Operations Management (2) Lessons 1 and 2 Prof. Upendra Kachru Forecasting.

OperationsManagement (2)

Lessons 1 and 2

Prof. Upendra Kachru

Forecasting

Operations ManagementProf. Upendra Kachru

Prediction Prediction

Reflects judgment after taking all considerations into account

Involves anticipated changes in future that may or may not happen

Based on intuition

It can be biased

No error analysis

Based on unique representations


Forecasting Forecasting

Involves the projection of the past into the future

Estimating the demand on the basis of factors that generated the demand

Based on theoretical model

It is objective

Error Analysis is possible

Results are replicable


A forecast is an estimate of a future event achieved by systematically combining and casting forward , in a predetermined way, data about the past.

DEFINING FORECASTING


Forecasting vs. Prediction

Forecasting Prediction

Involves the projection of the past into the future

Reflects management’s judgment after taking all considerations into account

Estimating the demand on the basis of factors that generated the demand

Involves anticipated changes in future that may or may not generate the demand

Based on theoretical model Based on intuition

It is objective It can be biased

Error Analysis is possible No error analysis

Results are replicable Based on unique representations


Forecasting is the start of any planning activity. The main purpose of forecasting is to estimate the occurrence, timing or magnitude of future events.

WHYFORECASTING?


The Decision making Cycle

Forecasts help management take into account external factors that impact operations and reduce the uncertainty.

The decision making cycle reflects how organizations use forecasting to reduce the impact of market forces on a business.


Decision Types requiring Forecasting

Forecasting horizon in years

Specific demand

Aggregate demand

Strategies & facilities

Types of Decision

Short term

Long term

Planning

Medium term

Operations ManagementProf. Upendra Kachru 9

Demand Forecasting Demand Forecasting is the activity of estimating the quantity of a product or service that consumers will purchase.

Demand forecasting involves techniques including both formal and informal methods.

Demand forecasting may be used in making scheduling decisions, in assessing future capacity requirements, or in making decisions on whether to enter a new market.


A

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand:Raw Materials, Component parts,Sub-assemblies, etc.

Independent Demand:Finished Goods

Types of Demand

Aggregate Planning is concerned with aggregate demand i.e. the amount of a particular economic good or service that a consumer or group of consumers will want to purchase (at a given price).


The firm should be able to forecast ideal levels of inventory.The relative cost of holding either too much or too little inventory might be different from the ideal levels because of poor forecasts of demand. If demand were less than

expected, the firm would incur extra inventories and the cost of holding them.

If demand were greater than expected, the firm would incur back-order or shortage cost and the possible opportunity costs of lost sales or a lower volume of activity.

Demand and Costs


Demand Management

Do I manage demand ?

Do I live with it?

Demand management describes the process of influencing the volume of consumption of the product or service through management decision so that firms can use their resources and production capacity more effectively.


Can take an active role to influence demand. For example, air conditioner manufactures offer discounts for their products in winter , when demand for the products falls.

Demand management is also used to spread demand more evenly. Telephone companies, world over, offer discounts for calls made during late hours or at night.

Can take a passive role and simply respond to demand

Independent Demand

What to do?

Operations Management

Eight Steps to Forecasting

Determining the use of the forecast--what are the objectives?

Select the items to be forecast Determine the time horizon of

the forecast Select the forecasting

model(s) Collect the data Validate the forecasting model Make the forecast Implement the results



Quantitative Time Series Analysis Exponential Method Regression Analysis Simulation/ Scenario Planning

Qualitative (Judgmental)

Types of Forecasts


Time Series

1. Extrapolation

2. Moving average Method

Exponential Method

3. Simple Exponential Method

4. Double Exponential Method

5. Triple Exponential Method

Regression Analysis

6. Simple Regression Analysis

7. Multiple Regression Analysis

Quantitative Approach


Time Series

There are five basic patterns in which demand varies with time that have been identified:

Horizontal Trend Seasonal Cyclical Random


Graphical Representation

Time

Demand (units)

Constant

Linear Trend Cyclical

Seasonal/ Cyclical

Turning Points


Moving Average Method

Where: Ft+1 is the moving average for the period t+1, At, At-1, At-2, At-3 etc. are actual values for the

corresponding period, and ‘n’ is the total number of periods in the average

Or it can be written as:

F = A + A + A +...+A

ntt-1 t-2 t-3 t-n

The general formula for moving average is:

Ft+1 = (At + At-1 + At-2 + At-3 + ……+ At-n+1) / n


Simple Moving Average Problem

Week Demand1 6502 6783 7204 7855 8596 9207 8508 7589 892

10 92011 78912 844

F = A + A + A +...+A

ntt-1 t-2 t-3 t-n

Question: What are the 3-week and 6-week moving average forecasts for demand? Assuming you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts

Question: What are the 3-week and 6-week moving average forecasts for demand? Assuming you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts


Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.33

10 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83

F4=(650+678+720)/3

=682.67F7=(650+678+720 +785+859+920)/6

=768.67

Calculating the moving averages gives us:

© The McGraw-Hill Companies, Inc., 2004


Problem (2) Data

Week Demand1 8202 7753 6804 6555 6206 6007 575

Question: What is the 3 week moving average forecast for this data? Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts

Question: What is the 3 week moving average forecast for this data? Assume you only have 3 weeks and 5 weeks of actual demand data for the respective forecasts


Problem (2) Solution

Week Demand 3-Week 5-Week1 8202 7753 6804 655 758.335 620 703.336 600 651.67 710.007 575 625.00 666.00

F4=(820+775+680)/3

=758.33F6=(820+775+680 +655+620)/5 =710.00


Weighted Moving Average

While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods

While the moving average formula implies an equal weight being placed on each value that is being averaged, the weighted moving average permits an unequal weighting on prior time periods

The general formula for the weighted moving average then changes to:

Ft+1 = [(wtAt + wt-1At-1 + wt-2At-2 + wt-3At-3 + ……+ wt-n+1At-n+1) / n

Where: Ft+1 is the weighted moving average for the period t+1,wt is the weighing factor, and ∑nt=1 wt = 1


Weights: t-1 .5t-2 .3t-3 .2

Week Demand1 6502 6783 7204

Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?

Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?

Note that the weights place more emphasis on the most recent data, that is time period “t-1”

Note that the weights place more emphasis on the most recent data, that is time period “t-1”

F = w A + w A + w A +...+w At 1 t-1 2 t-2 3 t-3 n t-n

w = 1ii=1

n

wt = weight given to time period “t” occurrence (weights must add to one)

wt = weight given to time period “t” occurrence (weights must add to one)

The formula for the moving average can also be written as:The formula for the moving average can also be written as:


Problem Solution

Week Demand Forecast1 6502 6783 7204 693.4

F4 = 0.5(720)+0.3(678)+0.2(650)=693.4


Problem (2) Data

Weights: t-1 .7t-2 .2t-3 .1

Week Demand1 8202 7753 6804 655

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?



Week Demand Forecast1 8202 7753 6804 6555 672

F5 = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672


Exponential method is a technique that is applied to time series data, either to produce smoothed data for presentation, or to make forecasts. Premise: The most recent

observations might have the highest predictive value. Therefore, we should give more weight to the more recent time periods when forecasting

Exponential Method


Exponential Smoothing Model

The exponential relationship be written as:

Ft+1 = α Dt + (1 - α) Ft

Where: Dt is the actual value

Ft is the forecasted value

α is the weighting factor, which ranges from 0 to 1

t is the current time period.

The variance is given by:

(Dt - Ft+1)2 / n = Variance


Problem (1) Data

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

10

Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using a=0.10 and a=0.60?Assume F1=D1

Which is a better choice?

Question: Given the weekly demand data, what are the exponential smoothing forecasts for periods 2-10 using a=0.10 and a=0.60?Assume F1=D1

Which is a better choice?


Week Demand 0.1 0.61 820 820.00 820.002 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

F3=775x0.1 + (1-0.1)x820 =815.50


Answer: Variance0.3 = 6675.61 and Variance0.6 = 5369.39. Therefore alpha as 0.6 is a better choice

Answer: Variance0.3 = 6675.61 and Variance0.6 = 5369.39. Therefore alpha as 0.6 is a better choice

Demand 0.1 D-W (D-W)2 0.6 D-W (D-W)2

820 820.00 0.00 0.00 820.00 0.00 0

775 820.00 -45.00 2025.00 820.00 -45.00 2025

680 815.50 -135.50 18360.25 793.00 -113.00 12769

655 801.95 -146.95 21594.30 725.20 -70.20 4928.04

750 787.26 -37.26 1387.94 683.08 66.92 4478.286

802 783.53 18.47 341.16 723.23 78.77 6204.398

798 785.38 12.62 159.35 770.49 27.51 756.6461

689 786.64 -97.64 9533.35 787.00 -98.00 9603.436

775 776.88 -1.88 3.52 728.20 46.80 2190.348

53404.87 42955.15

Which one?


Plotting the Solution

500

600

700

800

900

1 2 3 4 5 6 7 8 9 10

Week

Dem

and

Demand

0.1

0.6

Note how that the smaller alpha results in a smoother line in this example

Note how that the smaller alpha results in a smoother line in this example


Problem (2) Data

Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?

Assume F1=D1

Question: What are the exponential smoothing forecasts for periods 2-5 using a =0.5?

Assume F1=D1

Week Demand1 8202 7753 6804 6555



Week Demand 0.51 820 820.002 775 820.003 680 797.504 655 738.755 696.88

F1=820x0.5 + (1.0-0.5)x820 = 820

F3=775x0.5 + (1.0-0.5)x820 =797.75


Exponential Smoothing & Simple Moving Average

An exponentially weighted moving average with a smoothing constant a, corresponds roughly to a simple moving average of length (i.e., period) n, where α and n are related by:

α = 2/(n+1) OR n = (2 - α)/ α.


Double and Triple Smoothing

An exponential smoothing over an already smoothed time series is called double-exponential smoothing. It applies the process of exponential smoothing to a time series that is already exponentially smoothened. This is used when trends are not stationary.In the case of nonlinear trends it might be necessary to extend it even to a triple-exponential smoothing. Triple Exponential Smoothing is better at handling parabola trends and is normally used for such data.


Double Exponential Smoothing

What happens when there is a definite non-stationary trend?

A trendy clothing boutique has had the following salesover the past 6 months:

1 2 3 4 5 6510 512 528 530 542 552

480490500510520530540550560

1 2 3 4 5 6 7 8 9 10

Month

Demand

Actual

Forecast



All forecasts have errors. However, the ‘error’ in a forecast should be within confidence limits.

The error can be measured by or described by the standard error, the mean absolute deviation, or the variance.

ForecastingErrors


Forecast AccuracySource of forecast errors:

Model may be inadequate Irregular variations Incorrect use of forecasting

technique Random variation

Key to validity is randomness Accurate models: random

errors Invalid models: nonrandom

errors

Key question: How to determine if forecasting errors are random?


ForecastingErrors


Error measuresError - difference between actual value and predicted value

• Mean Absolute Deviation (MAD) - Average absolute error

• Mean Squared Error (MSE) - Average of squared error

• Mean Absolute Percent Error (MAPE) - Average absolute percent error


Error Measurements


MAD = Actual forecast

n

MSE = Actual forecast)

-1

2

n

(

Actual Forecast100

ActualMAPEn


Forecasting Error Formulae


1 MAD 0.8 standard deviation

1 standard deviation 1.25 MAD

The ideal MAD is zero which would mean there is no forecasting error

When the error is less than three standard deviations, it is considered as an acceptable forecast.

σ = √ (π/2) x MAD ≈ 1.25 MADWhere ‘σ’ is the standard deviation

The larger the MAD, the less the accurate the resulting model

MAD Characteristics


MAD Problem (1)

Month Sales Forecast1 220 n/a2 250 2553 210 2054 300 3205 325 315

Question: What is the MAD value given the forecast values in the table below?

Question: What is the MAD value given the forecast values in the table below?


Solution

MAD = A - F

n=

40

4= 10

t tt=1

n

Month Sales Forecast Abs Error1 220 n/a2 250 255 53 210 205 54 300 320 205 325 315 10

40

Note that by itself, the MAD only lets us know the mean error in a set of forecasts

Note that by itself, the MAD only lets us know the mean error in a set of forecasts

σ = 1.25 MAD = 12.5; 3 σ =37.5

All readings are within limits


Example (2)

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75MSE= 10.86

MAPE= 1.28

MAD = 22/8 = 2.75

MSE = 76/7 = 10.86

MAPE = 10.26/8 = 10.86



Deseasoning Demand: Seasonal Index

Seasonal index represents the extent of seasonal influence for a particular segment of the year. The calculation involves a comparison of the expected values of that period to the grand mean. The formula for computing seasonal factors is:

Si = Di/D, where: Si = the seasonal index for ‘i’ th period,Di = the average values of ‘i’ th period,D = grand average,i = the ith seasonal period of the cycle


Problem

The sales data for two years are given with the sales data aggregated in periods of two months.

Month, 2003

Sales Deseasoned Demand

Month, 2004

Sales Average Seasonal factor

Deseasoned Demand

Jan – Feb 109.0 125.29 Jan – Feb 115.0 112.0 0.87 132.18

Mar – Apr 104.0 125.30 Mar – Apr 112.0 108.0 0.83 130.12

May – June 150.0 126.05 May – June

159.0 154.51.19

133.61

Jul – Aug 170.0 125.00 Jul – Aug 182.0 176.01.36

133.82

Sept – Oct 120.0 126.32 Sept – Oct 126.0 123.0 0.95 132.63

Nov – Dec 100.0 125.00 Nov – Dec 106.0 103.0 0.80 132.50

Total 753 800

Step 2: Add data in Col. 2 and 5. Then divide by ‘2’

Step 1: Add data in Col. 2 and divide by ‘n’. Then add data in Col. 2 and divide by ‘n’. Determine the average. (753/6 + 800/6)/2 = (125.5 + 133.33)/2 = 129.42

Step 4: Divide Actual sales (Col. 2) with the seasonal factor (Col. 7)

Step 3: Divide Col. 6 112/129.42 = 0.87



Tracking Signals

Depending on the number of MAD’s selected, the TS can be used like a quality control chart indicating when the model is generating too much error in its forecasts.

The TS formula is:

The Tracking Signal or TS is a measure that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand.

MAD

demand)Forecast - demand (Actualn

1

ii


Control Charts

A control chart is: A visual tool for monitoring forecast errors Used to detect non-randomness in errors

Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are present



Controlling the forecast



Control chartsControl charts are based on the following assumptions:

when errors are random, they are Normally distributed around a mean of zero.

Standard deviation of error is 95.5% of data in a normal distribution is within 2 standard

deviation of the mean 99.7% of data in a normal distribution is within 3 standard

deviation of the mean Upper and lower control limits are often determine via

MSE

0 2 0 3MSE or MSE



Example Compute 2s control limits for forecast errors to determine if the forecast is accurate.

-6.59

-4.59

-2.59

-0.59

1.41

3.41

5.41

0 10

3.295

2 6.59

s MSE

s


Errors are all between -6.59 and +6.59

No pattern is observed

Therefore, according to control chart criterion, forecast is reliable

(Refer Slide 42)


Regression Analysis is a method of predicting the value of one variable based on the value of other variables.

It reflects the casual relationship underlying the demand being forecast and an independent variable.

Regression Analysis


Regression analysis is of two types: (a)Simple Linear Regression: A

regression using only one predictor is called a simple regression, and

(b)Multiple Regressions: Where there are two or more predictors, multiple regression analysis is employed.

There are two types of variables, one that is being forecasted and one from which the forecast is made.

The first one is known as the dependent variable, the latter as the independent variable.

Regression Analysis


Where: ‘yt’ is the dependent variable

‘a’ is the Y intercept

‘b’ is the slope of the line, and

‘x’ is the time period

Simple Regression Analysis

The functional relationship between the two can be visualized within a system of coordinates where the dependent variable is shown on the y and independent variable on the x-axis.

yt=f(x) or yt = a + bx


yt = a + bx0 1 2 3 4 5 x (Time)

YThe simple linear regression model seeks to fit a line through various data over time

The simple linear regression model seeks to fit a line through various data over time

Is the linear regression modelIs the linear regression model

a

Yt is the regressed forecast value or dependent variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.


Simple Linear Regression Formulas For Calculating “a” and “b”

a = y - bx

b =xy - n(y)(x)

x - n(x2 2

)


Problem

Week Sales1 1502 1573 1624 1665 177

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?


Week Week*Week Sales Week*Sales1 1 150 1502 4 157 3143 9 162 4864 16 166 6645 25 177 8853 55 162.4 2499

Average Sum Average Sum

b =xy - n(y)(x)

x - n(x=

2499 - 5(162.4)(3)=

a = y - bx = 162.4 - (6.3)(3) =

2 2

) ( )55 5 9

63

106.3

143.5

Answer: First, using the linear regression formulas, we can compute “a” and “b”

Answer: First, using the linear regression formulas, we can compute “a” and “b”

61


yt = 143.5 + 6.3x

180

Period

135140145150155160165170175

1 2 3 4 5

Sal

es

Sales

Forecast

The resulting regression model is:

Now if we plot the regression generated forecasts against the actual sales we obtain the following chart:

62


r = 1-S

S

xy2

2y

Correlation Analysis

Mathematically, correlation coefficient is defined by:

Where: Syx

2 is the standard error of the estimated regression

equation of the ‘y’ values on ‘x’, andSy

2 is the standard error for the ‘y’ values

Correlation analysis measures the degree of relationship between normally distributed dependent and independent variables and is signified by the correlation coefficient ‘r’.


Multiple Regression

With multiple regressions, we can use more than one predictor.

The forecast takes the form:

Y = β0 + β1 X1 + β2 X2 + . . .+ βn Xn,

Where: β0 is the intercept, and

β1, β2, . . . βn are coefficients representing the contribution of the independent variables X1, X2,..., Xn.


The Gillette Story & Demand Management

Gillette is one of the best practitioners of demand management in the consumer goods space.

With manufacturing plants in 51 locations in 20 countries, Gillette caters to the need of more than 200 countries around the world.

Globally, Gillette's portfolio of brands is organized into five business units: Blades and Razors, Personal Care, Oral Care, Duracell, and Braun.


Gillette Story In terms of volumes. Overall, Gillette was a $10 billion company. Out-of-stocks represented a large revenue loss. A 10 percent stock out rate could cost the company up to $1 billion.

The opportunity afforded by higher fill rates, even when discounted 50, 60 or 90 percent, could still be worth $100 million.

The challenge was to bridge supply and demand, especially as the manufacturer usually does not control replenishment.


Gillette Story

The key performance indicators which Gillette uses are forecast accuracy and case fill rates.

Gillette made significant improvements in forecast accuracy, from 40 percent in 2001 to 65 percent in 2003.

In the case of fill rate it improved from 80 percent in 2001 to 96 percent in 2003..


Gillette Story How did Gillette make these improvements? Gillette restructured its organization to improve the bridge between supply and demand.

Next, Gillette identified 11 key elements which it had to improve in order to improve overall value chain performance.

These elements included: increase in service levels, reduction in inventory, and improved costs.


Gillette Story

It worked with customers to map processes across company boundaries to avoid a gap between Gillette's processes and the customer's processes.

The key element that has made these initiatives possible is

Collaborative Planning, Forecasting, and Replenishment (CPFR),

data synchronization (UCCNET) and

Auto ID.


Gillette Story Gillette standardized the company's approach to forecasting across regions, customer-based forecasting for promotions, and redesigned some parts of the company's warehouse and transportation strategy to improve transit time to customers.

The Gillette story is the story of a company that had to undergo restructuring in 2001 due to large drop in its profit. It highlights how new techniques such as CPFR have reinforced the traditional models of demand planning and forecasting.


CPFR is forecasting based on the concept of supply chain management. It is a business model that takes a holistic approach to supply chain management and information exchange among trading partners.

It uses common metrics, standard language, and firm agreements to improve supply chain efficiencies for all participants.

Collaborative Planning Forecasting and Replenishment (CPFR)


In other words, CPFR is based on considering the entire supply chain or partnerships as a single unit and the sharing of information between the links in the chain. The objective is to collectively, as members of the supply chain, meet the needs of the final consumer. This is accomplished by supplying the right product at the right place, right time and right price to the customer.



CPFR usually begins with identifying a ‘forecasting champion’. The forecasting champion can be it a single person, a department, or a firm.

A forecast collaboration group is formed with each organization choosing its member in this group. Group members should represent a variety of functional areas including sales, marketing, logistics/operations, finance, and information systems.



The driving premise of CPFR is that all supply chain participants develop a synchronized forecast. A company can collaborate with numerous other supply network members both upstream and downstream in the supply network.

Every participant in a CPFR process — supplier, manufacturer, distributor, retailer — can view and amend forecast data to optimize the process from end to end.



Special Long-Term Forecast Methodologies

1. Identify and analyze the organizational issues that will provide the decision focus

2. Specify the key decision factors

3. Identify and analyze the key environmental forces

4. Establish the scenario logics

5. Select and elaborate the scenario

6. Interpret the scenario for their decision implications

Scenario Planning


Qualitative approach – (Judgmental)

Historical Analogy Method

Executive Opinion Method

Survey Methods The Delphi Method


Usually based on judgments about causal factors that underlie the demand of particular products or services

Do not require a demand history for the product or service, therefore are useful for new products/services

Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events

Qualitative Approaches


Executive Opinion Method

Technique Low Sales High SalesManager’s

Opinion 40.7% 39.6%

Executive’s Opinion 40.7% 41.6%

Sales Force Composite 29.6% 35.4%

Number in Sample 27 48



How to choose the right Tool





Whatever be the type of analysis you make, it is essential that the model you choose provides satisfaction on these two critical questions:

• Is the model adequate?

• Is the model stable?

Validating Model


Forecast control Using Standard

Computer Programs Trend effect in

exponential smoothening Delphi Method

Read at Home


Exercise

Design a Delphi Study on what should be the type of learning in a 3 year (part time) management program.

Please explain the logic behind the design.

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