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### Idea Behind Time Series Models

### Trends

Objectives

- Understand the role of forecasting
- Understand the issues
- Understand basic tools and techniques

EMBA 512 Demand Forecasting

Boise State University

Forecasting

- Developing predictions or estimates of future values
- Demand volume
- Price levels
- Lead times
- Resource availability
- ...

EMBA 512 Demand Forecasting

Boise State University

The Role of Forecasting

- Necessary Input to all Planning Decisions
- Operations: Inventory, Production Planning & Scheduling
- Finance: Plant Investment & Budgeting
- Marketing: Sales-Force Allocation, Pricing Promotions
- Human Resources: Workforce Planning

EMBA 512 Demand Forecasting

Boise State University

Demand Forecasting

For manufactured items and conventional goods, forecasts are used to determine

- Replenishment levels and safety stocks
- Set production plans
- Determine procurement schedules
- Capacity planning, financial planning, & workforce planning

EMBA 512 Demand Forecasting

Boise State University

Demand Forecasting

For services, demand forecasts are used for

- Capacity planning, workforce scheduling, procurement & budgeting.
- Because services cannot be stored, demand forecasting for services is often concerned with forecasting the peak demand, rather than the average demand and its range.

EMBA 512 Demand Forecasting

Boise State University

Characteristics of Forecasts

- Forecast are always wrong. A good forecast is more than a single value.
- Forecast accuracy decreases with the forecast horizon.
- Aggregate forecasts are more accurate than disaggregated forecasts.

EMBA 512 Demand Forecasting

Boise State University

Independent vs. Dependent Demand

- Independent
- Exogenously controlled
- Subject to random or unpredictable changes
- What we forecast
- Dependent or Derived
- Calculated or derived from other sources
- Do not forecast

EMBA 512 Demand Forecasting

Boise State University

Forecasting Methods

Qualitative or Judgmental

- Ask people who ought to know
- Historical Projection or Extrapolation
- Time Series Models
- Moving Averages
- Exponential Smoothing
- Regression based methods

EMBA 512 Demand Forecasting

Boise State University

Basic Approach to Demand Forecasting

- Identify the Objective of the Forecast
- Integrate Forecasting with Planning
- Identify the Factors that Influence the Demand Forecast
- Identify the Appropriate Forecasting Model
- Monitor the Forecast (Measure Errors)

EMBA 512 Demand Forecasting

Boise State University

Time Series Methods

- Appropriate when future demand is expected to follow past demand patterns.
- Future demand is assumed to be influenced by the current demand, as well as historical growth and seasonal patterns.

EMBA 512 Demand Forecasting

Boise State University

Time Series Models

With time series models observed demand can be broken down into two components: systematic and random.

Observed Demand = Systematic Component + Random Component

EMBA 512 Demand Forecasting

Boise State University

Time Series Methods

The systematic component is the expected demand value. It is comprised of the underlying average demand, the trend in demand, and the seasonal fluctuations (seasonality) in demand.

EMBA 512 Demand Forecasting

Boise State University

Distinguish between random fluctuations and true changes in underlying demand patterns.

EMBA 512 Demand Forecasting

Boise State University

Time Series Components of Demand

Demand

Random component

Time

EMBA 512 Demand Forecasting

Boise State University

Monthly chart of the DJIA's changes from month to month along with a 3 period simple moving average.

EMBA 512 Demand Forecasting

Boise State University

Time Series Methods

- The random component cannot be predicted. However, its size and variability can be estimated to provide a measure of forecast error. The objective of forecasting is to filter the random component and model (estimate) the systematic component.

EMBA 512 Demand Forecasting

Boise State University

Moving Averages

- Simple, widely used
- Reduce random noise
- One Extreme
- Prediction next period = Demand this period
- Another Extreme
- Prediction next period = Long run average
- Intermediate View
- Prediction next period = Average of last n periods

EMBA 512 Demand Forecasting

Boise State University

Period Demand

1 12

2 15

3 11

4 9

5 10

6 8

7 14

8 12

Moving Average Models

3-period moving average

forecast for Period 8:

= (14 + 8 + 10) / 3

= 10.67

EMBA 512 Demand Forecasting

Boise State University

Weighted Moving Averages

Forecast for Period 8

= [(0.5 14) + (0.3 8) + (0.2 10)] / (0.5 + 0.3 + 0.2)

= 11.4

What are the advantages?

What do the weights add up to?

Could we use different weights?

Compare with a simple 3-period moving average.

EMBA 512 Demand Forecasting

Boise State University

. . . and Resulting Graph

Note how the forecasts smooth out variations

EMBA 512 Demand Forecasting

Boise State University

Simple Exponential Smoothing

- Sophisticated weighted averaging model
- Needs only three numbers:

Ft = Forecast for the current period tDt = Actual demand for the current period t

a = Weight between 0 and 1

EMBA 512 Demand Forecasting

Boise State University

Exponential Smoothing

- Moving Averages
- Equal weight to older observations
- Exponential Smoothing
- More weight to more recent observations
- Forecast for next period is a weighted average of
- Observation for this period
- Forecast for this period

EMBA 512 Demand Forecasting

Boise State University

Simple Exponential Smoothing

Formula Ft+1 = Ft + a (Dt – Ft) = a ×Dt + (1 – a) × Ft

- Where did the current forecast come from?
- What happens as a gets closer to 0 or 1?
- Where does the very first forecast come from?

EMBA 512 Demand Forecasting

Boise State University

Exponential Smoothing Forecast with a = 0.3

F2 = 0.3×12 + 0.7×11

= 3.6 + 7.7

= 11.3

F3 = 0.3×15 + 0.7×11.3

= 12.41

EMBA 512 Demand Forecasting

Boise State University

Time Series with

Demand

random and trend components

Time

EMBA 512 Demand Forecasting

Boise State University

What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data?

EMBA 512 Demand Forecasting

Boise State University

Simple Exponential Smoothing Always Lags A Trend

Because the model

is based on

historical demand,

it always lags

the obvious

upward trend

EMBA 512 Demand Forecasting

Boise State University

SimpleLinear Regression

- Time Series
- Find best fit of proposed model to past data
- Project that fit forward
- Assumes a linear relationship: y = a + b(x)

y

x

EMBA 512 Demand Forecasting

Boise State University

Definitions

Y = a + b(X)

Y = predicted variable (i.e., demand) X = predictor variable

“X” is the time period for linear trend models.

EMBA 512 Demand Forecasting

Boise State University

Example:Regression Used to Estimate A Linear Trend Line

EMBA 512 Demand Forecasting

Boise State University

Resulting Regression Model:Forecast = 10 + 98×Period

EMBA 512 Demand Forecasting

Boise State University

Time series with

Demand

random, trend and seasonal components

June

June

June

June

EMBA 512 Demand Forecasting

Boise State University

Modeling Trend & Seasonal Components

Quarter Period Demand

Winter 07 1 80

Spring 2 240

Summer 3 300

Fall 4 440

Winter 08 5 400

Spring 6 720

Summer 7 700

Fall 8 880

EMBA 512 Demand Forecasting

Boise State University

Regression picks up trend, butnot the seasonality effect

EMBA 512 Demand Forecasting

Boise State University

Calculating Seasonal Index: Winter Quarter

(Actual / Forecast) for Winter Quarters: Winter ‘07: (80 / 90) = 0.89 Winter ‘08: (400 / 524.3) = 0.76

Average of these two = 0.83

Interpret!

EMBA 512 Demand Forecasting

Boise State University

Seasonally Adjusted Forecast Model

For Winter Quarter [ –18.57 + 108.57×Period ] × 0.83

Or more generally: [ –18.57 + 108.57 × Period ] ×Seasonal Index

EMBA 512 Demand Forecasting

Boise State University

Would You Expect the Forecast Model to Perform This Well With Future Data?

EMBA 512 Demand Forecasting

Boise State University

Forecast Error

- Building a Forecast
- Fit to historical data
- Project future data
- Forecast Error
- How well does model fit historical data
- Do we need to tune or refine the model
- Can we offer confidence intervals about our predictions

EMBA 512 Demand Forecasting

Boise State University

Forecast Error

- The forecast error measures the difference between the actual demand and the forecast of demand. The forecast is based on the systematic component and the random component is estimated based on the forecast error.
- Forecast Error = Actual – Forecast

EMBA 512 Demand Forecasting

Boise State University

Measures of Forecast Accuracy

- Forecast Errort (Et)= Demandt-Forecastt
- Mean Squared Error (MSE)
- Mean Absolute Deviation (MAD)
- Bias
- Tracking Signal
- Relative Forecast Errors

EMBA 512 Demand Forecasting

Boise State University

Mean Squared Error (MSE)

The MSE estimates the variance of the forecast error.

EMBA 512 Demand Forecasting

Boise State University

Mean Absolute Deviation (MAD)

The MAD can be used to estimate the standard deviation of the random component, assuming the random component is normally distributed:

σ = 1.25MAD

EMBA 512 Demand Forecasting

Boise State University

Bias

- To determine whether a forecasting method consistently over-or- underestimates demand, calculate the sum of the forecast errors:

EMBA 512 Demand Forecasting

Boise State University

Tracking Signal

The tracking signal (TS) is the ratio of the bias to the MAD. Tracking signals outside the range + 6 indicates that the forecast is biased and either under predicting (negative) or over predicting (positive) demand.

EMBA 512 Demand Forecasting

Boise State University

Forecast Accuracy & Demand Variability(Normally Distributed Demand)

EMBA 512 Demand Forecasting

Boise State University

Issues

- Forecasting is a necessary evil, try to reduce the need for it.
- Complexity costs money, does it provide better forecasts?
- Aggregation provides accuracy, but precludes local information
- Forecast the right thing

EMBA 512 Demand Forecasting

Boise State University

Taco Bell

Feed the dog

- Labor is 30% of revenue
- Make to order environment
- Significant “seasonality”
- 52% of days sales during lunch
- 25% of days sales during busiest hour
- Balance staff with demand

EMBA 512 Demand Forecasting

Boise State University

Value Meals

- Drove demand
- Forecasting system in each store
- forecasts arrivals within 15 minute intervals
- Simulation system
- “predicts” congestion and lost sales
- Optimization system
- Finds the minimum cost allocation of workers

EMBA 512 Demand Forecasting

Boise State University

Forecasting System

- Customer arrivals by 15-minute interval of day (e.g., 11:15-11:30 am Friday)
- Fed by in-store computer system
- 6-week moving average
- Estimated savings: Over $40 Million in 3 years.

EMBA 512 Demand Forecasting

Boise State University

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