Operations and Supply Chain Management

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BSYS841 Operations & SCM

Week 2

Forecasting

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Case study: (p.186) Develop a forecasting model, justifying its selection over other techniques and project attendance through 2020.

Forecasting Outline

Global Company Profile: Walt Disney Parks & Resorts

What Is Forecasting?

The Strategic Importance of Forecasting

Seven Steps in the Forecasting System

Forecasting Approaches

Time-Series Forecasting

Associative Forecasting Methods: Regression and Correlation Analysis

Monitoring and Controlling Forecasts

Forecasting in the Service Sector

Forecasting Provides a Competitive Advantage for Disney (1 of 2)

Global portfolio includes parks in Shanghai, Hong Kong, Paris, Tokyo, Orlando, and Anaheim

Revenues are derived from people - how many visitors and how they spend their money

Daily management report contains only the forecast and actual attendance at each park

Disney generates daily, weekly, monthly, annual, and 5-year forecasts

Forecast used by labor management, maintenance, operations, finance, and park scheduling

Forecast used to adjust opening times, rides, shows, staffing levels, and guests admitted

Forecasting Provides a Competitive Advantage for Disney (2 of 2)

20% of customers come from outside the USA

Economic model includes gross domestic product, cross-exchange rates, arrivals into the USA

A staff of 35 analysts and 70 field people survey 1 million park guests, employees, and travel professionals each year

Inputs to the forecasting model include airline specials, Federal Reserve policies, Wall Street trends, vacation/holiday schedules for 3,000 school districts around the world

Average forecast error for the 5-year forecast is 5%

Average forecast error for annual forecasts is between 0% and 3%

Learning Objectives

4.1 Understand the three time horizons and which models apply for each

4.2 Explain when to use each of the four qualitative models

4.3 Apply the naive, moving-average, exponential smoothing, and trend methods

4.4 Compute three measures of forecast accuracy

4.5 Develop seasonal indices

4.6 Conduct a regression and correlation analysis

4.7 Use a tracking signal

What is Forecasting?

Process of predicting a future event

Underlying basis of all business decisions

Production

Inventory

Personnel

Facilities

Forecasting Time Horizons

Short-range forecast

Up to 1 year, generally less than 3 months

Purchasing, job scheduling, workforce levels, job assignments, production levels

Medium-range forecast

3 months to 3 years

Sales and production planning, budgeting

Long-range forecast

3+ years

New product planning, facility location, capital expenditures, research and development

Distinguishing Differences

Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes

Short-term forecasting usually employs different methodologies than longer-term forecasting

Short-term forecasts tend to be more accurate than longer-term forecasts

Influence of Product Life Cycle

Introduction – Growth – Maturity – Decline

Introduction and growth require longer forecasts than maturity and decline

As product passes through life cycle, forecasts are useful in projecting

Staffing levels

Inventory levels

Factory capacity

Product Life Cycle (1 of 2)

Product Life Cycle (2 of 2)

Types of Forecasts

Economic forecasts

Address business cycle – inflation rate, money supply, housing starts, etc.

Technological forecasts

Predict rate of technological progress

Impacts development of new products

Demand forecasts

Predict sales of existing products and services

Strategic Importance of Forecasting

Supply Chain Management – Good supplier relations, advantages in product innovation, cost and speed to market

Human Resources – Hiring, training, laying off workers

Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share

Seven Steps in Forecasting

Determine the use of the forecast

Select the items to be forecasted

Determine the time horizon of the forecast

Select the forecasting model(s)

Gather the data needed to make the forecast

Make the forecast

Validate and implement the results

The Realities!

Forecasts are seldom perfect; unpredictable outside factors may impact the forecast

Most techniques assume an underlying stability in the system

Product family and aggregated forecasts are more accurate than individual product forecasts

Forecasting Approaches

Qualitative Methods

Used when situation is vague and little data exist

New products

New technology

Involves intuition, experience

e.g., forecasting sales on Internet

Quantitative Methods

Used when situation is ‘stable’ and historical data exist

Existing products

Current technology

Involves mathematical techniques

e.g., forecasting sales of smart phones

Overview of Qualitative Methods

Jury of executive opinion

Pool opinions of high-level experts, sometimes augmented by statistical models

2. Delphi method

Panel of experts, queried iteratively

3. Sales force composite

Estimates from individual salespersons are reviewed for reasonableness, then aggregated

4. Market Survey

Ask the customer

Jury of Executive Opinion

Involves small group of high-level experts and managers

Group estimates demand by working together

Combines managerial experience with statistical models

Relatively quick

‘Group-think’ disadvantage

Delphi Method

Iterative group process, continues until consensus is reached

Three types of participants

Decision makers

Staff

Respondents

Disadvantages:

Sales Force Composite

Each salesperson projects his or her sales

Combined at district and national levels

Sales reps know customers’ wants

May be overly optimistic

Market Survey

Ask customers about purchasing plans

Useful for demand and product design and planning

What consumers say and what they actually do may be different

May be overly optimistic

Overview of Quantitative Approaches

Time-Series Forecasting

Set of evenly spaced numerical data

Obtained by observing response variable at regular time periods

Forecast based only on past values, no other variables important

Assumes that factors influencing past and present will continue influence in future

Time-Series Components

Components of Demand

Figure 4.1

Trend Component

Persistent, overall upward or downward pattern

Changes due to population, technology, age, culture, etc.

Typically several years duration

Seasonal Component

Regular pattern of up and down fluctuations

Due to weather, customs, etc.

Occurs within a single year

PERIOD LENGTH	“SEASON” LENGTH	NUMBER OF “SEASON” IN PATTERN
Week	Day	7
Month	Week	4 – 4.5
Month	Day	28 – 31
Year	Quarter	4
Year	Month	12
Year	Week	52

Cyclical Component

Repeating up and down movements

Affected by business cycle, political, and economic factors

Multiple years duration

Often causal or associative relationships

Random Component

Erratic, unsystematic, ‘residual’ fluctuations

Due to random variation or unforeseen events

Short duration and nonrepeating

Naive Approach

Assumes demand in next period is the same as demand in most recent period

e.g., If January sales were 68, then February sales will be 68

Sometimes cost effective and efficient

Can be good starting point

Moving Averages

MA is a series of arithmetic means

Used if little or no trend

Used often for smoothing

Provides overall impression of data over time

Moving Average Example

Weighted Moving Average (1 of 3)

Used when some trend might be present

Older data usually less important

Weights based on experience and intuition

Weighted Moving Average (2 of 3)

Weighted Moving Average (3 of 3)

Potential Problems With Moving Average (1 of 2)

Increasing n smooths the forecast but makes it less sensitive to changes

Does not forecast trends well

Requires extensive historical data

Graph of Moving Averages

Figure 4.2

Potential Problems With Moving Average (2 of 2)

Form of weighted moving average

Weights decline exponentially

Most recent data weighted most

Requires smoothing constant (α)

Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of past data

Exponential Smoothing

New forecast = Last period’s forecast

+ α (Last period’s actual demand

− Last period’s forecast)

where Ft = new forecast

Ft – 1 = previous period’s forecast

α = smoothing (or weighting) constant (0 ≤ α ≤ 1)

At – 1 = previous period’s actual demand

Exponential Smoothing Example

Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant α = .20

Effect of Smoothing Constants

Smoothing constant generally .05 ≤ α ≤ .50

As α increases, older values become less significant

Impact of Different α (1 of 2)

Impact of Different α (2 of 2)

Choose high values of α when underlying average is likely to change

Choose low values of α when underlying average is stable

Selecting the Smoothing Constant

The objective is to obtain the most accurate forecast no matter the technique

We generally do this by selecting the model that gives us the lowest forecast error according to one of three preferred measures:

Mean Absolute Deviation (MAD)

Mean Squared Error (MSE)

Mean Absolute Percent Error (MAPE)

QUARTER	ACTUAL TONNAGE UNLOADED	FORECAST WITH α = .10	FORECAST WITH α = .50
1	180	175	175
2	168	175.50 = 175.00 + .10(180 − 175)	177.50
3	159	174.75 = 175.50 + .10(168 − 175.50)	172.75
4	175	173.18 = 174.75 + .10(159 − 174.75)	165.88
5	190	173.36 = 173.18 + .10(175 − 173.18)	170.44
6	205	175.02 = 173.36 + .10(190 − 173.36)	180.22
7	180	178.02 = 175.02 + .10(205 − 175.02)	192.61
8	182	178.22 = 178.02 + .10(180 − 178.02)	186.30
9	?	178.59 = 178.22 + .10(182 − 178.22)	184.15

Common Measures of Error—MAD

Mean Absolute Deviation (MAD)

Determining the MAD

Common Measures of Error—MSE

Mean Squared Error (MSE)

Common Measures of Error—MAPE

Mean Absolute Percent Error (MAPE)

Comparison of Measures

Table 4.1 Comparison of Measures of Forecast Error

MEASURE	MEANING	APPLICATION TO CHAPTER EXAMPLE
Mean absolute deviation (MAD)	How much the forecast missed the target	For α = .10 in Example 4, the forecast for grain unloaded was off by an average of 10.31 tons.
Mean squared error (MSE)	The square of how much the forecast missed the target	For α = .10 in Example 5, the square of the forecast error was 190.8. This number does not have a physical meaning, but is useful when compared to the MSE of another forecast.
Mean absolute percent error (MAPE)	The average percent error	For α = .10 in Example 6, the forecast is off by 5.59% on average. As in Examples 4 and 5, some forecasts were too high, and some were low.

Comparison of Forecast Error (1 of 5)

Comparison of Forecast Error (2 of 5)

Comparison of Forecast Error (3 of 5)

Comparison of Forecast Error (4 of 5)

Comparison of Forecast Error (5 of 5)

Exponential Smoothing with Trend Adjustment (1 of 3)

When a trend is present, exponential smoothing must be modified

MONTH	ACTUAL DEMAND	FORECAST (Ft) FOR MONTHS 1 – 5
1	100	F1 = 100 (given)
2	200	F2 = F1 + α(A1 − F1) = 100 + .4(100 − 100) = 100
3	300	F3 = F2 + α(A2 − F2) = 100 + .4(200 − 100) = 140
4	400	F4 = F3 + α(A3 − F3) = 140 + .4(300 − 140) = 204
5	500	F5 = F4 + α(A4 − F4) = 204 + .4(400 − 204) = 282

Exponential Smoothing with Trend Adjustment (2 of 3)

where Ft = exponentially smoothed forecast average

Tt = exponentially smoothed trend

At = actual demand

α = smoothing constant for average (0 ≤ α ≤ 1)

β = smoothing constant for trend (0 ≤ β ≤ 1)

Exponential Smoothing with Trend Adjustment (3 of 3)

Step 1: Compute Ft

Step 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt

Exponential Smoothing with Trend Adjustment Example

MONTH (t)	ACTUAL DEMAND (At)	MONTH (t)	ACTUAL DEMAND (At)
1	12	6	21
2	17	7	31
3	20	8	28
4	19	9	36
5	24	10	?

α = .2 β = .4

Exponential Smoothing with Trend Adjustment Example (1 of 5)

Table 4.2 Forecast with α = .2 and β = .4

Exponential Smoothing with Trend Adjustment Example (2 of 5)

Table 4.2 Forecast with α = .2 and β = .4

Exponential Smoothing with Trend Adjustment Example (3 of 5)

Table 4.2 Forecast with α = .2 and β = .4

Exponential Smoothing with Trend Adjustment Example (4 of 5)

Table 4.2 Forecast with α = .2 and β = .4

MONTH	ACTUAL DEMAND	SMOOTHED FORECAST AVERAGE, Ft	SMOOTHED TREND, Tt	FORECAST INCLUDING TREND, FITt
1	12	11	2	13.00
2	17	12.80	1.92	14.72
3	20	15.18	2.10	17.28
4	19	17.82	2.32	20.14
5	24	19.91	2.23	22.14
6	21	22.51	2.38	24.89
7	31	24.11	2.07	26.18
8	28	27.14	2.45	29.59
9	36	29.28	2.32	31.60
10	blank	32.48	2.68	35.16

Exponential Smoothing with Trend Adjustment Example (5 of 5)

Figure 4.3

Trend Projections (1 of 2)

Fitting a trend line to historical data points to project into the medium to long-range

Linear trends can be found using the least-squares technique

a = y-axis intercept

b = slope of the regression line

x = the independent variable

Least Squares Method (1 of 2)

Figure 4.4

Least Squares Method (2 of 2)

Equations to calculate the regression variables

Least Squares Example (1 of 4)

YEAR	ELECTRICAL POWER DEMAND	YEAR	ELECTRICAL POWER DEMAND
1	74	5	105
2	79	6	142
3	80	7	122
4	90	blank	blank

Least Squares Example (2 of 4)

Least Squares Example (3 of 4)

Least Squares Example (4 of 4)

Figure 4.5

Least Squares Requirements

We always plot the data to insure a linear relationship

We do not predict time periods far beyond the database

Deviations around the least squares line are assumed to be random

Seasonal Variations In Data (1 of 2)

The multiplicative seasonal model can adjust trend data for seasonal variations in demand

Seasonal Variations In Data (2 of 2)

Steps in the process for monthly seasons:

Find average historical demand for each month

Compute the average demand over all months

Compute a seasonal index for each month

Estimate next year’s total demand

Divide this estimate of total demand by the number of months, then multiply it by the seasonal index for that month

Seasonal Index Example (1 of 6)

Seasonal Index Example (2 of 6)

Seasonal Index Example (3 of 6)

Seasonal Index Example (4 of 6)

Seasonal Index Example (5 of 6)

Seasonal forecast for Year 4

Seasonal Index Example (6 of 6)

San Diego Hospital (1 of 5)

Figure 4.6

San Diego Hospital (2 of 5)

San Diego Hospital (3 of 5)

Figure 4.7

San Diego Hospital (4 of 5)

Period	67	68	69	70	71	72
Month	Jan	Feb	Mar	Apr	May	June
Forecast with Trend & Seasonality	9,911	9,265	9,764	9,691	9,520	9,542
Period	73	74	75	76	77	78
Month	July	Aug	Sept	Oct	Nov	Dec
Forecast with Trend & Seasonality	9,949	10,068	9,411	9,724	9,355	9,572

San Diego Hospital (5 of 5)

Figure 4.8

Adjusting Trend Data

Cyclical Variations

Cycles – patterns in the data that occur every several years

Forecasting is difficult

Wide variety of factors

Associative Forecasting

Used when changes in one or more independent variables can be used to predict the changes in the dependent variable

Most common technique is linear-regression analysis

We apply this technique just as we did in the time-series example

Trend Projections (2 of 2)

Forecasting an outcome based on predictor variables using the least squares technique

a = y-axis intercept

b = slope of the regression line

x = the independent variable

Associative Forecasting Example (1 of 6) （sales-area payroll)

Associative Forecasting Example (2 of 6)

Associative Forecasting Example (3 of 6)

Associative Forecasting Example (4 of 6)

Associative Forecasting Example (5 of 6)

If payroll next year is estimated to be $6 billion, then:

Sales (in $ millions) = 1.75 + .25(6)

= 1.75 + 1.5 = 3.25

Sales = $3,250,000

Associative Forecasting Example (6 of 6)

Standard Error of the Estimate (1 of 4)

A forecast is just a point estimate of a future value

This point is actually the mean or expected value of a probability distribution

Figure 4.9

Standard Error of the Estimate (2 of 4)

where y = y-value of each data point

yc = computed value of the dependent variable, from the regression equation

n = number of data points

Standard Error of the Estimate (3 of 4)

Computationally, this equation is considerably easier to use

We use the standard error to set up prediction intervals around the point estimate

Standard Error of the Estimate (4 of 4)

The standard error of the estimate is $306,000 in sales

Correlation (1 of 2)

How strong is the linear relationship between the variables?

Correlation does not necessarily imply causality!

Coefficient of correlation, r, measures degree of association

Values range from −1 to +1

Correlation Coefficient (1 of 4)

Figure 4.10

100

Correlation Coefficient (2 of 4)

101

Correlation Coefficient (3 of 4)

102

Correlation (2 of 2)

Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x

Values range from 0 to 1

Easy to interpret

For the Nodel Construction example:

r = .901

r2 = .81

103

Multiple-Regression Analysis (1 of 2)

If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables

Computationally, this is quite complex and generally done on the computer

104

Multiple-Regression Analysis (2 of 2)

In the Nodel example, including interest rates in the model gives the new equation:

An improved correlation coefficient of r = .96 suggests this model does a better job of predicting the change in construction sales

105

Monito