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					Operations Management (2)

Forecasting

Lessons 1 and 2
Prof. Upendra Kachru

Prediction
Prediction Reflects judgment after taking all considerations into account Based on intuition Involves anticipated changes in future that may or may not happen Based on unique representations It can be biased No error analysis

Prof. Upendra Kachru

Operations Management

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
Prof. Upendra Kachru

Operations Management

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

Prof. Upendra Kachru

Operations Management

Forecasting vs. Prediction
Forecasting Involves the projection of the past into the future Prediction 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 intuition It can be biased No error analysis Based on unique representations

Based on theoretical model It is objective Error Analysis is possible Results are replicable
Prof. Upendra Kachru

Operations Management

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

WHY FORECASTING?

Prof. Upendra Kachru

Operations Management

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

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

Operations Management

Decision Types requiring Forecasting
Types of Decision Short term Medium term Long term Planning Strategies & facilities Specific demand Aggregate demand

Forecasting horizon in years
Prof. Upendra Kachru

Operations Management

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.
Prof. Upendra Kachru

Operations Management

9

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).
Independent Demand: Finished Goods
A

B(4)

C(2)

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

D(2)

E(1)

D(3)

F(2)

Prof. Upendra Kachru

Operations Management 10

Demand and Costs

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.

Prof. Upendra Kachru

Operations Management

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.

Prof. Upendra Kachru

Operations Management

Independent Demand
 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.

What to do?
Prof. Upendra Kachru

 Can take a passive role and simply respond to demand
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Operations Management

 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
Prof. Upendra Kachru

Eight Steps to Forecasting

Operations Management

Types of Forecasts
Quantitative

  

Time Series Analysis
Exponential Method Regression Analysis Simulation/ Scenario Planning

Qualitative (Judgmental)
Prof. Upendra Kachru
15

Operations Management

Time Series

1. Extrapolation 2. Moving average Method Exponential Method
1. Simple Exponential Method 2. Double Exponential Method 3. Triple Exponential Method Regression Analysis 1. Simple Regression Analysis 2. Multiple Regression Analysis

Quantitative Approach

Prof. Upendra Kachru

Operations Management

Time Series

There are five basic patterns in which demand varies with time that have been identified:  Horizontal  Trend  Seasonal  Cyclical  Random
Prof. Upendra Kachru

Operations Management

Graphical Representation
Linear Trend Cyclical

Seasonal/ Cyclical
Demand (units)

Turning Points

Constant

Time

Prof. Upendra Kachru

Operations Management

Moving Average Method
The general formula for moving average is:

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

A t-1 + A t-2 + A t-3 +...+A t- n Ft = n
Prof. Upendra Kachru

Operations Management

Simple Moving Average Problem

Week 1 2 3 4 5 6 7 8 9 10 11 12

Demand 650 678 720 785 859 920 850 758 892 920 789 844

A t-1 + A t-2 + A t-3 +...+A t- n Ft = n
Question: What are the 3week 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

Prof. Upendra Kachru

Operations Management

Calculating the moving averages gives us:

Week 1 2 3 4 5 6 7 8 9 10 11 12

Demand 3-Week 6-Week 650 F4=(650+678+720)/3 678 =682.67 720 F7=(650+678+720 +785+859+920)/6 785 682.67 859 727.67 =768.67 920 788.00 850 854.67 768.67 758 876.33 802.00 892 842.67 815.33 920 833.33 844.00 789 856.67 866.50 844 867.00 854.83
Operations Management ©The McGraw-Hill Companies, Inc., 2004

Prof. Upendra Kachru

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 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
Prof. Upendra Kachru

Operations Management

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

Ft = w 1 A t -1 + w 2 A t - 2 + w 3 A t -3 + ...+ w n A t - n
wt = weight given to time period “t” occurrence (weights must add to one)

w
i=1

n

i

=1

Question: Given the weekly demand and weights, what is the forecast for the 4th period or Week 4?
Week 1 2 3 4 Demand 650 678 720

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

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

Operations Management

23

Problem Solution

Week 1 2 3 4

Demand Forecast 650 678 720 693.4

F4 = 0.5(720)+0.3(678)+0.2(650)=693.4
Prof. Upendra Kachru

Operations Management

24

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

Prof. Upendra Kachru

Operations Management

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

Prof. Upendra Kachru

Operations Management

26

Problem (1) Data
Week 1 2 3 4 5 6 7 8 9 10 Demand 820 775 680 655 750 802 798 689 775
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?

Prof. Upendra Kachru

Operations Management

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

Week 1 2 3 4 5 6 7 8 9 10
Prof. Upendra Kachru

Demand 820 775 680 655 750 802 798 689 775

0.1 0.6 F3=775x0.1 + (1820.00 820.00 0.1)x820 =815.50 820.00 815.50 801.95 787.26 783.53 785.38 786.64 776.88 776.69 820.00 793.00 725.20 683.08 723.23 770.49 787.00 728.20 756.28
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Operations Management

Which one?
Demand 820 775 0.1 820.00 820.00 D-W 0.00 -45.00 (D-W)2 0.00 2025.00 0.6 820.00 820.00 D-W 0.00 -45.00 (D-W)2 0 2025

680
655 750 802 798 689 775

815.50
801.95 787.26 783.53 785.38 786.64 776.88

-135.50
-146.95 -37.26 18.47 12.62 -97.64 -1.88

18360.25
21594.30 1387.94 341.16 159.35 9533.35 3.52 53404.87

793.00
725.20 683.08 723.23 770.49 787.00 728.20

-113.00
-70.20 66.92 78.77 27.51 -98.00 46.80

12769
4928.04 4478.286 6204.398 756.6461 9603.436 2190.348 42955.15

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

Therefore

Operations Management

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

900
Demand

800 700 600 500 1 2 3 4 5 6 7 8 9 10 Week

Demand 0.1 0.6

Prof. Upendra Kachru

Operations Management

30

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.

Prof. Upendra Kachru

Operations Management

Double and Triple Smoothing
An exponential smoothing over an already smoothed time series is called doubleexponential 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 tripleexponential smoothing. Triple Exponential Smoothing is better at handling parabola trends and is normally used for such data.

Prof. Upendra Kachru

Operations Management

Double Exponential Smoothing
What happens when there is a definite non-stationary trend?
A trendy clothing boutique has had the following sales over the past 6 months: 1 2 3 4 5 6 510 512 528 530 542 552
560 550 540 530 520 510 500 490 480 1 2 3

Actual Forecast

Demand

4

Month

5

6

7

8

9

10

Prof. Upendra Kachru

Operations Management

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.

Forecasting Errors

Prof. Upendra Kachru

Operations Management

Source of forecast errors: Forecast inadequate  Model may beAccuracy  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?
Prof. Upendra Kachru

Operations Management

Error measures
Error - 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

Prof. Upendra Kachru

Operations Management

MAD, MSE, and MAPE
MAD =
 Actual  forecast

n MSE =
 ( Actual  forecast) n -1
2

MAPE 
Prof. Upendra Kachru



Actual  Forecast  100 Actual n
Operations Management

MAD Characteristics
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 MAD
Where „σ‟ is the standard deviation

 The larger the MAD, the less the accurate the resulting model
Prof. Upendra Kachru
38

Operations Management

MAD Problem (1)
Question: What is the MAD value given the forecast values in the table below?

Month
1 2 3 4 5
Prof. Upendra Kachru

Sales Forecast 220 n/a 250 255 210 205 300 320 325 315
Operations Management
39

Solution
Month 1 2 3 4 5 Sales 220 250 210 300 325

σ = 1.25 MAD = 12.5; 3 σ =37.5 All readings are within limits
Forecast Abs Error n/a 255 5 205 5 20 320 315 10

40

A
MAD =
t=1

n

t

- Ft

n

40 = = 10 4

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

Prof. Upendra Kachru

Operations Management

Example (2)
Period Actual Forecast 1 217 215 2 213 216 3 216 215 4 210 214 5 213 211 MAD = 22/8 = 2.75 6 219 214 7 216 217 8 212 216 (A-F) 2 -3 1 -4 2 5 -1 -4 -2 |A-F| 2 3 1 4 2 5 1 4 22 (A-F)^2 4 9 1 16 4 25 1 16 76 (|A-F|/Actual)*100 0.92 1.41 0.46 1.90 0.94 2.28 0.46 1.89 10.26

MAD= MSE= MAPE=

2.75 10.86 1.28

MSE = 76/7 = 10.86 MAPE = 10.26/8 = 10.86
Operations Management

Prof. Upendra Kachru

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
Prof. Upendra Kachru
42

Operations Management

Actual ProblemStep 4: Dividewith the sales (Col. 2)

Step 2: Add data in Col. 2 and 5. Then divide by „2‟

seasonal factor The sales data for two(Col. 7) are given with the sales data years aggregated in periods of two months. Month, 2003 Jan – Feb Mar – Apr May – June Jul – Aug Sept – Oct Nov – Dec Total Sales 109.0 104.0 150.0 170.0 120.0 100.0 753
Deseasoned

Demand
125.29 125.30 126.05 125.00 126.32 125.00

Month, 2004 Jan – Feb Mar – Apr

Sales 115.0 112.0

Average 112.0 108.0

Seasonal

Deseasoned

factor
0.87 0.83

Demand
132.18 130.12 133.61 133.82 132.63 132.50

May – 159.0 June Jul – Aug Sept – Oct Nov – Dec 182.0 126.0 106.0 800

154.5 Step 3: Divide Col. 6 1.19 112/129.42 = 0.87 176.0 1.36 123.0 103.0 0.95 0.80

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 Prof. Upendra Kachru

Operations Management

Tracking Signals
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. 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:

 (Actual demand - Forecast demand)
i 1

n

i

MAD
Prof. Upendra Kachru

Operations Management

44

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
Prof. Upendra Kachru

Operations Management

Controlling the forecast

Prof. Upendra Kachru

Operations Management

Control charts
Control 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 MSE  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

0  2 MSE or 0  3 MSE

Prof. Upendra Kachru

Operations Management

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

s  MSE  3.295 2 s  6.59
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)

5.41 3.41

1.41 -0.59 0 -2.59

10

-4.59 -6.59

Prof. Upendra Kachru

Operations Management

Regression Analysis

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.

Prof. Upendra Kachru

Operations Management

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.

Regression Analysis

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.
Operations Management

Prof. Upendra Kachru

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

Where:
‘yt’ is the dependent variable ‘a’ is the Y intercept ‘b’ is the slope of the line, and ‘x’ is the time period

Prof. Upendra Kachru

Operations Management

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

Y

a
0 1 2 3 4 5 x (Time)

yt = a + bx
Is the linear regression model 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.
Prof. Upendra Kachru
52

Operations Management

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

a = y - bx
 xy - n(y)(x)  x - n(x )
2 2

b=

Prof. Upendra Kachru

Operations Management

53

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

Week 1 2 3 4 5
Prof. Upendra Kachru

Sales 150 157 162 166 177
Operations Management
54

55

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

Week Week*Week Sales Week*Sales 1 1 150 150 2 4 157 314 3 9 162 486 4 16 166 664 5 25 177 885 3 55 162.4 2499 Average Sum Average Sum

 xy - n( y)(x) = 2499 - 5(162.4)(3)  63 = 6.3 b= 55  5( 9 ) 10  x - n(x )
2 2

a = y - bx = 162.4 - (6.3)(3) = 143.5
Prof. Upendra Kachru

Operations Management

55

56

The resulting regression model is:

yt = 143.5 + 6.3x

Now if we plot the regression generated forecasts against the actual sales we obtain the following chart: 180 175 170 165 160 155 150 145 140 135 1
Prof. Upendra Kachru

Sales

Sales Forecast

2

3 Period

4

5
Operations Management
56

Correlation Analysis
Correlation analysis measures the degree of relationship between normally distributed dependent and independent variables and is signified by the correlation coefficient ‘r’. Mathematically, correlation coefficient is defined by:
r = 1Sxy Sy
2 2

Where: Syx2 is the standard error of the estimated regression equation of the ‘y’ values on ‘x’, and Sy2 is the standard error for the ‘y’ values
Prof. Upendra Kachru

Operations Management

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.

Prof. Upendra Kachru

Operations Management

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.
Operations Management

Prof. Upendra Kachru

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.
Operations Management

Prof. Upendra Kachru

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.
.

Prof. Upendra Kachru

Operations Management

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.
Operations Management

Prof. Upendra Kachru

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.
Prof. Upendra Kachru

Operations Management

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.
Operations Management

Prof. Upendra Kachru

Collaborative Planning Forecasting and Replenishment (CPFR)

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.

Prof. Upendra Kachru

Operations Management

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.
Operations Management

Prof. Upendra Kachru

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.
Prof. Upendra Kachru

Operations Management

Prof. Upendra Kachru

Operations Management

Prof. Upendra Kachru

Operations Management

Prof. Upendra Kachru

Operations Management

Collaborative Planning Forecasting and Replenishment (CPFR)

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.
Operations Management

Prof. Upendra Kachru

1.Specialand analyze the Forecast Identify Long-Term organizational issues Methodologies 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
Prof. Upendra Kachru

Scenario Planning

Operations Management

Qualitative approach – (Judgmental)
 Historical Analogy Method  Executive Opinion Method  Survey Methods  The Delphi Method

Prof. Upendra Kachru

Operations Management

Qualitative Approaches
 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

Operations Management

Executive Opinion Method
Technique
Manager’s Opinion Executive’s Opinion Sales Force Composite Number in Sample

Low Sales High Sales
40.7% 40.7% 29.6% 27 39.6% 41.6% 35.4% 48

Prof. Upendra Kachru

Operations Management

How to choose the right Tool

Prof. Upendra Kachru

Operations Management

Prof. Upendra Kachru

Operations Management

Prof. Upendra Kachru

Operations Management

Validating Model
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?

Prof. Upendra Kachru

Operations Management

Forecast control

 Using Standard Computer Programs  Delphi Method

Read at Home
Prof. Upendra Kachru

Operations Management

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.

Prof. Upendra Kachru

Operations Management

Operations Management (2)

Click to edit company slogan .


				
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