MEDI-CAPS INSTITUTE OF TECHNOLOGY &MANAGEMENT, INDORE

CERTIFICATE

This is to certify that –

Arpit Paruthi (0812ME081010)Krishnaditya Singh (0812ME081020)Vaibhav Kohli (0812ME081058)

have completed their project, titled –

“STUDY AND QUANTIFICATION OF BULLWHIP EFFECT IN SUPPLY CHAINS SYSTEMS”

as per the syllabus and have submitted a satisfactory report on this project as a partial fulfillment towards the degree of

Bachelor of Engineeringin

Mechanical Engineeringfrom

Rajiv Gandhi Proudyogiki Vishwavidyalaya, Bhopal

(Prof. Ram Janm Singh) (Prof. Jayesh Barve) Project Guide Project Coordinators

(Prof. V.K. Choudhary) (Dr S.C. Sharma) Project Guide Head of Department

ACKNOWLEDGEMENT1

We are thankful to the university RGPV, Bhopal for having given us a chance to showcase

our practical skills through this project.

We would also like to thank our project guide, Prof. Ram Janm Singh, without whose

valuable guidance, our project would not have been completed.

We would also like to express gratitude to our project coordinators, Prof. K.K Gupta and

Prof Jayesh Barve, for encouraging us and keeping a check on our progress.

We are thankful to the Head of Mechanical Engineering Department, Dr. S.C.Sharma, for

encouraging us regularly, and for providing us each & every facility.

Lastly, we are also thankful to each & every person involved directly or indirectly in the

project work.

Arpit ParuthiKrishnaditya Singh Vaibhav Kohli

CONTENTS2

List of notations

Abstract

Chapter 1 - Supply Chain Management

Chapter 2 - The Bullwhip Effect

Chapter 2 - Forecasting Techniques

Conclusion

Future Enhancement

References

ABSTRACT

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This study explored the simulation approach in quantifying the effect of bullwhip in supply

chain, using various forecasting methods such as time series and Monte Carlo method.

Supply chain exists due to the fact that it is difficult for any company to provide all that is

required from raw materials to final products and at the same time get the products to the

end users. Successful supply chain management requires a change from managing

individual functions to integrating activities into key supply chain process; hence, accurate

information is of essence. One of the key factors that can adversely affect effective and

efficient supply chain process is information distortion.

The data for milk was collected from Reliance Fresh and the data for shampoo was

collected from a local store.

The analysis was performed on EXCEL. Empirical relations were used to quantify the

bullwhip effect. The results reveal that adjusted exponential smoothing is the most efficient

method for reducing Bullwhip effect.

Keywords: information distortion, supply chain, simulation, quantifying bullwhip effect

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CHAPTER 1-

SUPPLY CHAIN MANAGEMENT

Chapter 1

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1.0 INTRODUCTION TO SUPPLY CHAIN MANAGEMENT

Supply chain management(SCM) is the term used to describe the management of the flow

of materials, information, and funds across the entire supply chain, from suppliers to

component producers to final assemblers to distribution (warehouses and retailers), and

ultimately to the consumer. In fact, it often includes after-sales service and returns or

recycling.

Supply chain management has generated much interest in recent years for a number of

reasons. Many managers now realize that actions taken by one member of the chain can

influence the profitability of all others in the chain. Firms are increasingly thinking in terms

of competing as part of a supply chain against other supply chains, rather than as a

single firm against other individual firms. Also, as firms successfully streamline their own

operations, the next opportunity for improvement is through better coordination with their

suppliers and customers. The costs of poor coordination can be extremely high. In the

Italian pasta industry, consumer demand is quite steady throughout the year.

However, because of trade promotions, volume discounts, long lead times, full-truckload

discounts, and end-of-quarter sales incentives the orders seen at the manufacturers are

highly variable (Hammond(1994)). In fact, the variability increases in moving up the supply

chain from consumer to grocery store to distribution center to central warehouse to factory,

a phenomenon that is often called the bullwhip effect.

It seems that integration, long the dream of management gurus, has finally been sinking into

the minds of western managers. Some would argue that managers have long been interested

in integration, but the lack of information technology made it impossible to implement

amore “systems-oriented” approach. With the recent explosion of inexpensive information

technology, it seems only natural that business would become more supply chain focused.

However, while technology is clearly an enabler of integration, it alone cannot explain the

radical organizational changes in both individual firms and whole industries. Changes in

both technology and management theory set the stage for integrated supply chain

management.

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One reason for the change in management theory is the power shift from manufacturers to

retailers. Wal-Mart has forced many manufacturers to improve their management of

inventories, and even to manage inventories of their products at Wal-Mart. While

integration, information technology and retail power may be the key catalysts in the surge

of interest surrounding supply chains, eBusiness is fueling even stronger excitement.

eBusiness facilitates the virtual supply chain, and as companies manage these virtual

networks, the importance of integration is magnified. Firms likeAmazon.com are superb at

managing the flow of information and funds, via the Internet and electronic funds transfer.

Now, the challenge is to efficiently manage the flow of products. Some would argue that the

language and metaphors are wrong. “Chains” evoke images of linear, unchanging, and

powerless. “Supply” feels pushy and reeks of mass production rather than mass

customization. Better names, like “demand networks” or “customer driven webs” have been

proposed by many a potential book author hoping to invent a new trend.

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1.1 EFFECTIVE SUPPLY CHAIN MANAGEMENT

The complexities of getting material ordered, manufactured and delivered overload most

supply chain management (SCM) systems. The fact is, most systems are just not up to

handling all the variables up and down the supply chain. For years, it was thought that it

was

enough for manufacturers to have an MRP or ERP system that could help answer

fundamental questions such as: What are we going to make? What do we need to make the

products? What do we have now? What materials do we need, and when? What resources/

capacity do we need and when? Manufacturers need to know a lot more today to have a

truly effective supply chain. There are a number of fundamental weaknesses in the old

system logic.

Many planning and scheduling systems in use today assume that lead times are fixed,

queues do not change, queues must exist, capacity is infinite and backward scheduling logic

will produce valid load profiles and good shop floor schedules. These assumptions are

totally illogical, and following them causes many schedule compliance problems. An

effective fix is first to streamline operations and then to apply predictive, preventive forms

of advanced planning and scheduling. SCM involves two flows. Information flow signals

the need to start the flow of material. In a supply chain, the fast flow of high-quality

information and material is inextricably linked and of paramount importance to SCM

success.

Untimely or low-quality information virtually guarantees poor performance. Manufacturers

need to develop flexible supply chain processes that can adapt to the needs of various

customer segments. They must also develop supply chain strategy, processes and

supporting systems that conform to current and future requirements.

Generally, an effective SCM approach must focus on:

• Flexible supply and production processes that can very quickly respond to changing

customer demand

• A short-cycle, demand-driven order-to-delivery process

• Accurate, relevant information that is available on demand throughout the supply chain.

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Throughout the supply chain, there are some absolutely critical and predictive questions

your system should accurately and quickly answer:

• When will specific orders really ship?

• Which orders will be late?

• Why will these orders be late?

• What are the specific problems that are delaying the schedule?

• What are the future schedule problems and when will they occur?

• What is the best schedule that can be executed now?

If management can answer predictive questions, its decisions will greatly improve.

Preventive actions can offset what were once unforeseen problems. The supply chain will

be managed more effectively and improve chances of gaining a competitive advantage.

In the early 1980s, with the introduction of just-in-time production to the United States,

many were convinced that pull signals (kanbans) and instant material deliveries would

eradicate the need for MRP. The announcement of MRP’s death was premature, except for

firms with simple products and absolute control of supplier deliveries. Those with more

complex products requiring more supply sources for more parts discovered that longer lead

times and demand and supply variability were still issues to be dealt with. Simply put, the

more diverse your product line and the more complex your products, more valuable the

MRP is for planning raw material needs.

This is not to say pull logic is not useful for raw material planning, because it is. Yet for

most, it is not necessary (or desirable) to put every part number from every supplier on a

pull system. Scheduling production with MRP push logic, however, is like pushing a rope.

You don’t know what direction it will go. Pull systems will eventually dominate the entire

supply chain—to customers and from suppliers, as well as internal material movement. Yet,

MRP can, and must, coexist with pull scheduling. Cycle time compression should be the

first objective in the order-to-delivery process. Midrange manufacturers often have limited

clout with suppliers, making across-the-board mandatory lead-time reductions unlikely.

While there are many ways to workout mutually beneficial and necessary improvements

with suppliers, the real enemy is time. The alternative is to work selectively on supply

improvements while using a rationalized inventory deployment strategy to support the first

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objective—reducing order-to-delivery cycle time. Good collaborative forecasting, good

planning and realistic replenishment scheduling are essential to effective SCM. Further

improvements come from redesigning supplier links to make them firm, fast and flexible for

the benefit of the entire supply chain.

1.2 SCM FLOW DIAGRAM

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1.3ROLE OF INFORMATION

Information could be overlooked as a major supply chain driver because it does not have a

physical presence. Information, however, deeply affects every part of supply chain. Its

impact is easy to under estimate as information affects a supply chain in many

different ways. Consider the following:

1) Information serves as the connection between the supply chain’s various stages, allowing

them to coordinate and bring out many of the benefits of maximizing total supply chain

profitability.

2) Information is also crucial to the daily operation of each stage in supply chain. For

instance, a production scheduling system uses information on Demand to create a schedule

that allows a factory to produce the right products in an efficient manner .A warehouse

management system uses information to create a visibility of the warehouse’s inventory.

The company can then use this information to determine whether new orders can be filled.

Further we can classify information as follows:

Centralized information: One of the most frequent suggestions for reducing the

bullwhip effect is to centralized demand information within a supply chain that is to

provide each stage of supply chain with complete information on the actual

customer demand. if the demand information is centralized, each stage of supply

chain can use the actual customer demand data to create more accurate forecasts,

rather than relying on the orders received from the previous which can vary

significantly more than the actual customer demand.

Decentralized information-: second type of supply chain that we consider is the

decentralize supply chain. In this case the retailer does not make its forecast mean

demand available to the remainder of supply chain. Instead, the wholesaler must

estimate the mean demand based on the orders received from the retailer.

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Information is a driver whose importance has grown as companies have used it to become

both more efficient and more responsive. Another key decision involves what information is

most valuable in reducing cost and improving responsiveness within a supply chain. This

decision will vary depending on the supply chain structure and the market segments served.

Some companies target Customers who require customized product that carry a premium

price tag. This company might find that investment in information allow them to respond

more quickly to their customers.

1.4 SUPPLY CHAIN UNCERTAINTY AND INVENTORY

One of the company’s main objectives in managing its supply chain is to synchronize the

upstream flow of incoming materials, parts, subassemblies, and services with production

and distribution downstream so that it can respond to uncertainty in customer demand

without creating costly excess inventory. Examples of factors that contribute to uncertainty,

and hence variability, in the supply chain are inaccurate demand forecasting, long variable

lead times for orders, late deliveries, incomplete shipments, product changes, batch

ordering, price fluctuations and discounts, and inflated orders. If deliveries from suppliers

are late or incomplete, they slow down the flow of goods and services through the supply

chain, ultimately resulting in poor quality customer service. Companies cope with this

uncertainty and try to avoid delays with their own form of “insurance” inventory.

Supply chain members carry buffer inventory at various stages of the supply chain to

minimize the negative effects of uncertainty and to keep goods and services flowing

smoothly from suppliers to customers. For examples, if a part order arrives late from a

supplier, the producer is able to continue production and maintain its delivery schedule to

its customers by using parts it has stored in inventory for just such an occurrence.

Companies also accumulate inventory because they may order in large bathes in order to

keep down order and transportation costs or to receive a discount or special price from a

supplier. However, inventory is very costly. Products sitting on a shelf or in a warehouse are

just like money sitting there not being used when it could be used for something else. It is

estimated that the cost of carrying a retail product in inventory for one year is over 25% of

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what the item costs. Inventory carrying costs is over $300 billion per year in the United

States. As such, suppliers and customers would like to minimize or eliminate it.

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CHAPTER 2

THE BULLWHIP EFFECT

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Chapter 2

2.0 INTRODUCTION

The Bullwhip Effect (or Whiplash Effect) is an observed phenomenon in forecast-driven

distribution channels. Since the oscillating demand magnification upstream a supply chain

reminds someone of a cracking whip it became famous as the Bullwhip Effect.

The bullwhip effect is the magnification of demand fluctuations, not the magnification of

demand. The bullwhip effect is evident in a supply chain when demand increases and

decreases. The effect is that these increases and decreases are exaggerated up the supply

chain.

The essence of the bullwhip effect is that orders to suppliers tend to have larger variance

than sales to the buyer. The more chains in the supply chain the more complex this issue

becomes. This distortion of demand is amplified the farther demand is passed up the supply

chain.

Proctor & Gamble coined the term “bullwhip effect” by studying the demand fluctuations

for Pampers (disposable diapers). This is a classic example of a product with very little

consumer demand fluctuation. P&G observed that distributor orders to the factory varied far

more than the preceding retail demand. P & G orders to their material suppliers fluctuated

even more.

Babies use diapers at a very predictable rate, and retail sales resemble this fact. Information

is readily available concerning the number of babies in all stages of diaper wearing. Even so

P&G observed that this product with uniform demand created a wave of changes up the

supply chain due to very minor changes in demand.

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2.1 LITERARTURE REVIEW

1) Boute et al studied that:

A major cause of supply chain deficiencies is the bullwhip problem, which refers to the

tendency of replenishment orders to increase in variability as they move up a

supply chain. Conventional bullwhip reduction is only one side of the coin, however. In

developing a replenishment rule one has to consider the impact on the inventory variance as

well.

2) According to Huang et al. research:

The bullwhip effect refers to the phenomenon of the amplification of demand variability

from a downstream site to an upstream site in the supply chain.

3) According to Sterman et al study:

The Bullwhip effect stems from a non-optimal solution applied by members of the supply

chain who see their strategies as a sum of individual strategies rather than a unit.

4) Forrester observed that:

A small change in the rate of sale at the retail level could result in a much larger change in

demand for the manufacturer. The magnitude of the distortion in the demand information is

amplified as one travels up through the supply chain.

5) Seokcheon Lee et al found that:

As supply chains become bigger and dynamically structured involving multiple

organizations with different interests, it is impossible for a single organization to control a

whole supply chain. So, decentralization of decision rights is an inevitable facet of

managing modern supply chains.

6) J. NIENHAUS et al found that:

The aspects of human behaviour need to be recognised as further amplifying the bullwhip

effect. Humans act as obstacles for information flow in supply chains in practice and by that

increase the lead time of information and as a consequence the bullwhip effect.

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7). Riddalls and Bennett:

Disruptions can be costly in supply chain systems and can cause variety of problems such as

long lead-times, stock-outs, inability to meet customer demand and increases in costs and

finds that disruptions in an supply chain can lead to unexpected costs when shipping lead-

times are long.

8).Goldbergs et al:

Genetic algorithms do not carry out examinations sequentially but search in parallel mode

using a multi individual population, where each individual is being examined at the same

time.

2.2 CAUSES

Because customer demand is rarely perfectly stable, businesses must forecast demand to

properly position inventory and other resources. Forecasts are based on statistics, and they

are rarely perfectly accurate. Because forecast errors are a given, companies often carry an

inventory buffer called “safety stock”.

Moving up the supply chain from end-consumer to raw materials supplier, each supply

chain participant has greater observed variation in demand and thus greater need for safety

stock. In periods of rising demand, down-stream participants increase orders. In periods of

falling demand, orders fall or stop, thereby not reducing inventory. The effect is that

variations are amplified as one moves upstream in the supply chain (further from the

customer).

The four main causes of the bullwhip effect have been identified, which are –

Demand Forecast Updating

Order Batching

Rationing and Shortage Gaming

Price Variations

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2.2.1 Demand forecast updating

Forecasting data used are normally based on the previous orders received by the company

from its customers. The main reason for this problem is that the data are usually based on

forecast orders and not actual customer demand. As most companies are untrusting, this

leads to companies not wanting to share information about demand, which leads to

information distortion throughout the supply chain. Various methods of forecasting such as

exponential smoothing or moving average forecasting have been employed by many

companies to find the ‘truest’ demand. Unfortunately, any type of forecasting can cause the

bullwhip effect. However, it is possible to reduce the bullwhip effect significantly by using

centralized

information and allowing only one member of the supply chain to place orders on behalf of

all other members via Vendor Managed Inventory (VMI) and Continuous Replenishment

Programs (CRP).

2.2.2 Order batching

Order batching has been identified as another major cause of the bullwhip effect. Order

batching refers to a company ordering a large quantity of a product in one week and not

ordering any for many weeks. The main reason for a company ordering in batches is that it

may prove to be less costly because of transportation costs or the company will receive a

discount if a large quantity is ordered in one period. Although this may reduce the cost for

the company, the other members of the supply chain are likely to suffer. The impact of

batch ordering is simple to understand. Where the retailer uses batch ordering, the

manufacturer will observe a very large order, followed by several periods of no orders and

then another large order, etc. The manufacturer forecast demand will be greatly distorted as

it will base future demand forecasts on orders rather than actual sales. One method of

reducing the bullwhip effect is by ordering less product and more frequently, which will

allow the supplier to determine the true demand.

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2.2.3 Rationing and shortage gaming

When a product demand exceeds supply, a manufacturer often rations its product to

customers. Rationing schemes that allocate limited production in proportion to the orders

placed by retailers lead to a magnification of the bullwhip effect. When this problem arises,

many customers will exaggerate their orders to ensure that they receive a sufficient amount

of the required product. This can cause major problems, as when demand is not as high, the

orders will stop, and cancellations will begin to arise. This leaves the manufacturer with

excess inventory and no customer orders. This also makes it difficult for the manufacturer

to believe that there is an increase in demand, whereas customer demand is actually

unchanged.

2.2.4 Price variations/sales promotions

If the price of products changes dramatically, customers will purchase the product when it is

cheapest. This may cause customers to buy in bulk, which also adds to the order-matching

problem. Manufacturers and distributors occasionally have special promotions like price

discounts, quantity discounts, coupons, rebates, etc. All these price promotions result in

price fluctuations, and the customers’ ordering patterns will not reflect the true demand

pattern.

One method of avoiding price fluctuations is by stabilizing prices. If companies can reduce

the price of their product to a single reduced price, the fluctuations in demand will not be as

aggressive. Sales promotion is another major contributor to this problem. If the consumer

purchases more of the product because of the promotion, this will cause a large spike to

appear in demand and further upstream the supply chain. Despite the lowered price for

consumers, this will have the opposite effect on the supply chain causing forecast

information to be distorted and in effect causing inefficiencies, i.e. excessive inventory,

quality problems, higher raw-material costs, overtime expenses, shipping costs, poor

customer service, and missed production schedule.

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Retailers use promotions to meet monthly quotas for products, which can result in the

overuse of promotions. The result is an addiction to incentives that turn simple predictable

demand patterns into a chaotic series of spikes that only add to cost (Fisher 1997). No

matter where a promotion occurs, whether it is a sales promotion to consumer to buy a

specific product or a discount for retailers from a manufacturer, it is more prudent to

provide lower prices all year round and disregard promotional strategies altogether (Fisher

1997). In an ideal world, companies would use everyday low pricing. Unfortunately, this is

not the case, as companies compete with other competitors by using price promotions to

increase profits and improve market share.

The causes can further be divided into behavioral and operational causes:

Behavioral causes

misuse of base-stock policies

misapplication of trinomial theorem

misperceptions of feedback and time delays

panic ordering reactions after unmet demand

perceived risk of other players’ bounded rationality

Operational causes

Dependent demand processing

Forecast Errors

Adjustment of inventory control parameters with each demand observation

Lead-time Variability (forecast error during replenishment lead time)

Lot-sizing/order synchronization

Consolidation of demands

Transaction motive

Quantity discount

Trade promotion and forward buying

Anticipation of shortages

Allocation rule of suppliers

Shortage gaming

Lean and JIT style management of inventories and a chase production

strategy22

2.3 CONSEQUENCES

In addition to greater safety stocks, the described effect can lead to either inefficient

production or excessive inventory as the producer needs to fulfill the demand of its

predecessor in the supply chain. This also leads to a low utilization of the distribution

channel.

In spite of having safety stocks there is still the hazard of stock-outs which result in poor

customer service. Furthermore, the Bullwhip effect leads to a row of financial costs.

Next to the (financially) hard measurable consequences of poor customer services and the

damage of public image and loyalty an organization has to cope with the ramifications of

failed fulfillment which can lead to contract penalties. Moreover the hiring and dismissals

of employees to manage the demand variability induce further costs due to training and

possible pay-offs.

2.4 COUNTER MEASURES

Theoretically the Bullwhip effect does not occur if all orders exactly meet the demand of

each period. This is consistent with findings of supply chain experts who have recognized

that the Bullwhip Effect is a problem in forecast-driven supply chains, and careful

management of the effect is an important goal for Supply Chain Managers. Therefore it is

necessary to extend the visibility of customer demand as far as possible.

One way to achieve this is to establish a demand-driven supply chain which reacts to actual

customer orders. In manufacturing, this concept is called Kanab. This model has been most

successfully implemented in Wal-Mart’s distribution system. Individual Wal-Mart stores

transmit point-of-sale (POS) data from the cash register back to corporate headquarters

several times a day. This demand information is used to queue shipments from the Wal-

Mart distribution centre to the store and from the supplier to the Wal-Mart distribution

centre. The result is near-perfect visibility of customer demand and inventory movement

throughout the supply chain.

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Better information leads to better inventory positioning and lower costs throughout the

supply chain. Barriers to the implementation of a demand-driven supply chain include the

necessary investment in information technology and the creation of a corporate culture of

flexibility and focus on customer demand. Another prerequisite is that all members of a

supply chain recognize that they can gain more if they act as a whole which requires trustful

collaboration and information sharing.

Methods intended to reduce uncertainty, variability, and lead time:

Vendor Managed Inventory (VMI)

Just In Time replenishment (JIT)

Strategic partnership

Information sharing

smooth the flow of products

coordinate with retailers to spread deliveries evenly

reduce minimum batch sizes

smaller and more frequent replenishments

eliminate pathological incentives

every day low price policy

restrict returns and order cancellations

order allocation based on past sales instead of current size in case of shortage

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CHAPTER 3

FORECASTING TECHNIQUES

Chapter 3

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3.0 FORECASTING

Forecasting is the process of making statements about events whose actual outcomes

(typically) have not yet been observed. A commonplace example might be estimation for

some variable of interest at some specified future date. Prediction is a similar, but more

general term. Both might refer to formal statistical methods employing time series, cross-

sectional or longitudinal data, or alternatively to less formal judgmental methods. Usage can

differ between areas of application: for example in hydrology, the terms "forecast" and

"forecasting" are sometimes reserved for estimates of values at certain specific future times,

while the term "prediction" is used for more general estimates, such as the number of times

floods will occur over a long period. Risk and uncertainty are central to forecasting and

prediction; it is generally considered good practice to indicate the degree of uncertainty

attaching to forecasts. The process of climate change and increasing energy prices has led to

the usage of Again Forecasting of buildings. The method uses Forecasting to reduce the

energy needed to heat the building, thus reducing the emission of greenhouse gases.

Forecasting is used in the practice of Customer Demand Planning in everyday business

forecasting for manufacturing companies. The discipline of demand planning, also

sometimes referred to as supply chain forecasting, embraces both statistical forecasting and

a consensus process. An important, albeit often ignored aspect of forecasting, is the

relationship it holds with planning. Forecasting can be described as predicting what the

future will look like, whereas planning predicts what the future should look like. There is no

single right forecasting method to use. Selection of a method should be based on your

objectives and your conditions.

Forecasting can be done in the following ways –

Time series methods

Regressive methods

Qualitative methods

3.2 TIME SERIES METHODS

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These are statistical techniques that make use of historical data accumulated over a period

of time. Time series methods assume that what has occurred in the past will continue to

occur in the future. As the name suggests, these methods relate the forecasts to only factor

that is time. These methods assume that identifiable historical patterns or trends for

demands over time will repeat themselves. Almost 70% of the firms use time series models.

Time series methods use historical data as the basis of estimating future outcomes.

Moving average

Weighted moving average

Exponential smoothing

Autoregressive moving average (ARMA)

Autoregressive integrated moving average (ARIMA)

Extrapolation

Linear prediction

Trend estimation

Growth curve

3.2.1 SIMPLE MOVING AVERAGE

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In financial applications a simple moving average (SMA) is the un-weighted mean of the

previous n data points. However, in science and engineering the mean is normally taken

from an equal number of data either side of a central value. This ensures that variations in

the mean are aligned with the variations in the data rather than being shifted in time. An

example of a simple un-weighted running mean for a 10-day sample of closing price is the

mean of the previous 10 days' closing prices. If those prices are

then the formula is

The period selected depends on the type of movement of interest, such as short,

intermediate, or long term. In financial terms moving average levels can be interpreted as

resistance in a rising market, or support in a falling market.

If the data used is not centred around the mean, a simple moving average lags behind the

latest data point by half the sample width. A SMA can also be disproportionately influenced

by old data points dropping out or new data coming in. One characteristic of the SMA is

that if the data have a periodic fluctuation, then applying an SMA of that period will

eliminate that variation (the average always containing one complete cycle). But a perfectly

regular cycle is rarely encountered.

For a number of applications it is advantageous to avoid the shifting induced by using only

'past' data. Hence a central moving average can be computed, using data equally spaced

either side of the point in the series where the mean is calculated. This requires using an odd

number of data points in the sample window.

3.2.2 EXPONENTIAL SMOOTHING

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Exponential smoothing is a technique that can be applied to time series data, either to

produce smoothed data for presentation, or to make forecasts. The time series data

themselves are a sequence of observations. The observed phenomenon may be an

essentially random process, or it may be an orderly, but noisy, process. Whereas in the

simple moving average the past observations are weighted equally, exponential smoothing

assigns exponentially decreasing weights over time.

Exponential smoothing is commonly applied to financial market and economic data, but it

can be used with any discrete set of repeated measurements. The raw data sequence is often

represented by {xt}, and the output of the exponential smoothing algorithm is commonly

written as {st}, which may be regarded as a best estimate of what the next value of x will be.

When the sequence of observations begins at time t = 0, the simplest form of exponential

smoothing is given by the formulas.

where α is the smoothing factor, and 0 < α < 1.

3.2.3 ADJUSTED EXPONENTIAL SMOOTHING

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Trend estimation is a statistical technique to aid interpretation of data. When a series of

measurements of a process are treated as a time series, trend estimation can be used to make

and justify statements about tendencies in the data. By using trend estimation it is possible

to construct a model which is independent of anything known about the nature of the

process of an incompletely understood system (for example, physical, economic, or other

system). This model can then be used to describe the behaviour of the observed data.

In particular, it may be useful to determine if measurements exhibit an increasing or

decreasing trend which is statistically distinguished from random behaviour. Some

examples are: determining the trend of the daily average temperatures at a given location,

from winter to summer; or the trend in a global temperature series over the last 100 years. In

the latter case, issues of homogeneity are important (for example, about whether the series

is equally reliable throughout its length).

F t+1 = αDt + (1- α)Ft

T t+1 = β(F t+1 -Ft) + (1- β)Tt

Tt=1 = trend factor for the next period.

Tt = trend factor for the current period

β = smoothing constant for the trend adjustment factor.

3.2.4 MONTE CARLO SIMULATION

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Risk analysis is part of every decision we make. We are constantly faced with uncertainty,

ambiguity, and variability. And even though we have unprecedented access to information,

we can’t accurately predict the future. Monte Carlo simulation (also known as the Monte

Carlo Method) lets you see all the possible outcomes of your decisions and assess the

impact of risk, allowing for better decision making under uncertainty.

What is Monte Carlo simulation?

Monte Carlo simulation is a computerized mathematical technique that allows people to

account for risk in quantitative analysis and decision making. The technique is used by

professionals in such widely disparate fields as finance, project management, energy,

manufacturing, engineering, research and development, insurance, oil & gas, transportation,

and the environment.

Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and

the probabilities they will occur for any choice of action.. It shows the extreme possibilities

—the outcomes of going for broke and for the most conservative decision—along with all

possible consequences for middle-of-the-road decisions.

The technique was first used by scientists working on the atom bomb; it was named for

Monte Carlo, the Monaco resort town renowned for its casinos. Since its introduction in

World War II, Monte Carlo simulation has been used to model a variety of physical and

conceptual systems.

How Monte Carlo simulation works:

Monte Carlo simulation performs risk analysis by building models of possible results by

substituting a range of values—a probability distribution—for any factor that has inherent

uncertainty. It then calculates results over and over, each time using a different set of

random values from the probability functions. Depending upon the number of uncertainties

and the ranges specified for them, a Monte Carlo simulation could involve thousands or tens

of thousands of recalculations before it is complete. Monte Carlo simulation produces

distributions of possible outcome values.

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By using probability distributions, variables can have different probabilities of different

outcomes occurring.  Probability distributions are a much more realistic way of describing

uncertainty in variables of a risk analysis

CONCLUSION

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The study was aimed at quantifying the Bullwhip effect in manufacturing firms.

Information distortion in supply chain management has been found to be a major

contributor to the bullwhip effect in the manufacturing sector. However, since life itself is

dynamic and the environment in which manufacturing organizations operates changes

constantly, order and demand for products cannot be static. Moreover, the complexity

facing several manufacturers today requires that manufacturing organizations should be

proactive and dynamic. Hence the great need for the use of appropriate forecasting tools to

map out strategies of operations for the future, and the simulation techniques, based on

knowledge of past experience has been found to be a vital tool.

In our project, we used Moving Average, Exponential Smoothing, Adjusted Exponential

Smoothing, and Monte Carlo Simulation to quantify the Bullwhip Effect. It is safe to

conclude that various forecasting techniques help in reducing the value of Bullwhip Effect,

which is the ratio of variance of order to the variance of demand.

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FUTURE ENHANCEMENTS

1. To study the information distortion in an industry and quantify the Bullwhip Effect in its

Supply Chain.

2. To study the researches made on Supply chain Management and The Bullwhip Effect.

3. To study and apply a mathematical model to quantify THE Bullwhip Effect.

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REFERENCES

1. Wikipedia.com2. Operations Management along the Supply Chain – Russell and Taylor3. Operations Management – P.B. Mahapatra4. Youtube.com5. Various case studies and papers on Bullwhip

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