding costs of the manufacturer in the case of DIS and NIS and the service level is made. To obtain the same service level, the average holding costs in the situation of DIS are lower than in the case of NIS.

So, in the base case, the service level of the manufacturer in the case of DIS is lower than the service level of the manufacturer in the case of NIS for target service levels between 0.75 and 0.99. But to obtain the same service level, the average holding costs are lower in the situation of DIS than in the situation of NIS. To determine how robust these observations are, the parameters T , N , µ, σ, `

, `

, z

and ρ are varied one by one in the base case. The results of these experiments are discussed below.

4.3 Experiment 2: variation of the number of consecutive peri- ods T .

In the second experiment, the parameter T is varied in the base case, the rest of the

parameters remains the same. The values T = 100 and T = 1000 are considered.

Figure 2: The service level of the manufacturer in the situation of DIS and NIS in the base case for different target service levels.

In Figure 4 the service level of the manufacturer in the situation of DIS and NIS is shown for different target service levels for the case that T = 100 and T = 1000. If these cases are compared with the base case where T = 10 000, the difference between the service levels in the case of DIS and NIS is the smallest in the base case, followed by the situation where T = 1000. If T = 100 the difference between the service levels in the two situations is the largest. This can be explained by the fact that there is more variation in retailer’s orders for T = 100 and T = 1000 than if T = 10000, since the av- erage is taken over less consecutive periods. Therefore there is more difference between the service levels in the situation of DIS and NIS. Hence, if the number of consecutive periods becomes larger, the difference between the service level in the situation of DIS and NIS becomes smaller, but still the service level of the manufacturer in the situa- tion of NIS is always higher than in the situation of DIS for different target service levels.

In Figure 5 a trade-off between the average holding costs of the manufacturer in the

situation of DIS and NIS and the service level is made in the case where T is varied. In

both situations the average holding costs in the case of DIS are lower than in the case of

NIS as in the base case. If T = 100, the difference between the average holding costs in

both situations is a little bit larger than if T = 1000. Where for T = 1000 the difference

between the average holding costs is a little bit larger than in the base case.

Figure 3: A trade-off between the average holding costs of the manufacturer in the situ- ation of DIS and NIS and the service level in the base case

T = 100 T = 1000

Figure 4: The service level of the manufacturer in the situation of DIS and NIS where T is varied in the base case for different target service levels.

4.4 Experiment 3: variation of the number of periods for moving average N .

In experiment 3 the parameter N is varied in the base case, the rest of the parameters remains the same. The values N = 1 and N = 12 are considered.

In Figure 6 the service level of the manufacturer is shown in the case of NIS and DIS

T = 100 T = 1000

Figure 5: The service level of the manufacturer in the situation of DIS and NIS where T is varied in the base case for different target service levels.

N = 1 N = 12

Figure 6: The service level of the manufacturer in the situation of DIS and NIS where N is varied in the base case for different target service levels.

for N = 1 and N = 12. If N = 1, the estimates of the mean demand and the mean squared error of demand are only based on the demand from one period ahead, hence the forecasts are less accurate than in the case where N = 4. As a consequence, the average order-up-to levels of the retailer and manufacturer in the two situations are higher. There is more variation in retailer’s orders than in the base case and the av- erage stock on hand is larger. The difference between the average stock on hand of the manufacturer in the case of DIS and NIS is larger. Hence, the difference between the service levels is larger than in the case where N = 4. For N = 12, the estimates of the mean demand and the mean squared error are more precise than in the case of N = 4. Hence, there is less variation in retailer’s orders than in the base case. The average stock on hand is smaller as well as the difference between the average stock on hand of the manufacturer in both situations. Therefore, the difference between the ser- vice levels of the manufacturer in the case of DIS and NIS is smaller than in the base case.

In Figure 7 a trade-off between the average holding costs of the manufacturer in the

case of DIS and NIS and the service level is made in the situation that N is varied. To

obtain the same service level, the average holding costs in the situation of DIS are lower

than in the case of NIS. If N = 1 the difference between the average holding costs in

N = 1 N = 12

Figure 7: The service level of the manufacturer in the situation of DIS and NIS where N is varied in the base case for different target service levels.

µ = 200 µ = 300

Figure 8: The service level of the manufacturer in the situation of DIS and NIS where µ is varied in the base case for different target service levels.

both situations is larger than in the base case. If N = 12 the difference between the average holding costs in the case of DIS and NIS is smaller than in the base case.

4.5 Experiment 4: variation of the mean demand µ.

In this experiment the parameter µ is varied in the base case, the rest of the parameters remains the same. A mean demand of µ = 200 and µ = 300 are considered.

In Figure 8 the achieved service level of the manufacturer is plotted against the desired service level for the situation that µ = 200 and µ = 300. In these situations the average order-up-to level is higher, since the mean demand is higher, but the safety stocks are the same. The variance in retailer’s orders is the same as in the base case, therefore, the service level of the manufacturer in the situation of DIS and NIS remains the same.

So, there is no difference with the base case.

In Figure 9 a trade-off between the average holding costs of the manufacturer in the

case of DIS and NIS and the service level is made in the case where µ is varied. In both

µ = 200 µ = 300

Figure 9: A trade-off between the average holding costs of the manufacturer in the situ- ation of DIS and NIS and the service level in the case where µ is varied.

σ = 10 σ = 30

Figure 10: The service level of the manufacturer in the situation of DIS and NIS where σ is varied in the base case for different target service levels.

cases, the average holding costs in the case of DIS are lower than in the case of NIS.

4.6 Experiment 5: variation of the standard deviation of de- mand σ.

In experiment 5 the parameter σ is varied in the base case, all other parameters remain the same. The values σ = 10 and σ = 30 are considered.

Consider Figure 10, here the service level of the manufacturer is plotted against the

desired service level for σ = 10 and σ = 30 in the base case. In the situation that

σ = 10, the average order-up-to level of the retailer and manufacturer in both situation

is lower than in the base case. The variance in the retailer’s orders is lower, as well as

the average stock on hand. The difference between the average stock-on hand in the

situation of DIS and NIS is smaller than in the base case. Therefore, the difference

between the service levels in both situation is smaller as well. If σ = 30, the average

order-up-to level is higher than in the base case. The variance in the retailer’s orders is

higher than in the base case as well as the the average stock on hand. The difference

between the average stock on hand in the situation of DIS and NIS is higher. Hence,

σ = 10 σ = 30

Figure 11: A trade-off between the average holding costs of the manufacturer in the situation of DIS and NIS and the service level in the case where σ is varied.

z

= 0.67 z

= 2.32

Figure 12: The service level of the manufacturer in the situation of DIS and NIS where z

is varied in the base case for different target service levels.

the difference between the service level of the manufacturer in these situations is higher.

In Figure 11 a trade-off between the average holding costs of the manufacturer in the case of DIS and NIS and the service level is made in the case where σ is varied. In both cases, the average holding costs in the case of DIS are lower than in the case of NIS. If σ = 10, the average holding costs are lower than in the base case. Furthermore, the difference between the average holding costs is smaller in this case. If σ = 30, the average holding costs are higher than in the base case. The difference between the average holding costs is higher than in the base case as well.

4.7 Experiment 6: variation of the desired service of the retailer z

.

In this experiment the parameter z

is varied in the base case, the other parameters remain the same. Values of z

= 0.67 and z

= 2.33 are considered, these values corre- spond to desired service levels of 75% and 99% respectively.

In Figure 12, the service level of the manufacturer in the situation of DIS and NIS is

shown where z

is varied. If z

= 0.67, the average order-up-to level of the manufacturer

z

= 0.67 z

= 2.32

Figure 13: A trade-off between the average holding costs of the manufacturer in the situation of DIS and NIS and the service level in the case where z

is varied.

in both cases is smaller than in the base case. The variance in retailer’s orders is smaller as well as the average stock on hand. The difference between the average stock on hand in the case of DIS and NIS is smaller and hence the difference between the service levels is smaller. If z

= 2.33, so the desired service level of the retailer is higher than in the base case, the average order-up-to level is higher. There is more variation in retailer’s orders and the average stock on hand is larger. The difference between the average stock on hand of the manufacturer in the case of DIS and NIS is larger than in the base case.

Therefore, the difference between the service level in both situations is larger.

In Figure 13 a trade-off between the average holding costs of the manufacturer in the case of DIS and NIS and the service level is made in the case where z

is varied. In both cases, the average holding costs in the case of DIS are lower than in the case of NIS. If z

= 0.67, the difference between the average holding costs in both situations is smaller than in the base case. If z

= 2.32, the difference between the average holding costs in both situations is larger.

4.8 Experiment 7: variation of the lead time `

and `

.

In the seventh experiment the parameters `

and `

are varied in the base case. A lead-time of `

= `

= 1 and `

= `

= 3 is considered.

The service level of the manufacturer in the case of DIS and NIS for different target service levels where `

and `

are varied is shown in Figure 14. If ell

= `

= 1, the average stock on hand is smaller than in the base case. Also the variance in retailer’s orders is smaller and the average stock on hand. The difference between the average stock on hand of the manufacturer in the case of DIS and NIS is smaller than in the base case. Therefore, the difference in the service levels in these situations is smaller as well. If `

= `

= 3, the average stock on hand is larger, the variance in retailer’s orders is larger as well as the average stock on hand. The difference between the average stock on hand of the manufacturer in the situation of DIS and NIS is larger than in the base case. Hence, if the lead time of both the retailer and the manufacturer becomes larger, the service in the case of DIS compared to the situation of NIS, becomes more worse than if the lead time is smaller.

In Figure 15 a trade-off between the average holding costs of the manufacturer in the

case of DIS and NIS and the service level is made in the case where `

and `

are

`

= `

= 1 `

= `

= 3

Figure 14: The service level of the manufacturer in the situation of DIS and NIS where

`

and `

are varied in the base case for different target service levels.

l

= l

= 1 l

= l

= 3

Figure 15: A trade-off between the average holding costs of the manufacturer in the situation of DIS and NIS and the service level in the case where `

and `

are varied.

varied. In both cases, the average holding costs in the case of DIS are lower than in the case of NIS. If `

= `

= 1, the average holding costs are lower than in the base case. The difference between the average holding costs in both situations is smaller. If

`

= `

= 3, the average holding costs are higher than in the base case. Furthermore, the difference between the average holding costs in both situations is larger than in the base case.

4.9 Experiment 8: variation of the correlation coefficient ρ.

In the last experiment the parameter ρ is varied in the base case, the rest of the param- eters remains the same. A value of ρ = 0.4 and ρ = 0.7 is considered.

When the correlation coefficient ρ is no longer equal to 0, so the demands are no longer

independent and identically distributed, the safety stocks for the retailer and manufac-

turer in both situations should be determined in a way where the correlation coefficient

is taken into consideration. To determine the safety stock for the retailer, formula (3.4)

in the paper of Lee et al. [2004] is used, which is

v

= 1 (1 − ρ)

l_r

X

j=1

(1 − ρ

)

. The order-up-to level of the retailer is then given by

S

= F

+ z

q

v

· M SE

. (20)

To determine the safety stock for the manufacturer (DIS), formula (3.12) in the paper of Lee et al. [2004] is used, which is

v

= 1

(1 − ρ)

(1 − ρ

)

+

`_m

X

i=1

(1 − ρ

)

! . The order-up-to level of the manufacturer (DIS) is given by

S

= F

+ z

q

v

· M SE

. (21) To determine the safety stock for the manufacturer (NIS), formula (3.9) in the paper of Lee et al. [2004] is used, which is

v

= 1

(1 − ρ)

(1 − ρ

)

+

`m

X

i=1

(1 − ρ

)

+ ρ

(1 − ρ

)

(1 − ρ

)

(1 − ρ)

! .

The order-up-to level of the manufacturer (NIS) is given by S

= F

+ z

q

v

· M SE

. (22) Using these formulas, the same simulations are performed. In Figure 16 the service level of the manufacturer in the situation of DIS and NIS is shown for different target service levels in the case that ρ is varied. If ρ = 0.4, the average order-up-to level is higher than in the base case. There is more variation in retailer’s orders and the average stock on hand is larger. Furthermore, the difference between the average stock on hand in the case of DIS and NIS is larger. Hence, the difference between the service levels in both situation is larger than in the base case. If ρ = 0.7, the average order-up-to level is higher than in the case that ρ = 0.4. Also there is more variation in retailer’s orders and the average stock on hand is larger than if ρ = 0.7. The difference between the average stock on hand in both situations is larger than if ρ = 0.4. Hence, the difference between the service levels in the case of DIS and NIS is larger than if ρ = 0.4.

In Figure 17 a trade-off between the average holding costs of the manufacturer in the case of DIS and NIS and the service level is made in the case where ρ is varied. In both cases, the average holding costs in the case of DIS are lower than in the case of NIS. If ρ = 0.4, the average holding costs are higher than in the base case. The difference be- tween the average holding costs in both cases is larger than in the base case. If ρ = 0.7, the average holding costs are higher than if ρ = 0.4. Furthermore, the difference be- tween the average holding costs in both situation is larger than in the case where ρ = 0.4.

In experiment 2 until 8 all parameters were varied in the base case, we saw that these

variations had no influence on the observations made in the base case.

ρ = 0.4 ρ = 0.7

Figure 16: The service level of the manufacturer in the situation of DIS and NIS where ρ is varied in the base case for different target service levels.

ρ = 0.4 ρ = 0.7

Figure 17: A trade-off between the average holding costs of the manufacturer in the situation of DIS and NIS and the service level in the case where ρ is varied.

5 Conclusion

An important phenomenon observed in supply chains that reduces the efficiency of these chains is called the bullwhip effect. The bullwhip effect refers to the phenomenon of demand variability amplification as one moves up the supply chain. In the literature on the bullwhip effect, the papers of Lee et al. (2000) and Chen et al. were given a strong academic interest. In these papers, the benefits of information sharing were quantified in a two-level supply chain consisting of one manufacturer and one retailer where the underlying demand process is autocorrelated. They compared the bullwhip effect under demand information sharing (DIS) to the situation with no information sharing (NIS).

They did so by comparing variances of the manufacturer’s orders based on customer

demands (DIS), to manufacturer’s orders based on retailer demands (NIS). However,

this comparison is unfair, since the service performance is different in the two situa-

tions as shown in this thesis. Therefore, a comparison between the bullwhip effect and

the service performance is made in this thesis. This thesis showed that there is a ben-

efit of demand information sharing, but that it is much smaller than previously thought.

These results were shown in a two-stage supply chain consisting of a single retailer and manufacturer using a simulation model. In the simulation model, the inventory of both the retailer and the manufacturer was controlled by periodic review. A moving average was used to forecast demand and an order-up-to policy was used to replenish the inven- tory. With this simulation model several experiments were performed.

First a base case was considered. In the base case, the bullwhip effect was observed.

Furthermore, the bullwhip effect was reduced by demand information sharing but not completely eliminated. However, the simulations showed that the service level in the case of demand information sharing (DIS) was lower than in the case of no demand information sharing (NIS). This can be explained by the fact that the average order-up to level in the case of DIS was lower, since it is based on customer demands instead of retailer’s orders. To compare the situation of DIS and NIS in a different way, a trade-off between the average holding costs and the service level was made. To obtain, the same service level, the average holding costs in the situation of DIS are lower than in the case of NIS. After that all parameters in the base case were varied one by one to determine how robust the observations were. The same observations were made. Hence, this thesis showed that there is a benefit of demand information sharing, but that it is much smaller than previously thought.

There are many open research issues that could be extended. For example, instead of

a two-stage supply chain, these results could be analyzed for a multiple-stage supply

chain. Furthermore, another customer demand process could be considered as well as a

different forecasting technique and ordering policy. One could also try to find analytical

results instead of numerical results for the results in this paper.

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